# Publications

Publications from the Division of Automatic Control are available in the DiVA database and the most recent ones are listed below.

## Recent Publications

## Journal papers

This paper presents a data-driven approach to diagnostics of systems that operate in a repetitive manner. Considering that data batches collected from a repetitive operation will be similar unless in the presence of an abnormality, a condition change is inferred by comparing the monitored data against an available nominal batch. The method proposed considers the comparison of data in the distribution domain, which reveals information of the data amplitude. This is achieved with the use of kernel density estimates and the Kullback–Leibler distance. To decrease sensitivity to disturbances while increasing sensitivity to faults, the use of a weighting vector is suggested which is chosen based on a labeled dataset. The framework is simple to implement and can be used without process interruption, in a batch manner. The approach is demonstrated with successful experimental and simulation applications to wear diagnostics in an industrial robot gearbox and for diagnostics of gear faults in a rotating machine.

```
@article{diva2:737658,
author = {Carvalho Bittencourt, Andr\'{e} and Saarinen, Kari and Sander Tavallaey, Shiva and Gunnarsson, Svante and Norrlöf, Mikael},
title = {{A data-driven approach to diagnostics of repetitive processesin the distribution domain:
Applications to gearbox diagnosticsin industrial robots and rotating machines}},
journal = {Mechatronics (Oxford)},
year = {2014},
}
```

The effects of wear to friction are studied based on constant-speed friction data collected from dedicated experiments during accelerated wear tests. It is shown how the effects of temperature and load uncertainties produce larger changes to friction than those caused by wear, motivating the consideration of these effects. Based on empirical observations, an extended friction model is proposed to describe the effects of speed, load, temperature, and wear. Assuming the availability of such a model and constant-speed friction data, a maximum likelihood wear estimator is proposed. The performance of the wear estimator under load and temperature uncertainties is found by means of simulations and verified under three case studies based on real data. Practical issues related to experiment length are considered based on an optimal selection of speed points to collect friction data, improving the achievable performance bound for any unbiased wear estimator. As it is shown, reliable wear estimates can be achieved even under load and temperature uncertainties, making condition-based maintenance of industrial robots possible.

```
@article{diva2:737464,
author = {Carvalho Bittencourt, Andre and Axelsson, Patrik},
title = {{Modeling and Experiment Design for Identification of Wear in a Robot Joint Under Load and Temperature Uncertainties Based on Friction Data}},
journal = {IEEE/ASME transactions on mechatronics},
year = {2014},
volume = {19},
number = {5},
pages = {1694--1706},
}
```

We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite relaxations that are computationally cheaper, but potentially weaker, than the standard semidefinite relaxation. Our numerical results show that the new relaxations often produce the same results as the standard semidefinite relaxation, but at a lower computational cost.

```
@article{diva2:737375,
author = {Andersen, Martin S. and Hansson, Anders and Vandenberghe, Lieven},
title = {{Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow Problems}},
journal = {IEEE Transactions on Power Systems},
year = {2014},
volume = {29},
number = {4},
pages = {1855--1863},
}
```

Anomaly detection in large populations is a challenging but highly relevant problem. It is essentially a multi-hypothesis problem, with a hypothesis for every division of the systems into normal and anomalous systems. The number of hypothesis grows rapidly with the number of systems and approximate solutions become a necessity for any problem of practical interest. In this paper we take an optimization approach to this multi-hypothesis problem. It is first shown to be equivalent to a non-convex combinatorial optimization problem and then is relaxed to a convex optimization problem that can be solved distributively on the systems and that stays computationally tractable as the number of systems increase. An interesting property of the proposed method is that it can under certain conditions be shown to give exactly the same result as the combinatorial multi-hypothesis problem and the relaxation is hence tight.

```
@article{diva2:729561,
author = {Ohlsson, Henrik and Chen, Tianshi and Khoshfetratpakazad, Sina and Ljung, Lennart and Sastry, S. Shankar},
title = {{Scalable anomaly detection in large homogeneous populations}},
journal = {Automatica},
year = {2014},
volume = {50},
number = {5},
pages = {1459--1465},
}
```

A method to identify linear parameter varying models through minimisation of an -norm objective is presented. The method uses a direct nonlinear programming approach to a non-convex problem. The reason to use -norm is twofold. To begin with, it is a well-known and widely used system norm, and second, the cost functions described in this paper become differentiable when using the -norm. This enables us to have a measure of first-order optimality and to use standard quasi-Newton solvers to solve the problem. The specific structure of the problem is utilised in great detail to compute cost functions and gradients efficiently. Additionally, a regularised version of the method, which also has a nice computational structure, is presented. The regularised version is shown to have an interesting interpretation with connections to worst-case approaches.

```
@article{diva2:724339,
author = {Petersson, Daniel and Löfberg, Johan},
title = {{Optimisation-based modelling of LPV systems using an -objective}},
journal = {International Journal of Control},
year = {2014},
volume = {87},
number = {8},
pages = {1536--1548},
}
```

In this paper, we address the problem of multi-target detection and tracking over a network of separately located Doppler-shift measuring sensors. For this challenging problem, we propose to use the probability hypothesis density (PHD) filter and present two implementations of the PHD filter, namely the sequential Monte Carlo PHD (SMC-PHD) and the Gaussian mixture PHD (GM-PHD) filters. Performances of both filters are carefully studied and compared for the considered challenging tracking problem. Simulation results show that both PHD filter implementations successfully track multiple targets using only Doppler shift measurements. Moreover, as a proof-of-concept, an experimental setup consisting of a network of microphones and a loudspeaker was prepared. Experimental study results reveal that it is possible to track multiple ground targets using acoustic Doppler shift measurements in a passive multi-static scenario. We observed that the GM-PHD is more effective, efficient and easy to implement than the SMC-PHD filter.

```
@article{diva2:720101,
author = {Guldogan, Mehmet B. and Lindgren, David and Gustafsson, Fredrik and Habberstad, Hans and Orguner, Umut},
title = {{Multi-target tracking with PHD filter using Doppler-only measurements}},
journal = {Digital signal processing (Print)},
year = {2014},
volume = {27},
pages = {1--11},
}
```

In this paper, the measurements of individual wheel speeds and the absolute position from a global positioning system are used for high-precision estimation of vehicle tire radii. The radii deviation from its nominal value is modeled as a Gaussian random variable and included as noise components in a simple vehicle motion model. The novelty lies in a Bayesian approach to estimate online both the state vector and the parameters representing the process noise statistics using a marginalized particle filter (MPF). Field tests show that the absolute radius can be estimated with submillimeter accuracy. The approach is tested in accordance with regulation 64 of the United Nations Economic Commission for Europe on a large data set (22 tests, using two vehicles and 12 different tire sets), where tire deflations are successfully detected, with high robustness, i.e., no false alarms. The proposed MPF approach outperforms common Kalman-filter-based methods used for joint state and parameter estimation when compared with respect to accuracy and robustness.

```
@article{diva2:716647,
author = {Lundquist, Christian and Karlsson, Rickard and Özkan, Emre and Gustafsson, Fredrik},
title = {{Tire Radii Estimation Using a Marginalized Particle Filter}},
journal = {IEEE transactions on intelligent transportation systems (Print)},
year = {2014},
volume = {15},
number = {2},
pages = {663--672},
}
```

Most of the currently used techniques for linear system identification are based on classical estimation paradigms coming from mathematical statistics. In particular, maximum likelihood and prediction error methods represent the mainstream approaches to identification of linear dynamic systems, with a long history of theoretical and algorithmic contributions. Parallel to this, in the machine learning community alternative techniques have been developed. Until recently, there has been little contact between these two worlds. The first aim of this survey is to make accessible to the control community the key mathematical tools and concepts as well as the computational aspects underpinning these learning techniques. In particular, we focus on kernel-based regularization and its connections with reproducing kernel Hilbert spaces and Bayesian estimation of Gaussian processes. The second aim is to demonstrate that learning techniques tailored to the specific features of dynamic systems may outperform conventional parametric approaches for identification of stable linear systems.

```
@article{diva2:716642,
author = {Pillonetto, Gianluigi and Dinuzzo, Francesco and Chen, Tianshi and De Nicolao, Giuseppe and Ljung, Lennart},
title = {{Kernel methods in system identification, machine learning and function estimation: A survey}},
journal = {Automatica},
year = {2014},
volume = {50},
number = {3},
pages = {657--682},
}
```

A marginal version of the enumeration Bayesian Cramer-Rao Bound (EBCRB) for jump Markov systems is proposed. It is shown that the proposed bound is at least as tight as EBCRB and the improvement stems from better handling of the nonlinearities. The new bound is illustrated to yield tighter results than BCRB and EBCRB on a benchmark example.

```
@article{diva2:710357,
author = {Fritsche, Carsten and Orguner, Umut and Svensson, Lennart and Gustafsson, Fredrik},
title = {{The Marginal Enumeration Bayesian Cramer-Rao Bound for Jump Markov Systems}},
journal = {IEEE Signal Processing Letters},
year = {2014},
volume = {21},
number = {4},
pages = {464--468},
}
```

Random set based methods have provided a rigorous Bayesian framework and have been used extensively in the last decade for point object estimation. In this paper, we emphasize that the same methodology offers an equally powerful approach to estimation of so called extended objects, i.e., objects that result in multiple detections on the sensor side. Building upon the analogy between Bayesian state estimation of a single object and random finite set estimation for multiple objects, we give a tutorial on random set methods with an emphasis on multiple extended object estimation. The capabilities are illustrated on a simple yet insightful real life example with laser range data containing several occlusions.

```
@article{diva2:708079,
author = {Granström, Karl and Lundquist, Christian and Gustafsson, Fredrik and Orguner, Umut},
title = {{Random Set Methods:
Estimation of Multiple Extended Objects}},
journal = {IEEE robotics \& automation magazine},
year = {2014},
volume = {21},
number = {2},
pages = {73--82},
}
```

In this article we present a parametric branch and bound algorithm for computation of optimal and suboptimal solutions to parametric mixed-integer quadratic programs and parametric mixed-integer linear programs. The algorithm returns an optimal or suboptimal parametric solution with the level of suboptimality requested by the user. An interesting application of the proposed parametric branch and bound procedure is suboptimal explicit MPC for hybrid systems, where the introduced user-defined suboptimality tolerance reduces the storage requirements and the online computational effort, or even enables the computation of a suboptimal MPC controller in cases where the computation of the optimal MPC controller would be intractable. Moreover, stability of the system in closed loop with the suboptimal controller can be guaranteed a priori.

```
@article{diva2:706645,
author = {Axehill, Daniel and Besselmann, Thomas and Martino Raimondo, Davide and Morari, Manfred},
title = {{A parametric branch and bound approach to suboptimal explicit hybrid MPC}},
journal = {Automatica},
year = {2014},
volume = {50},
number = {1},
pages = {240--246},
}
```

We consider robust geolocation in mixed line-of-sight (LOS)/non-LOS (NLOS) environments in cellular radio networks. Instead of assuming known propagation channel states (LOS or NLOS), we model the measurement error with a general two-mode mixture distribution although it deviates from the underlying error statistics. To avoid offline calibration, we propose to jointly estimate the geographical coordinates and the mixture model parameters. Two iterative algorithms are developed based on the well-known expectation-maximization (EM) criterion and joint maximum a posteriori-maximum likelihood (JMAP-ML) criterion to approximate the ideal maximum-likelihood estimator (MLE) of the unknown parameters with low computational complexity. Along with concrete examples, we elaborate the convergence analysis and the complexity analysis of the proposed algorithms. Moreover, we numerically compute the Cramer-Rao lower bound (CRLB) for our joint estimation problem and present the best achievable localization accuracy in terms of the CRLB. Various simulations have been conducted based on a real-world experimental setup, and the results have shown that the ideal MLE can be well approximated by the JMAP-ML algorithm. The EM estimator is inferior to the JMAP-ML estimator but outperforms other competitors by far.

```
@article{diva2:699610,
author = {Yin, Feng and Fritsche, Carsten and Gustafsson, Fredrik and Zoubir, Abdelhak M.},
title = {{EM- and JMAP-ML Based Joint Estimation Algorithms for Robust Wireless Geolocation in Mixed LOS/NLOS Environments}},
journal = {IEEE Transactions on Signal Processing},
year = {2014},
volume = {62},
number = {1},
pages = {168--182},
}
```

An important class of optimisation problems in control and signal processing involves the constraint that a Popov function is non-negative on the unit circle or the imaginary axis. Such a constraint is convex in the coefficients of the Popov function. It can be converted to a finite-dimensional linear matrix inequality via the Kalman-Yakubovich-Popov lemma. However, the linear matrix inequality reformulation requires an auxiliary matrix variable and often results in a very large semidefinite programming problem. Several recently published methods exploit problem structure in these semidefinite programmes to alleviate the computational cost associated with the large matrix variable. These algorithms are capable of solving much larger problems than general-purpose semidefinite programming packages. In this paper, we address the same problem by presenting an alternative to the linear matrix inequality formulation of the non-negative Popov function constraint. We sample the constraint to obtain an equivalent set of inequalities of low dimension, thus avoiding the large matrix variable in the linear matrix inequality formulation. Moreover, the resulting semidefinite programme has constraints with low-rank structure, which allows the problems to be solved efficiently by existing semidefinite programming packages. The sampling formulation is obtained by first expressing the Popov function inequality as a sum-of-squares condition imposed on a polynomial matrix and then converting the constraint into an equivalent finite set of interpolation constraints. A complexity analysis and numerical examples are provided to demonstrate the performance improvement over existing techniques.

```
@article{diva2:697193,
author = {Hansson, Anders and Vandenberghe, Lieven},
title = {{Sampling method for semidefinite programmes with non-negative Popov function constraints}},
journal = {International Journal of Control},
year = {2014},
volume = {87},
number = {2},
pages = {330--345},
}
```

The dependence of radio signal propagation on the environment is well known, and both statistical and deterministic methods have been presented in the literature. Such methods are either based on randomised or actual reflectors of radio signals. In this work, we instead aim at estimating the location of the reflectors based on geo-localised radio channel impulse reponse measurements and using methods from synthetic aperture radar (SAR). Radio channel data measurements from 3GPP E-UTRAN have been used to verify the usefulness of the proposed approach. The obtained images show that the estimated reflectors are well correlated with the aerial map of the environment. Also, which part of the trajectory contributed to different reflectors have been estimated with promising results.

```
@article{diva2:646427,
author = {Sjanic, Zoran and Gunnarsson, Fredrik and Frtische, Carsten and Gustafsson, Fredrik},
title = {{Cellular Network Non-Line-of-Sight Reflector Localisation Based on Synthetic Aperture Radar Methods}},
journal = {IEEE Transactions on Antennas and Propagation},
year = {2014},
volume = {62},
number = {4},
pages = {2284--2287},
}
```

With the electromagnetic theory as basis, we present a sensor model for three-axis magnetometers suitable for localization and tracking as required in intelligent transportation systems and security applications. The model depends on a physical magnetic dipole model of the target and its relative position to the sensor. Both point target and extended target models are provided as well as a target orientation dependent model. The suitability of magnetometers for tracking is analyzed in terms of local observability and the Cramér Rao lower bound as a function of the sensor positions in a two sensor scenario. The models are validated with real field test data taken from various road vehicles which indicate excellent localization as well as identification of the magnetic target model suitable for target classification. These sensor models can be combined with a standard motion model and a standard nonlinear filter to track metallic objects in a magnetometer network.

```
@article{diva2:606532,
author = {Wahlström, Niklas and Gustafsson, Fredrik},
title = {{Magnetometer Modeling and Validation for Tracking Metallic Targets}},
journal = {IEEE TRANSACTIONS ON SIGNAL PROCESSING},
year = {2014},
volume = {62},
number = {3},
pages = {545--556},
}
```

This paper considers the problem of dynamic modeling and identification of robot manipulators with respect to their elasticities. The so-called flexible joint model, modeling only the torsional gearbox elasticity, is shown to be insufficient for modeling a modern industrial manipulator accurately. The extended flexible joint model, where non-actuated joints are added to model the elasticity of the links and bearings, is used to improve the model accuracy. The unknown elasticity parameters are estimated using a frequency domain gray-box identification method. The conclusion is that the obtained model describes the movements of the motors and the tool mounted on the robot with significantly higher accuracy. Similar elasticity model parameters are obtained when using two different output variables for the identification, the motor position and the tool acceleration.

```
@article{diva2:370692,
author = {Moberg, Stig and Wernholt, Erik and Hanssen, Sven and Brogårdh, Torgny},
title = {{Modeling and Parameter Estimation of Robot Manipulators using Extended Flexible Joint Models}},
journal = {Journal of Dynamic Systems Measurement, and Control},
year = {2014},
volume = {136},
number = {3},
pages = {031005--},
}
```

Regular and moderate physical activity practice provides many physiological benefits. It reduces the risk of disease outcomes and is the basis for proper rehabilitation after a severe disease. Aerobic activity and strength exercises are strongly recommended in order to maintain autonomy with ageing. Balanced activity of both types is important, especially to the elderly population. Several methods have been proposed to monitor aerobic activities. However, no appropriate method is available for controlling more complex parameters of strength exercises. Within this context, the present article introduces a personalized, home-based strength exercise trainer designed for the elderly. The system guides a user at home through a personalized exercise program. Using a network of wearable sensors the user's motions are captured. These are evaluated by comparing them to prescribed exercises, taking both exercise load and technique into account. Moreover, the evaluation results are immediately translated into appropriate feedback to the user in order to assist the correct exercise execution. Besides the direct feedback, a major novelty of the system is its generic personalization by means of a supervised teach-in phase, where the program is performed once under supervision of a physical activity specialist. This teach-in phase allows the system to record and learn the correct execution of exercises for the individual user and to provide personalized monitoring. The user-driven design process, the system development and its underlying activity monitoring methodology are described. Moreover, technical evaluation results as well as results concerning the usability of the system for ageing people are presented. The latter has been assessed in a clinical study with thirty participants of 60 years or older, some of them showing usual diseases or functional limitations observed in elderly population.

```
@article{diva2:668528,
author = {Bleser, Gabriele and Steffen, Daniel and Weber, Markus and Hendeby, Gustaf and Stricker, Didier and Fradet, Laetitia and Marin, Fr\'{e}d\'{e}ric and Ville, Nathalie and Carr\'{e}, Francois},
title = {{A personalized exercise trainer for the elderly}},
journal = {Journal of Ambient Intelligence and Smart Environments},
year = {2013},
volume = {5},
number = {6},
pages = {547--562},
}
```

Monte Carlo methods, in particular those based on Markov chains and on interacting particle systems, are by now tools that are routinely used in machine learning. These methods have had a profound impact on statistical inference in a wide range of application areas where probabilistic models are used. Moreover, there are many algorithms in machine learning which are based on the idea of processing the data sequentially, first in the forward direction and then in the backward direction. In this tutorial we will review a branch of Monte Carlo methods based on the forward-backward idea, referred to as backward simulators. These methods are useful for learning and inference in probabilistic models containing latent stochastic processes. The theory and practice of backward simulation algorithms have undergone a significant development in recent years and the algorithms keep finding new applications. The foundation for these methods is sequential Monte Carlo (SMC). SMC-based backward simulators are capable of addressing smoothing problems in sequential latent variable models, such as general, nonlinear/non-Gaussian state-space models (SSMs). However, we will also clearly show that the underlying backward simulation idea is by no means restricted to SSMs. Furthermore, backward simulation plays an important role in recent developments of Markov chain Monte Carlo (MCMC) methods. Particle MCMC is a systematic way of using SMC within MCMC. In this framework, backward simulation gives us a way to significantly improve the performance of the samplers. We review and discuss several related backward-simulation-based methods for state inference as well as learning of static parameters, both using a frequentistic and a Bayesian approach.

```
@article{diva2:654562,
author = {Lindsten, Fredrik and Schön, Thomas B.},
title = {{Backward simulation methods for Monte Carlo statistical inference}},
journal = {Foundations and Trends in Machine Learning},
year = {2013},
volume = {6},
number = {1},
pages = {1--143},
}
```

Direct torque control (DTC) is considered as one of the most efficient techniques for speed and/or position tracking control of induction motor drives. However, this control scheme has several drawbacks: the switching frequency may exceed the maximum allowable switching frequency of the inverters, and the ripples in current and torque, especially at low speed tracking, may be too large. In this brief, we propose a new approach that overcomes these problems. The suggested controller is a model predictive controller, which directly controls the inverter switches. It is easy to implement in real time and it outperforms all previous approaches. Simulation results show that the new approach has as good tracking properties as any other scheme, and that it reduces the average inverter switching frequency about 95% as compared to classical DTC.

```
@article{diva2:649991,
author = {Thomas, Jean and Hansson, Anders},
title = {{Speed Tracking of a Linear Induction Motor-Enumerative Nonlinear Model Predictive Control}},
journal = {IEEE Transactions on Control Systems Technology},
year = {2013},
volume = {21},
number = {5},
pages = {1956--1962},
}
```

Boundary effects in iterative learning control (ILC) algorithms are considered in this article. ILC algorithms involve filtering of input and error signals over finite-time intervals, often using non-causal filters, and it is important that the boundary effects of the filtering operations are handled in an appropriate way. The topic is studied using both a proposed theoretical framework and simulations, and it is shown that the method for handling the boundary effects has impact on the stability and convergence properties of the ILC algorithm.

```
@article{diva2:644837,
author = {Wall\'{e}n, Johanna and Gunnarsson, Svante and Norrlöf, Mikael},
title = {{Analysis of boundary effects in iterative learning control}},
journal = {International Journal of Control},
year = {2013},
volume = {86},
number = {3},
pages = {410--415},
}
```

Courses at the Master’s level in automatic control and signal processing cover mathematical theories and algorithms for control, estimation, and filtering. However, giving students practical experience in how to use these algorithms is also an important part of these courses. A goal is that the students should not only be able to understand and derive these algorithms, but also be able to apply them to real-life technical problems. The latter is achieved by assigning more time to the laboratory tutorials and designing them in such a way that the exercises are open for interpretation; an example of this would be giving the students more freedom to decide how to acquire the data needed to solve the given exercises.The students are asked to hand in a laboratory report in which they describe how they solved the exercises. This paper presents a double-blind peer-review process for laboratory reports, introduced at the Department of Electrical Engineering, Linköping University, Sweden. A survey was administered to students, and the results are summarized in this paper. Also discussed are the teachers’ experiences of peer review and of how students perform later in their education in writing their Master’s theses.

```
@article{diva2:643738,
author = {Lundquist, Christian and Skoglund, Martin and Granström, Karl and Glad, Torkel},
title = {{Insights from Implementing a System for Peer-Review}},
journal = {IEEE Transactions on Education},
year = {2013},
volume = {56},
number = {3},
pages = {261--267},
}
```

This paper gives an overview of the identificationof linear systems. It covers the classical approach ofparametric methods by means of maximum likelihood andpredicion error methods, as well all classical non-parametricmethods through spectral analysis. It also covers very recenttechniques dealing with convex formulations by regularizationof FIR and ARX models, as well as new alternatives tospectral analysis, through local linear models. An example of identification of aircraft dynamics illustrates the approaches.

```
@article{diva2:643191,
author = {Ljung, Lennart},
title = {{Some Classical and Some New Ideas for Identification of Linear Systems}},
journal = {Journal of Control, Automation and Electrical Systems},
year = {2013},
volume = {24},
number = {1-2},
pages = {3--10},
}
```

We present a system identification method for problems with partially missing inputs and outputs. The method is based on a subspace formulation and uses the nuclear norm heuristic for structured low-rank matrix approximation, with the missing input and output values as the optimization variables. We also present a fast implementation of the alternating direction method of multipliers (ADMM) to solve regularized or non-regularized nuclear norm optimization problems with Hankel structure. This makes it possible to solve quite large system identification problems. Experimental results show that the nuclear norm optimization approach to subspace identification is comparable to the standard subspace methods when no inputs and outputs are missing, and that the performance degrades gracefully as the percentage of missing inputs and outputs increases.

```
@article{diva2:642977,
author = {Liu, Zhang and Hansson, Anders and Vandenberghe, Lieven},
title = {{Nuclear norm system identification with missing inputs and outputs}},
journal = {Systems \& control letters (Print)},
year = {2013},
volume = {62},
number = {8},
pages = {605--612},
}
```

We present a novel method for Wiener system identification. The method relies on a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process model for the static nonlinearity. We avoid making strong assumptions, such as monotonicity, on the nonlinear mapping. Stochastic disturbances, entering both as measurement noise and as process noise, are handled in a systematic manner. The nonparametric nature of the Gaussian process allows us to handle a wide range of nonlinearities without making problem-specific parameterizations. We also consider sparsity-promoting priors, based on generalized hyperbolic distributions, to automatically infer the order of the underlying dynamical system. We derive an inference algorithm based on an efficient particle Markov chain Monte Carlo method, referred to as particle Gibbs with ancestor sampling. The method is profiled on two challenging identification problems with good results. Blind Wiener system identification is handled as a special case.

```
@article{diva2:641716,
author = {Lindsten, Fredrik and Schön, Thomas and Jordan, Michael I.},
title = {{Bayesian semiparametric Wiener system identification}},
journal = {Automatica},
year = {2013},
volume = {49},
number = {7},
pages = {2053--2063},
}
```

There has been recently a trend to study linear system identification with high order finite impulse response (FIR) models using the regularized least-squares approach. One key of this approach is to solve the hyper-parameter estimation problem that is usually nonconvex. Our goal here is to investigate implementation of algorithms for solving the hyper-parameter estimation problem that can deal with both large data sets and possibly ill-conditioned computations. In particular, a QR factorization based matrix-inversion-free algorithm is proposed to evaluate the cost function in an efficient and accurate way. It is also shown that the gradient and Hessian of the cost function can be computed based on the same QR factorization. Finally, the proposed algorithm and ideas are verified by Monte-Carlo simulations on a large data-bank of test systems and data sets.

```
@article{diva2:641676,
author = {Chen, Tianshi and Ljung, Lennart},
title = {{Implementation of algorithms for tuning parameters in regularized least squares problems in system identification}},
journal = {Automatica},
year = {2013},
volume = {49},
number = {7},
pages = {2213--2220},
}
```

This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has been derived by Mahler, and different implementations have been proposed recently. To achieve better estimation performance this work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers. A gamma Gaussian inverse Wishart mixture implementation, which is capable of estimating the target extents and measurement rates as well as the kinematic state of the target, is proposed, and it is compared to its PHD counterpart in a simulation study. The results clearly show that the CPHD filter has a more robust cardinality estimate leading to smaller OSPA errors, which confirms that the extended target CPHD filter inherits the properties of its point target counterpart.

```
@article{diva2:633671,
author = {Lundquist, Christian and Granström, Karl and Orguner, Umut},
title = {{An Extended Target CPHD Filter and a Gamma Gaussian Inverse Wishart Implementation}},
journal = {IEEE Journal on Selected Topics in Signal Processing},
year = {2013},
volume = {7},
number = {3},
pages = {472--483},
}
```

Knowledge of the noise distribution is typically crucial for the state estimation of general state-space models. However, properties of the noise process are often unknown in the majority of practical applications. The distribution of the noise may also be non-stationary or state dependent and that prevents the use of off-line tuning methods. For linear Gaussian models, Adaptive Kalman filters (AKF) estimate unknown parameters in the noise distributions jointly with the state. For nonlinear models, we provide a Bayesian solution for the estimation of the noise distributions in the exponential family, leading to a marginalized adaptive particle filter (MAPF) where the noise parameters are updated using finite dimensional sufficient statistics for each particle. The time evolution model for the noise parameters is defined implicitly as a Kullback-Leibler norm constraint on the time variability, leading to an exponential forgetting mechanism operating on the sufficient statistics. Many existing methods are based on the standard approach of augmenting the state with the unknown variables and attempting to solve the resulting filtering problem. The MAPF is significantly more computationally efficient than a comparable particle filter that runs on the full augmented state. Further, the MAPF can handle sensor and actuator offsets as unknown means in the noise distributions, avoiding the standard approach of augmenting the state with such offsets. We illustrate the MAPF on first a standard example, and then on a tire radius estimation problem on real data.

```
@article{diva2:633613,
author = {Özkan, Emre and Smidl, Vaclav and Saha, Saikat and Lundquist, Christian and Gustafsson, Fredrik},
title = {{Marginalized Adaptive Particle Filtering for Nonlinear Models with Unknown Time-Varying Noise Parameters}},
journal = {Automatica},
year = {2013},
volume = {49},
number = {6},
pages = {1566--1575},
}
```

*H*

_{2}analysis of uncertain systems with application to flight comfort analysis", Control Engineering Practice, 21(6): 887-897, 2013.

In many applications, design or analysis is performed over a finite-frequency range of interest. The importance of the *H*_{2} norm highlights the necessity of computing this norm accordingly. This paper provides different methods for computing upper bounds of the robust finite-frequency *H*_{2} norm for systems with structured uncertainties. An application of the robust finite-frequency *H*_{2} norm for a comfort analysis problem of an aero-elastic model of an aircraft is also presented.

```
@article{diva2:632007,
author = {Garulli, Andrea and Hansson, Anders and Khoshfetrat Pakazad, Sina and Masi, Alfio and Wallin, Ragnar},
title = {{Robust finite-frequency \emph{H}$_{2}$ analysis of uncertain systems with application to flight comfort analysis}},
journal = {Control Engineering Practice},
year = {2013},
volume = {21},
number = {6},
pages = {887--897},
}
```

We investigate the unsupervised K-means clustering and the semi-supervised hidden Markov model (HMM) to automatically detect anomalous motion patterns in groups of people (crowds). Anomalous motion patterns are typically people merging into a dense group, followed by disturbances or threatening situations within the group. The application of K-means clustering and HMM are illustrated with datasets from four surveillance scenarios. The results indicate that by investigating the group of people in a systematic way with different K values, analyze cluster density, cluster quality and changes in cluster shape we can automatically detect anomalous motion patterns. The results correspond well with the events in the datasets. The results also indicate that very accurate detections of the people in the dense group would not be necessary. The clustering and HMM results will be very much the same also with some increased uncertainty in the detections.

```
@article{diva2:628236,
author = {Andersson, Maria and Gustafsson, Fredrik and St-Laurent, Louis and Prevost, Donald},
title = {{Recognition of Anomalous Motion Patterns in Urban Surveillance}},
journal = {IEEE Journal on Selected Topics in Signal Processing},
year = {2013},
volume = {7},
number = {1},
pages = {102--110},
}
```

This paper proposes a general convex framework for the identification of switched linear systems. The proposed framework uses over-parameterization to avoid solving the otherwise combinatorially forbidding identification problem, and takes the form of a least-squares problem with a sum-of-norms regularization, a generalization of the *ℓ*_{1}-regularization. The regularization constant regulates the complexity and is used to trade off the fit and the number of submodels.

```
@article{diva2:621693,
author = {Ohlsson, Henrik and Ljung, Lennart},
title = {{Identification of Switched Linear Regression Models using Sum-of-Norms Regularization}},
journal = {Automatica},
year = {2013},
volume = {49},
number = {4},
pages = {1045--1050},
}
```

We consider time-of-arrival based robust geolocation in harsh line-of-sight/non-line-of-sight environments. Herein, we assume the probability density function (PDF) of the measurement error to be completely unknown and develop an iterative algorithm for robust position estimation. The iterative algorithm alternates between a PDF estimation step, which approximates the exact measurement error PDF (albeit unknown) under the current parameter estimate via adaptive kernel density estimation, and a parameter estimation step, which resolves a position estimate from the approximate log-likelihood function via a quasi-Newton method. Unless the convergence condition is satisfied, the resolved position estimate is then used to refine the PDF estimation in the next iteration. We also present the best achievable geolocation accuracy in terms of the Cramér-Rao lower bound. Various simulations have been conducted in both real-world and simulated scenarios. When the number of received range measurements is large, the new proposed position estimator attains the performance of the maximum likelihood estimator (MLE). When the number of range measurements is small, it deviates from the MLE, but still outperforms several salient robust estimators in terms of geolocation accuracy, which comes at the cost of higher computational complexity.

```
@article{diva2:621674,
author = {Yin, Feng and Fritsche, Carsten and Gustafsson, Fredrik and Zoubir, Abdelhak M},
title = {{TOA-Based Robust Wireless Geolocation and Cram\'{e}r-Rao Lower Bound Analysis in Harsh LOS/NLOS Environments}},
journal = {IEEE Transactions on Signal Processing},
year = {2013},
volume = {61},
number = {9},
pages = {2243--2255},
}
```

The Quantization Theorem I (QT I) implies that the likelihood function can be reconstructed from quantized sensor observations, given that appropriate dithering noise is added before quantization. We present constructive algorithms to generate such dithering noise. The application to *maximum likelihood estimation* (mle) is studied in particular. In short, dithering has the same role for amplitude quantization as an anti-alias filter has for sampling, in that it enables perfect reconstruction of the dithered but unquantized signal’s likelihood function. Without dithering, the likelihood function suffers from a kind of aliasing expressed as a counterpart to Poisson’s summation formula which makes the exact mle intractable to compute. With dithering, it is demonstrated that standard mle algorithms can be re-used on a smoothed likelihood function of the original signal, and statistically efficiency is obtained. The implication of dithering to the Cramér–Rao Lower Bound (CRLB) is studied, and illustrative examples are provided.

```
@article{diva2:612333,
author = {Gustafsson, Fredrik and Karlsson, Rickard},
title = {{Generating Dithering Noise for Maximum Likelihood Estimation from Quantized Data}},
journal = {Automatica},
year = {2013},
volume = {49},
number = {2},
pages = {554--560},
}
```

The performance of an optimal filter is lower bounded by the Bayesian Cramer-Rao Bound (BCRB). In some cases, this bound is tight (achieved by the optimal filter) asymptotically in information, i.e., high signal-to-noise ratio (SNR). However, for jump Markov linear Gaussian systems (JMLGS) the BCRB is not necessarily achieved for any SNR. In this paper, we derive a new bound which is tight for all SNRs. The bound evaluates the expected covariance of the optimal filter which is represented by one deterministic term and one stochastic term that is computed with Monte Carlo methods. The bound relates to and improves on a recently presented BCRB and an enumeration BCRB for JMLGS. We analyze their relations theoretically and illustrate them on a couple of examples.

```
@article{diva2:608232,
author = {Fritsche, Carsten and Gustafsson, Fredrik},
title = {{Bounds on the Optimal Performance for Jump Markov Linear Gaussian Systems}},
journal = {IEEE Transactions on Signal Processing},
year = {2013},
volume = {61},
number = {1},
pages = {92--98},
}
```

This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein-Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and colored stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method developed here addresses the blind Wiener estimation problem as a special case.

```
@article{diva2:608221,
author = {Wills, Adrian and Schön, Thomas and Ljung, Lennart and Ninness, Brett},
title = {{Identification of Hammerstein-Wiener Models}},
journal = {Automatica},
year = {2013},
volume = {49},
number = {1},
pages = {70--81},
}
```

In extended/group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix framework. The paper proposes functions that should be provided by the tracking filter in such a scenario. The results, which are obtained by a gamma Gaussian inverse Wishart implementation of an extended target probability hypothesis density filter, confirms that the proposed functions improve the performance of the tracking filter for spawning and combination events.

```
@article{diva2:557430,
author = {Granström, Karl and Orguner, Umut},
title = {{On Spawning and Combination of Extended/Group Targets Modeled with Random Matrices}},
journal = {IEEE Transactions on Signal Processing},
year = {2013},
volume = {61},
number = {3},
pages = {678--692},
}
```

This paper presents a model-based phase-only predistortion method suitable for outphasing radio frequency (RF) power amplifiers (PA). The predistortion method is based on a model of the amplifier with a constant gain factor and phase rotation for each outphasing signal, and a predistorter with phase rotation only. Exploring the structure of the outphasing PA, the problem can be reformulated from a nonconvex problem into a convex least-squares problem, and the predistorter can be calculated analytically. The method has been evaluted for 5MHz Wideband Code-Division Multiple Access (WCDMA) and Long Term Evolution (LTE) uplink signals with Peak-to-Average Power Ratio (PAPR) of 3.5 dB and 6.2 dB, respectively, applied to a fully integrated Class-D outphasing RF PA in 65nm CMOS. At 1.95 GHz for a 5.5V supply voltage, the measured output power of the PA was +29.7dBm with a power-added efficiency (PAE) of 26.6 %. For the WCDMA signal with +26.0dBm of channel power, the measured Adjacent Channel Leakage Ratio (ACLR) at 5MHz and 10MHz offsets were -46.3 dBc and -55.6 dBc with predistortion, compared to -35.5 dBc and -48.1 dBc without predistortion. For the LTE signal with +23.3dBm of channel power, the measured ACLR at 5MHz offset was -43.5 dBc with predistortion, compared to -34.1 dBc without predistortion.

```
@article{diva2:454672,
author = {Jung, Ylva and Fritzin, Jonas and Enqvist, Martin and Alvandpour, Atila},
title = {{Least-Squares Phase Predistortion of a +30dBm Class-D Outphasing RF PA in 65nm CMOS}},
journal = {IEEE Transactions on Circuits and Systems Part 1},
year = {2013},
volume = {60},
number = {7},
pages = {1915--1928},
}
```

A Design-Build-Test (DBT) course in electronics is presented. The course is designed based on the CDIO (Conceive-Design-Implement-Operate) framework for engineering education. It is part of the curriculum of two engineering programs at Linköping University, Sweden, where it has been given successfully for a number of years. The cornerstones of the course consist of carefully designed learning outcomes based on the CDIO Syllabus, a structured project management model such that the project tasks are carried out according to professional and industry-like routines, with well-designed organisation of the staff supporting the course, and challenging project tasks.

```
@article{diva2:647743,
author = {Svensson, Tomas and Gunnarsson, Svante},
title = {{A Design-Build-Test course in electronics based on the CDIO framework for engineering education}},
journal = {International Journal of Electrical Engineering Education},
year = {2012},
volume = {49},
number = {4},
pages = {349--364},
}
```

Received signal strength (RSS) can be used in sensor networks as a ranging measurement for positioning and localization applications. This contribution studies the realistic situation where neither the emitted power nor the power law decay exponent be assumed to be known. The application in mind is a rapidly deployed network consisting of a number of sensor nodes with low-bandwidth communication, each node measuring RSS of signals traveled through air (microphones) and ground (geophones). The first contribution concerns validation of a model in logarithmic scale, that is, linear in the unknown nuisance parameters (emitted power and power loss constant). The parameter variation is studied over time and space. The second contribution is a localization algorithm based on this model, where the separable least squares principle is applied to the non-linear least squares (NLS) cost function, after which a cost function of only the unknown position is obtained. Results from field trials are presented to illustrate the method, together with fundamental performance bounds. The ambition is to pave the way for sensor configuration design and more thorough performance evaluations as well as filtering and target tracking aspects.

```
@article{diva2:642959,
author = {Gustafsson, Fredrik and Gunnarsson, Fredrik and Lindgren, David},
title = {{Sensor models and localization algorithms for sensor networks based on received signal strength}},
journal = {EURASIP Journal on Wireless Communications and Networking},
year = {2012},
volume = {1},
number = {16},
}
```

This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a partially augmented Lagrangian method. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance and speed.

```
@article{diva2:580091,
author = {Ankelhed, Daniel and Helmersson, Anders and Hansson, Anders},
title = {{A Partially Augmented Lagrangian Method for Low Order H-Infinity Controller Synthesis Using Rational Constraints}},
journal = {IEEE Transactions on Automatic Control},
year = {2012},
volume = {57},
number = {11},
pages = {2901--2905},
}
```

This correspondence is a companion paper to [J. Dong, M. Verhaegen, and F. Gustafsson, "Robust Fault Detection With Statistical Uncertainty in Identified Parameters," IEEE Trans. Signal Process., vol. 60, no. 10, Oct. 2012], extending it to fault isolation. Also, here, use is made of a linear in the parameters model representation of the input-output behavior of the nominal system (i.e. fault-free). The projection of the residual onto directions only sensitive to individual faults is robustified against the stochastic errors of the estimated model parameters. The correspondence considers additive error sequences to the input and output quantities that represent failures like drift, biased, stuck, or saturated sensors/actuators.

```
@article{diva2:564020,
author = {Dong, Jianfei and Verhaegen, Michel and Gustafsson, Fredrik},
title = {{Robust Fault Isolation With Statistical Uncertainty in Identified Parameters}},
journal = {IEEE Transactions on Signal Processing},
year = {2012},
volume = {60},
number = {10},
pages = {5556--5561},
}
```

Detection of faults that appear as additive unknown input signals to an unknown LTI discrete-time MIMO system is considered. State of the art methods consist of the following steps. First, either the state space model or certain projection matrices are identified from data. Then, a residual generator is formed based on these identified matrices, and this residual generator is used for online fault detection. Existing techniques do not allow for compensating for the identification uncertainty in the fault detection. This contribution explores a recent data-driven approach to fault detection. We show first that the identified parametric matrices in this method depend linearly on the noise contained in the identification data, and then that the on-line computed residual also depends linearly on the noise. This allows an analytic design of a robust fault detection scheme, that takes both the noise in the online measurements as well as the identification uncertainty into account. We illustrate the benefits of the new method on a model of aircraft dynamics extensively studied in literature.

```
@article{diva2:564012,
author = {Dong, Jianfei and Verhaegen, Michel and Gustafsson, Fredrik},
title = {{Robust Fault Detection With Statistical Uncertainty in Identified Parameters}},
journal = {IEEE Transactions on Signal Processing},
year = {2012},
volume = {60},
number = {10},
pages = {5064--5076},
}
```

We consider the smoothing problem for a general state space system using sequential Monte Carlo(SMC) methods. The marginal smoother is assumed to be available in the form of weighted randomparticles from the SMC output. New algorithms are developed to extract the smoothed marginal maximuma posteriori (MAP) estimate of the state from the existing marginal particle smoother. Our method doesnot need any kernel ﬁtting to obtain the posterior density from the particle smoother. The proposedestimator is then successfully applied to ﬁnd the unknown initial state of a dynamical system and toaddress the issue of parameter estimation problem in state space models

```
@article{diva2:561304,
author = {Saha, Saikat and Mandal, Pranab K and Bagchi, Arunabha and Boers, Yvo and Driessen, Johannes N.},
title = {{Particle Based Smoothed Marginal MAP Estimation For General State Space Models}},
journal = {IEEE Transactions on Signal Processing},
year = {2012},
volume = {61},
number = {2},
pages = {264--273},
}
```

The Kronecker canonical form (KCF) can be employed when solving H-infinity synthesis problem. The KCF structure reveals variables that can be eliminated in the semidefinite program that defines the controller. The structure can also be used to remove states in the controller without sacrificing performance. In order to find the KCF structure, we can transform the relevant matrices to a generalized upper triangular (Guptri) form using orthogonal transformations. Thus, we can avoid finding the KCF structure explicitly, which is a badly conditioned problem.

```
@article{diva2:561487,
author = {Helmersson, Anders},
title = {{Employing Kronecker Canonical Form for LMI-Based H-infinity Synthesis Problems}},
journal = {IEEE Transactions on Automatic Control},
year = {2012},
volume = {57},
number = {8},
pages = {2062--2067},
}
```

In this paper we derive the maximum likelihood problem for missing data from a Gaussian model. We present in total eight different equivalent formulations of the resulting optimization problem, four out of which are nonlinear least squares formulations. Among these formulations are also formulations based on the expectation-maximization algorithm. Expressions for the derivatives needed in order to solve the optimization problems are presented. We also present numerical comparisons for two of the formulations for an ARMAX model.

```
@article{diva2:560163,
author = {Hansson, Anders and Wallin, Ragnar},
title = {{Maximum Likelihood Estimation of Gaussian Models with Missing Data:
Eight Equivalent Formulations}},
journal = {Automatica},
year = {2012},
volume = {48},
number = {9},
pages = {1955--1962},
}
```

This paper considers high-speed control of constrained linear parameter-varying systems using model predictive control. Existing model predictive control schemes for control of constrained linear parameter-varying systems typically require the solution of a semi-definite program at each sampling instance. Recently, variants of explicit model predictive control were proposed for linear parameter-varying systems with polytopic representation, decreasing the online computational effort by orders of magnitude. Depending on the mathematical structure of the underlying system, the constrained finite-time optimal control problem can be solved optimally, or close-to-optimal solutions can be computed. Constraint satisfaction, recursive feasibility and asymptotic stability can be guaranteed a priori by an appropriate selection of the terminal state constraints and terminal cost. The paper at hand gathers previous developments and provides new material such as a proof for the optimality of the solution, or, in the case of close-to-optimal solutions, a procedure to determine a bound on the suboptimality of the solution.

```
@article{diva2:558818,
author = {Besselmann, Thomas and Löfberg, Johan and Morari, Manfred},
title = {{Explicit MPC for LPV Systems: Stability and Optimality}},
journal = {IEEE Transactions on Automatic Control},
year = {2012},
volume = {57},
number = {9},
pages = {2322--2332},
}
```

This paper presents a random set based approach to tracking of an unknown number of extended targets, in the presence of clutter measurements and missed detections, where the targets extensions are modeled as random matrices. For this purpose, the random matrix framework developed recently by Koch et al. is adapted into the extended target PHD framework, resulting in the Gaussian inverse Wishart PHD (GIW-PHD) filter. A suitable multiple target likelihood is derived, and the main filter recursion is presented along with the necessary assumptions and approximations. The particularly challenging case of close extended targets is addressed with practical measurement clustering algorithms. The capabilities and limitations of the resulting extended target tracking framework are illustrated both in simulations and in experiments based on laser scans.

```
@article{diva2:557424,
author = {Granström, Karl and Orguner, Umut},
title = {{A PHD Filter for Tracking Multiple Extended Targets using Random Matrices}},
journal = {IEEE Transactions on Signal Processing},
year = {2012},
volume = {60},
number = {11},
pages = {5657--5671},
}
```

This paper presents a Gaussian-mixture implementation of the phd filter for tracking extended targets. The exact filter requires processing of all possible measurement set partitions, which is generally infeasible to implement. A method is proposed for limiting the number of considered partitions and possible alternatives are discussed. The implementation is used on simulated data and in experiments with real laser data, and the advantage of the filter is illustrated. Suitable remedies are given to handle spatially close targets and target occlusion.

```
@article{diva2:454802,
author = {Granström, Karl and Lundquist, Christian and Orguner, Umut},
title = {{Extended Target Tracking Using a Gaussian-Mixture PHD Filter}},
journal = {IEEE Transactions on Aerospace and Electronic Systems},
year = {2012},
volume = {48},
number = {4},
pages = {3268--3286},
}
```

A sensor fusion method for state estimation of a flexible industrial robot is developed. By measuring the acceleration at the end-effector, the accuracy of the arm angular position, as well as the estimated position of the end-effector are improved. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; the extended Kalman filter and the particle filter. In a simulation study on a realistic flexible industrial robot, the angular position performance is shown to be close to the fundamental Cramér-Rao lower bound. The technique is also verified in experiments on an ABB robot, where the dynamic performance of the position for the end-effector is significantly improved.

```
@article{diva2:557237,
author = {Axelsson, Patrik and Karlsson, Rickard and Norrlöf, Mikael},
title = {{Bayesian State Estimation of a Flexible Industrial Robot}},
journal = {Control Engineering Practice},
year = {2012},
volume = {20},
number = {11},
pages = {1220--1228},
}
```

Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements. We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression. The main issue is how to determine a suitable regularization matrix (Bayesian prior or kernel). Several regularization matrices are provided and numerically evaluated on a data bank of test systems and data sets. Our findings based on the data bank are as follows. The classical regularization approach with carefully chosen regularization matrices shows slightly better accuracy and clearly better robustness in estimating the impulse response than the standard approach - the prediction error method/maximum likelihood (PEM/ML) approach. If the goal is to estimate a model of given order as well as possible, a low order model is often better estimated by the PEM/ML approach, and a higher order model is often better estimated by model reduction on a high order regularized FIR model estimated with careful regularization. Moreover, an optimal regularization matrix that minimizes the mean square error matrix is derived and studied. The importance of this result lies in that it gives the theoretical upper bound on the accuracy that can be achieved for this classical regularization approach.

```
@article{diva2:556599,
author = {Chen, Tianshi and Ohlsson, Henrik and Ljung, Lennart},
title = {{On the Estimation of Transfer Functions, Regularizations and Gaussian Processes - Revisited}},
journal = {Automatica},
year = {2012},
volume = {48},
number = {8},
pages = {1525--1535},
}
```

In this paper, a structure exploiting algorithm for semidefinite programs derived from the Kalmatz-Yakubovich-Popov lemma, where some of the constraints appear as complicating constraints is presented. A decomposition algorithm is proposed, where the structure of the problem can be utilized. In a numerical example, where a controller that minimizes the stun of the H-2-norm and the H-infinity-norm is designed, the algorithm, is shown to be faster than SeDuMi and the special purpose solver KYPD.

```
@article{diva2:553051,
author = {Falkeborn, Rikard and Hansson, Anders},
title = {{A Decomposition Algorithm for KYP-SDPs}},
journal = {European Journal of Control},
year = {2012},
volume = {18},
number = {3},
pages = {249--256},
}
```

Modeling physical systems often leads to discrete time state-space models with dependent process and measurement noises. For linear Gaussian models, the Kalman filter handles this case, as is well described in literature. However, for nonlinear or non-Gaussian models, the particle filter as described in literature provides a general solution only for the case of independent noise. Here, we present an extended theory of the particle filter for dependent noises with the following key contributions: i) The optimal proposal distribution is derived; ii) the special case of Gaussian noise in nonlinear models is treated in detail, leading to a concrete algorithm that is as easy to implement as the corresponding Kalman filter; iii) the marginalized (Rao-Blackwellized) particle filter, handling linear Gaussian substructures in the model in an efficient way, is extended to dependent noise; and, finally, iv) the parameters of a joint Gaussian distribution of the noise processes are estimated jointly with the state in a recursive way.

```
@article{diva2:543907,
author = {Saha, Saikat and Gustafsson, Fredrik},
title = {{Particle Filtering With Dependent Noise Processes}},
journal = {IEEE Transactions on Signal Processing},
year = {2012},
volume = {60},
number = {9},
pages = {4497--4508},
}
```

This article considers a sensor management problem where a number of road bounded vehicles are monitored by an unmanned aerial vehicle (UAV) with a gimballed vision sensor. The problem is to keep track of all discovered targets and simultaneously search for new targets by controlling the pointing direction of the vision sensor and the motion of the UAV. A planner based on a state-machine is proposed with three different modes; target tracking, known target search, and new target search. A high-level decision maker chooses among these sub-tasks to obtain an overall situational awareness. A utility measure for evaluating the combined search and target tracking performance is also proposed. By using this measure it is possible to evaluate and compare the rewards of updating known targets versus searching for new targets in the same framework. The targets are assumed to be road bounded and the road network information is used both to improve the tracking and sensor management performance. The tracking and search are based on flexible target density representations provided by particle mixtures and deterministic grids.

```
@article{diva2:546133,
author = {Skoglar, Per and Orguner, Umut and Törnqvist, David and Gustafsson, Fredrik},
title = {{Road Target Search and Tracking with Gimballed Vision Sensor on an Unmanned Aerial Vehicle}},
journal = {Remote Sensing},
year = {2012},
volume = {4},
number = {7},
pages = {2076--2111},
}
```

In this paper, we deal with the problem of continuous-time time-varying parameter estimation in stochastic systems, under three different kinds of stochastic perturbations: additive and multiplicative white noise, and coloured noise. The proposed algorithm is based on the least squares method with forgetting factor. Some numerical examples illustrate the effectiveness of the proposed algorithm. An analysis of the estimation error for the system under the three different kinds of perturbations is presented.

```
@article{diva2:544969,
author = {Escobar, Jesica},
title = {{Time-Varying Parameter Estimation under Stochastic Perturbations using LSM}},
journal = {IMA Journal of Mathematical Control and Information},
year = {2012},
volume = {29},
number = {2},
pages = {235--258},
}
```

This correspondence proposes a new measurement update for extended target tracking under measurement noise when the target extent is modeled by random matrices. Compared to the previous measurement update developed by Feldmann et al., this work follows a more rigorous path to derive an approximate measurement update using the analytical techniques of variational Bayesian inference. The resulting measurement update, though computationally more expensive, is shown via simulations to be better than the earlier method in terms of both the state estimates and the predictive likelihood for moderate amounts of prediction errors.

```
@article{diva2:544137,
author = {Orguner, Umut},
title = {{A Variational Measurement Update for Extended Target Tracking With Random Matrices}},
journal = {IEEE Transactions on Signal Processing},
year = {2012},
volume = {60},
number = {7},
pages = {3827--3834},
}
```

This paper presents the robust optimization framework in the modelling language YALMIP, which carries out robust modelling and uncertainty elimination automatically and allows the user to concentrate on the high-level model. While introducing the software package, a brief summary of robust optimization is given, as well as some comments on modelling and tractability of complex convex uncertain optimization problems.

```
@article{diva2:523936,
author = {Löfberg, Johan},
title = {{Automatic Robust Convex Programming}},
journal = {Optimization Methods and Software},
year = {2012},
volume = {27},
number = {1},
pages = {115--129},
}
```

This article presents a pedestrian tracking methodology using an infrared sensor for surveillance applications. A distinctive feature of this study compared to the existing pedestrian tracking approaches is that the road network information is utilized for performance enhancement. A multiple model particle filter, which uses two different motion models, is designed for enabling the tracking of both road-constrained (on-road) and unconstrained (off-road) targets. The lateral position of the pedestrians on the walkways are taken into account by a specific on-road target model. The overall framework seamlessly integrates the negative information of occlusion events into the algorithm for which the required modifications are discussed. The resulting algorithm is illustrated on real data from a field trial for different scenarios.

```
@article{diva2:517378,
author = {Skoglar, Per and Orguner, Umut and Törnqvist, David and Gustafsson, Fredrik},
title = {{Pedestrian Tracking with an Infrared Sensor using Road Network Information}},
journal = {EURASIP Journal on Advances in Signal Processing},
year = {2012},
volume = {1},
number = {26},
pages = {2012a--},
}
```

One of the most fundamental problems in model predictive control (MPC) is the lack of guaranteed stability and feasibility. It is shown how Farkas Lemma in combination with bilevel programming and disjoint bilinear programming can be used to search for problematic initial states which lack recursive feasibility, thus invalidating a particular MPC controller. Alternatively, the method can be used to derive a certificate that the problem is recursively feasible. The results are initially derived for nominal linear MPC, and thereafter extended to the additive disturbance case.

```
@article{diva2:515434,
author = {Löfberg, Johan},
title = {{Oops! I cannot do it again:
Testing for Recursive Feasibility in MPC}},
journal = {Automatica},
year = {2012},
volume = {48},
number = {3},
pages = {550--555},
}
```

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

```
@article{diva2:505951,
author = {Gustafsson, Fredrik and Hendeby, Gustaf},
title = {{Some Relations Between Extended and Unscented Kalman Filters}},
journal = {IEEE Transactions on Signal Processing},
year = {2012},
volume = {60},
number = {2},
pages = {545--555},
}
```

In optimization routines used for on-line Model Predictive Control (MPC), linear systems of equations are solved in each iteration. This is true both for Active Set (AS) solvers as well as for Interior Point (IP) solvers, and for linear MPC as well as for nonlinear MPC and hybrid MPC. The main computational effort is spent while solving these linear systems of equations, and hence, it is of great interest to solve them efficiently. In high performance solvers for MPC, this is performed using Riccati recursions or generic sparsity exploiting algorithms. To be able to get this performance gain, the problem has to be formulated in a sparse way which introduces more variables. The alternative is to use a smaller formulation where the objective function Hessian is dense. In this work, it is shown that it is possible to exploit the structure also when using the dense formulation. More specifically, it is shown that it is possible to efficiently compute a standard Cholesky factorization for the dense formulation. This results in a computational complexity that grows quadratically in the prediction horizon length instead of cubically as for the generic Cholesky factorization.

```
@article{diva2:475656,
author = {Axehill, Daniel and Morari, Manfred},
title = {{An Alternative use of the Riccati Recursion for Efficient Optimization}},
journal = {Systems \& control letters (Print)},
year = {2012},
volume = {61},
number = {1},
pages = {37--40},
}
```

Friction is the result of complex interactions between contacting surfaces in down to a nanoscale perspective. Depending on the application, the different models available are more or less suitable. Static friction models are typically considered to be dependent only on relative speed of interacting surfaces. However, it is known that friction can be affected by other factors than speed.

In this paper, the typical friction phenomena and models used in robotics are reviewed. It is shown how such models can be represented as a sum of functions of relevant states which are linear and nonlinear in the parameters, and how the identification method described in Golub and Pereyra (1973) can be used to identify them when all states are measured. The discussion follows with a detailed experimental study of friction in a robot joint under changes of joint angle, load torque and temperature. Justified by their significance, load torque and temperature are included in an extended static friction model. The proposed model is validated in a wide operating range, considerably improving the prediction performance compared to a standard model.

```
@article{diva2:464263,
author = {Carvalho Bittencourt, Andr\'{e} and Gunnarsson, Svante},
title = {{Static Friction in a Robot Joint:
Modeling and Identification of Load and Temperature Effects}},
journal = {Journal of Dynamic Systems Measurement, and Control},
year = {2012},
volume = {134},
number = {5},
}
```

The presence of abrupt changes, such as impulsive and load disturbances, commonly occur in applications, but make the state estimation problem considerably more difficult than in the standard setting with Gaussian process disturbance. Abrupt changes often introduce a jump in the state, and the problem is therefore readily and often treated by change detection techniques. In this paper, we take a different approach. The state smoothing problem for linear state space models is here formulated as a constrained least-squares problem with sum-of-norms regularization, a generalization of l1-regularization. This novel formulation can be seen as a convex relaxation of the well known generalized likelihood ratio method by Willsky and Jones. Another nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade off fit and the number of jumps. Good practical choices of this parameter along with an extension to nonlinear state space models are given.

```
@article{diva2:360027,
author = {Ohlsson, Henrik and Gustafsson, Fredrik and Ljung, Lennart and Boyd, Stephen},
title = {{Smoothed State Estimates under Abrupt Changes using Sum-of-Norms Regularization}},
journal = {Automatica},
year = {2012},
volume = {48},
number = {4},
pages = {595--605},
}
```

In this paper we address the loop closure detection problem in simultaneous localization and mapping (SLAM), and present a method for solving the problem using pairwise comparison of point clouds in both two and three dimensions. The point clouds are mathematically described using features that capture important geometric and statistical properties. The features are used as input to the machine learning algorithm AdaBoost, which is used to build a non-linear classifier capable of detecting loop closure from pairs of point clouds. Vantage point dependency in the detection process is eliminated by only using rotation invariant features, thus loop closure can be detected from an arbitrary direction. The classifier is evaluated using publicly available data, and is shown to generalize well between environments. Detection rates of 66%, 63% and 53% for 0% false alarm rate are achieved for 2D outdoor data, 3D outdoor data and 3D indoor data, respectively. In both two and three dimensions, experiments are performed using publicly available data, showing that the proposed algorithm compares favourably with related work.

```
@article{diva2:480845,
author = {Granström, Karl and Schön, Thomas and Ramos, Fabio T. and Nieto, Juan I.},
title = {{Learning to Close Loops from Range Data}},
journal = {The international journal of robotics research},
year = {2011},
volume = {30},
number = {14},
pages = {1728--1754},
}
```

Model-based engineering becomes more and more important in industrial practice. System identification is a vital technology for producing the necessary models, and has been an active area of research and applications in the automatic control community during half a century. At the same time, increasing demands require the area to constantly develop and sharpen its tools. This paper deals with how system identification does that by amalgamating concepts, features and methods from other fields. It describes encounters with four areas in systems theory and engineering: Networked Systems, Particle Filtering Techniques, Sparsity and Compressed Sensing, and Machine Learning. The impacts on System Identification methodology by these encounters are described and illustrated.

```
@article{diva2:476380,
author = {Ljung, Lennart and Hjalmarsson, Hakan and Ohlsson, Henrik},
title = {{Four Encounters with System Identification}},
journal = {European Journal of Control},
year = {2011},
volume = {17},
number = {5-6},
pages = {449--471},
}
```

Many control-related problems can be cast as semidefinite programs. Even though there exist polynomial time algorithms and excellent publicly available solvers, the time it takes to solve these problems can be excessive. What many of these problems have in common, in particular in control, is that some of the variables enter as matrix-valued variables. This leads to a low-rank structure in the basis matrices which can be exploited when forming the Newton equations. In this article, we describe how this can be done, and show how our code, called STRUL, can be used in conjunction with the semidefinite programming solver SDPT3. The idea behind the structure exploitation is classical and is implemented in LMI Lab, but we show that when using a modern semidefinite programming framework such as SDPT3, the computational time can be significantly reduced. Finally, we describe how the modelling language YALMIP has been changed in such a way that our code, which can be freely downloaded, can be interfaced using standard YALMIP commands. This greatly simplifies modelling and usage.

```
@article{diva2:471330,
author = {Falkeborn, Rikard and Löfberg, Johan and Hansson, Anders},
title = {{Low-Rank Exploitation in Semidefinite Programming for Control}},
journal = {International Journal of Control},
year = {2011},
volume = {84},
number = {12},
pages = {1975--1982},
}
```

A vessel navigating in a critical environment such as an archipelago, requires very accurate movement estimates. Intentional or unintentional jamming makes gps unreliable as the only source of information and an additional independent navigation system should be used. In this paper we suggest estimating the vessel movements using a sequence of radar images from the preexisting body-fixed radar. Island landmarks in the radar scans are tracked between multiple scans using visual features. This provides information not only about the position of the vessel but also of its course and velocity. We present here a complete navigation framework that requires no additional hardware than the already existing naval radar sensor. Experiments show that visual radar features can be used to accurately estimate the vessel trajectory over an extensive data set.

```
@article{diva2:460050,
author = {Callmer, Jonas and Törnqvist, David and Gustafsson, Fredrik and Svensson, Henrik and Carlbom, Pelle},
title = {{RADAR SLAM using Visual Features}},
journal = {EURASIP Journal on Advances in Signal Processing},
year = {2011},
volume = {2011},
number = {71},
}
```

Input saturation is inevitable in many engineering applications. Most existing iterative learning control (ILC) algorithms that can deal with input saturation require that the reference signal is realizable within the saturation bound. For engineering systems without precise models, it is hard to verify this requirement. In this note, a "reference governor" (RG) is introduced and is incorporated with the available ILC algorithms (primary ILC algorithms). The role of the RG is to re-design the reference signal so that the modified reference signal is realizable. Two types of the RG are proposed: one modifies the amplitude of the reference signal and the other modifies the frequency. Our main results provide design guidelines for two RGs. Moreover, a design trade-off between the convergence speed and tracking performance is also discussed. A simple simulation result verifies the effectiveness of the proposed methods.

```
@article{diva2:456020,
author = {Tan, Ying and Xu, Jian-Xin and Norrlöf, Mikael and Freeman, Christopher},
title = {{On Reference Governor in Iterative Learning Control for Dynamic Systems with Input Saturation}},
journal = {Automatica},
year = {2011},
volume = {47},
number = {11},
pages = {2412--2419},
}
```

This brief presents a behavioral model structure and a model-based phase-only predistortion method that are suitable for outphasing RF amplifiers. The predistortion method is based on a model of the amplifier with a constant gain factor and phase rotation for each outphasing signal, and a predistorter with phase rotation only. The method has been used for enhanced data rates for GSM evolution (EDGE) and wideband code-division multiple-access (WCDMA) signals applied to a Class-D outphasing RF amplifier with an on-chip transformer used for power combining in 90-nm CMOS. The measured peak power at 2 GHz was +10.3 dBm with a drain efficiency and power-added efficiency of 39% and 33%, respectively. For an EDGE 8 phase-shift-keying (8-PSK) signal with a phase error of 3 degrees between the two input outphasing signals, the measured power at 400 kHz offset was -65.9 dB with predistortion, compared with -53.5 dB without predistortion. For a WCDMA signal with the same phase error between the input signals, the measured adjacent channel leakage ratio at 5-MHz offset was -50.2 dBc with predistortion, compared with -38.0 dBc without predistortion.

```
@article{diva2:453945,
author = {Fritzin, Jonas and Jung, Ylva and Landin, Per Niklas and Handel, Peter and Enqvist, Martin and Alvandpour, Atila},
title = {{Phase Predistortion of a Class-D Outphasing RF Amplifier in 90 nm CMOS}},
journal = {IEEE Transactions on Circuits and Systems - II - Express Briefs},
year = {2011},
volume = {58},
number = {10},
pages = {642--646},
}
```

A given explicit piecewise affine representation of an MPC feedback law is approximated by a single polynomial, computed using linear programming. This polynomial state feedback control law guarantees closed-loop stability and constraint satisfaction. The polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage.

```
@article{diva2:451825,
author = {Kvasnica, Michal and Löfberg, Johan and Fikar, Miroslav},
title = {{Stabilizing Polynomial Approximation of Explicit MPC}},
journal = {Automatica},
year = {2011},
volume = {47},
number = {10},
pages = {2292--2297},
}
```

Random multisines have successfully been used as input signals in many system identification experiments. In this paper, it is shown that scalar random multisine signals with a flat amplitude spectrum are separable of order one. The separability property means that certain conditional expectations are linear and it implies that random multisines can easily be used to obtain accurate estimates of the linear time-invariant part of a Hammerstein system. Furthermore, higher order separability is investigated.

```
@article{diva2:444862,
author = {Enqvist, Martin},
title = {{Separability of Scalar Random Multisine Signals}},
journal = {Automatica},
year = {2011},
volume = {47},
number = {9},
pages = {1860--1867},
}
```

The framework of differential algebra, especially Ritts algorithm, has turned out to be a useful tool when analyzing the identifiability of certain nonlinear continuous-time model structures. This framework provides conceptually interesting means to analyze complex nonlinear model structures via the much simpler linear regression models. One difficulty when working with continuous-time signals is dealing with white noise in nonlinear systems. In this paper, difference algebraic techniques, which mimic the differential-algebraic techniques, are presented. Besides making it possible to analyze discrete-time model structures, this opens up the possibility of dealing with noise. Unfortunately, the corresponding discrete-time identifiability results are not as conclusive as in continuous time. In addition, an alternative elimination scheme to Ritts algorithm will be formalized and the resulting algorithm is analyzed when applied to a special form of the NFIR model structure.

```
@article{diva2:444834,
author = {Lyzell, Christian and Glad, Torkel and Enqvist, Martin and Ljung, Lennart},
title = {{Difference Algebra and System Identification}},
journal = {Automatica},
year = {2011},
volume = {47},
number = {9},
pages = {1896--1904},
}
```

The particle filter has become an important tool in solving nonlinear filtering problems for dynamic systems. This correspondence extends our recent work, where we proved that the particle filter converges for unbounded functions, using *L ^{4}*-convergence. More specifically, the present contribution is that we prove that the particle filter converge for unbounded functions in the sense of

*Lp*-convergence, for an arbitrary

*p*≥ 2.

```
@article{diva2:433465,
author = {Hu, Xiao-Li and Schön, Thomas and Ljung, Lennart},
title = {{A General Convergence Result for Particle Filtering}},
journal = {IEEE Transactions on Signal Processing},
year = {2011},
volume = {59},
number = {7},
pages = {3424--3429},
}
```

This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a quasi-Newton primal-dual interior point method. The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method has comparable performance and speed.

```
@article{diva2:433299,
author = {Ankelhed, Daniel and Helmersson, Anders and Hansson, Anders},
title = {{A Quasi-Newton Interior Point Method for Low Order H-Infinity Controller Synthesis}},
journal = {IEEE Transactions on Automatic Control},
year = {2011},
volume = {56},
number = {6},
pages = {1462--1467},
}
```

Signal propagation delays are hardly a problem for target tracking with standard sensors such as radar and vision due to the fact that the speed of light is much higher than the speed of the target. This contribution studies the case where the ratio of the target and the propagation speed is not negligible, as in the case of sensor networks with microphones, geophones or sonars for instance, where the signal speed in air, ground and water causes a state dependent and stochastic delay of the observations. The proposed approach utilizes an augmentation of the state vector with the propagation delay in a particle filtering framework to compensate for the negative effects of the delays. The model of the physics rules governing the propagation delays is used in interaction with the target motion model to yield an iterative prediction update step in the particle filter which is called the propagation delayed measurement particle filter (PDM-PF). The performance of PDM-PF is illustrated in a challenging target tracking scenario by making comparisons to alternative particle filters that can be used in similar cases.

```
@article{diva2:421233,
author = {Orguner, Umut and Gustafsson, Fredrik},
title = {{Target Tracking With Particle Filters Under Signal Propagation Delays}},
journal = {IEEE Transactions on Signal Processing},
year = {2011},
volume = {59},
number = {6},
pages = {2485--2495},
}
```

We propose a probabilistic method to compute the near mid-air collision risk as a function of predicted flight trajectory. The computations use state estimate and covariance from a target tracking filter based on angle-only sensors such as digital video cameras. The majority of existing work is focused on risk estimation at a certain time instant. Here we derive an expression for the integrated risk over the critical time horizon. This is possible using probability for level-crossing, and the expression applies to a three-dimensional piecewise straight flight trajectory. The Monte Carlo technique provides a method to compute the probability, but a huge number of simulations is needed to get sufficient reliability for the small risks that the applications require. Instead we propose a method which through sound geometric and numerical approximations yields a solution suitable for real-time implementations. The algorithm is applied to realistic angle-only tracking data, and shows promising results when compared with the Monte Carlo solution.

```
@article{diva2:418143,
author = {Nordlund, Per-Johan and Gustafsson, Fredrik},
title = {{Probabilistic Noncooperative Near Mid-Air Collision Avoidance}},
journal = {IEEE Transactions on Aerospace and Electronic Systems},
year = {2011},
volume = {47},
number = {2},
pages = {1265--1276},
}
```

A robust, accurate positioning system with seamless outdoor and indoor coverage is a highly needed tool for increasing safety in emergency response and military urban operations. It must be lightweight, small, inexpensive, and power efficient, and still provide meter-level accuracy during extended operations. GPS receivers, inertial sensors, and local radio-based ranging are natural choices for a multisensor positioning system. Inertial navigation with foot-mounted sensors is suitable as the core system in GPS denied environments, since it can yield meter-level accuracies for a few minutes. However, there is still a need for additional supporting sensors to keep the accuracy at acceptable levels during the duration of typical soldier and first responder operations. Suitable aiding sensors are three-axis magnetometers, barometers, imaging sensors, Doppler radars, and ultrasonic sensors. Furthermore, cooperative positioning, where first responders exchange position and error estimates in conjunction with performing radio-based ranging, is deemed a key technology. This article provides a survey on technologies and concepts for high accuracy soldier and first responder positioning systems, with an emphasis on indoor positioning.

```
@article{diva2:416868,
author = {Rantakokko, Jouni and Rydell, Joakim and Stromback, Peter and Handel, Peter and Callmer, Jonas and Törnqvist, David and Gustafsson, Fredrik and Jobs, Magnus and Gruden, Mathias},
title = {{Accurate and Reliable Soldier and First Responder Indoor Positioning:
Multi-Sensor Systems and Cooperative Localization}},
journal = {IEEE wireless communications},
year = {2011},
volume = {18},
number = {2},
pages = {10--18},
}
```

The reference frame theory constitutes an essential aspect of electric machine analysis and control. In this study, apart from the conventional applications, it is reported that the reference frame theory approach can successfully be applied to real-time fault diagnosis of electric machinery systems as a powerful toolbox to find the magnitude and phase quantities of fault signatures with good precision as well. The basic idea is to convert the associated fault signature to a dc quantity, followed by the computation of the signals average in the fault reference frame to filter out the rest of the signal harmonics, i.e., its ac components. As a natural consequence of this, neither a notch filter nor a low-pass filter is required to eliminate fundamental component or noise content. Since the incipient fault mechanisms have been studied for a long time, the motor fault signature frequencies and fault models are very well-known. Therefore, ignoring all other components, the proposed method focuses only on certain fault signatures in the current spectrum depending on the examined motor fault. Broken rotor bar and eccentricity faults are experimentally tested online using a TMS320F2812 digital signal processor (DSP) to prove the effectiveness of the proposed method. In this application, only the readily available drive hardware is used without employing additional components such as analog filters, signal conditioning board, external sensors, etc. As the motor drive processing unit, the DSP is utilized both for motor control and fault detection purposes, providing instantaneous fault information. The proposed algorithm processes the measured data in real time to avoid buffering and large-size memory needed in order to enhance the practicability of this method. Due to the short-time convergence capability of the algorithm, the fault status is updated in each second. The immunity of the algorithm against non-ideal cases such as measurement offset errors and phase unbalance is theoretically and experimentally verified. Being a model-independent fault analyzer, this method can be applied to all multiphase and single-phase motors.

```
@article{diva2:414731,
author = {Akin, Bilal and Choi, Seungdeog and Orguner, Umut and Toliyat, Hamid A},
title = {{A Simple Real-Time Fault Signature Monitoring Tool for Motor-Drive-Embedded Fault Diagnosis Systems}},
journal = {IEEE transactions on industrial electronics (1982. Print)},
year = {2011},
volume = {58},
number = {5},
pages = {1990--2001},
}
```

A framework for iterative learning control (ILC) is proposed for the situation when an ILC algorithm uses an estimate of the controlled variable obtained from an observer-based estimation procedure. Assuming that the ILC input converges to a bounded signal, a general expression for the asymptotic error of the controlled variable is given. The asymptotic error is exemplified by an ILC algorithm applied to a flexible two-mass model of a robot joint.

```
@article{diva2:411272,
author = {Wall\'{e}n, Johanna and Norrlöf, Mikael and Gunnarsson, Svante},
title = {{A Framework for Analysis of Observer-Based ILC}},
journal = {Asian journal of control},
year = {2011},
volume = {13},
number = {1},
pages = {3--14},
}
```

A localization algorithm based on cell identification (Cell-ID) information is proposed. Instead of building the localization decisions only on the serving base station, all the detected Cell-IDs (serving or nonserving) by the mobile station are utilized. The statistical modeling of user motion and the measurements are done via a hidden Markov model (HMM), and the localization decisions are made with maximum a posteriori estimation criterion using the posterior probabilities from an HMM filter. The results are observed and compared with standard alternatives on an example whose data were collected from a worldwide interoperability for microwave access network in a challenging urban area in the Brussels capitol city.

```
@article{diva2:409394,
author = {Bshara, Mussa and Orguner, Umut and Gustafsson, Fredrik and Van Biesen, Leo},
title = {{Robust Tracking in Cellular Networks Using HMM Filters and Cell-ID Measurements}},
journal = {IEEE Transactions on Vehicular Technology},
year = {2011},
volume = {60},
number = {3},
pages = {1016--1024},
}
```

Mapping stationary objects is essential for autonomous vehicles and many autonomous functions in vehicles. In this contribution the probability hypothesis density (PHD) filter framework is applied to automotive imagery sensor data for constructing such a map, where the main advantages are that it avoids the detection, the data association and the track handling problems in conventional multiple-target tracking, and that it gives a parsimonious representation of the map in contrast to grid based methods. Two original contributions address the inherent complexity issues of the algorithm: First, a data clustering algorithm is suggested to group the components of the PHD into different clusters, which structures the description of the prior and considerably improves the measurement update in the PHD filter. Second, a merging step is proposed to simplify the map representation in the PHD filter. The algorithm is applied to multi-sensor radar data collected on public roads, and the resulting map is shown to well describe the environment as a human perceives it.

```
@article{diva2:404125,
author = {Lundquist, Christian and Hammarstrand, Lars and Gustafsson, Fredrik},
title = {{Road Intensity Based Mapping using Radar Measurements with a Probability Hypothesis Density Filter}},
journal = {IEEE Transactions on Signal Processing},
year = {2011},
volume = {59},
number = {4},
pages = {1397--1408},
}
```

In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested subproblems and then handles the two nested subproblems using PFs. The DPF has the advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and can thus be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results of two examples indicate that the DPF has a potential to achieve in a shorter execution time the same level of performance as the regular PF.

```
@article{diva2:402173,
author = {Chen, Tianshi and Schön, Thomas and Ohlsson, Henrik and Ljung, Lennart},
title = {{Decentralized Particle Filter with Arbitrary State Decomposition}},
journal = {IEEE Transactions on Signal Processing},
year = {2011},
volume = {59},
number = {2},
pages = {465--478},
}
```

This paper is concerned with the parameter estimation of a general class of nonlinear dynamic systems in state-space form. More specifically, a Maximum Likelihood (ML) framework is employed and an Expectation Maximisation (EM) algorithm is derived to compute these ML estimates. The Expectation (E) step involves solving a nonlinear state estimation problem, where the smoothed estimates of the states are required. This problem lends itself perfectly to the particle smoother, which provides arbitrarily good estimates. The maximisation (M) step is solved using standard techniques from numerical optimisation theory. Simulation examples demonstrate the efficacy of our proposed solution.

```
@article{diva2:400661,
author = {Schön, Thomas and Wills, Adrian and Ninness, Brett},
title = {{System Identification of Nonlinear State-Space Models}},
journal = {Automatica},
year = {2011},
volume = {47},
number = {1},
pages = {39--49},
}
```

We provide a sensor fusion framework for solving the problem of joint egomotion and road geometry estimation. More specifically we employ a sensor fusion framework to make systematic use of the measurements from a forward looking radar and camera, steering wheel angle sensor, wheel speed sensors and inertial sensors to compute good estimates of the road geometry and the motion of the ego vehicle on this road. In order to solve this problem we derive dynamical models for the ego vehicle, the road and the leading vehicles. The main difference to existing approaches is that we make use of a new dynamic model for the road. An extended Kalman filter is used to fuse data and to filter measurements from the camera in order to improve the road geometry estimate. The proposed solution has been tested and compared to existing algorithms for this problem, using measurements from authentic traffic environments on public roads in Sweden. The results clearly indicate that the proposed method provides better estimates.

```
@article{diva2:273742,
author = {Lundquist, Christian and Schön, Thomas},
title = {{Joint Ego-Motion and Road Geometry Estimation}},
journal = {Information Fusion},
year = {2011},
volume = {12},
number = {4},
pages = {253--263},
}
```

This paper presents an extended target tracking framework which uses polynomials in order to model extended objects in the scene of interest from imagery sensor data. State-space models are proposed for the extended objects which enables the use of Kalman filters in tracking. Different methodologies of designing measurement equations are investigated. A general target tracking algorithm that utilizes a specific data association method for the extended targets is presented. The overall algorithm must always use some form of prior information in order to detect and initialize extended tracks from the point tracks in the scene. This aspect of the problem is illustrated on a real life example of road-map estimation from automotive radar reports along with the results of the study.

```
@article{diva2:383079,
author = {Lundquist, Christian and Orguner, Umut and Gustafsson, Fredrik},
title = {{Extended Target Tracking Using Polynomials With Applications to Road-Map Estimation}},
journal = {IEEE Transactions on Signal Processing},
year = {2011},
volume = {59},
number = {1},
pages = {15--26},
}
```

To improve our understanding of the climate process and to assess the human impact on current global warming, past climate reconstruction is essential. The chemical composition of a bivalve shell is strongly coupled to environmental variations and therefore ancient shells are potential climate archives. The nonlinear nature of the relation between environmental condition (e.g. the seawater temperature) and proxy composition makes it hard to predict the former from the latter, however. In this paper we compare the ability of three nonlinear system identification methods to reconstruct the ambient temperature from the chemical composition of a shell. The comparison shows that nonlinear multi-proxy approaches are potentially useful tools for climate reconstructions and that manifold based methods result in smoother and more precise temperature reconstruction.

```
@article{diva2:375041,
author = {Bauwens, Maite and Ohlsson, Henrik and Barb\'{e}, Kurt and Beelaerts, Veerle and Dehairs, Frank and Schoukens, Johan},
title = {{On Climate Reconstruction Using Bivalve Shells:
Three Methods To Interpret the Chemical Signature of a Shell}},
journal = {Computer Methods and Programs in Biomedicine},
year = {2011},
volume = {104},
number = {2},
pages = {104--111},
}
```

In this paper, we study the problem of estimating unknown parameters in nonlinear gray-box models that may be multivariable, nonlinear, unstable, and resonant at the same time. A straightforward use of time-domain predication-error methods for this type of problem easily ends up in a large and numerically stiff optimization problem. We therefore propose an identification procedure that uses intermediate local models that allow for data compression and a less complex optimization problem. The procedure is based on the estimation of the nonparametric frequency response function (FRF) in a number of operating points. The nonlinear gray-box model is linearized in the same operating points, resulting in parametric FRFs. The optimal parameters are finally obtained by minimizing the discrepancy between the nonparametric and parametric FRFs. The procedure is illustrated by estimating elasticity parameters in a six-axes industrial robot. Different parameter estimators are compared and experimental results show the usefulness of the proposed identification procedure. The weighted logarithmic least squares estimator achieves the best result and the identified model gives a good global description of the dynamics in the frequency range of interest for robot control.

```
@article{diva2:370701,
author = {Wernholt, Erik and Moberg, Stig},
title = {{Nonlinear Gray-Box Identification Using Local Models Applied to Industrial Robots}},
journal = {Automatica},
year = {2011},
volume = {47},
number = {4},
pages = {650--660},
}
```

For computational efficiency, it is important to utilize model structure in particle filtering. One of the most important cases occurs when there exists a linear Gaussian substructure, which can be efficiently handled by Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF). This contribution suggests an alternative formulation of this well-known result that facilitates reuse of standard filtering components and which is also suitable for object-oriented programming. Our RBPF formulation can be seen as a Kalman filter bank with stochastic branching and pruning.

```
@article{diva2:412640,
author = {Hendeby, Gustaf and Karlsson, Rickard and Gustafsson, Fredrik},
title = {{The Rao-Blackwellized Particle Filter:
A Filter Bank Implementation}},
journal = {EURASIP Journal on Advances in Signal Processing},
year = {2010},
volume = {2010},
number = {724087},
}
```

The state estimation problem for linear systems with linear state equality constraints was dealt with in Ko andamp; Bitmead [Ko, S., andamp; Bitmead, R. (2007). State estimation for linear systems with state equality constraints. Automatica, 43, 1363-1368]. In this correspondence, it is first shown that a necessary assumption on the covariance of the process noise is missing in the main result of the paper. It is then shown that the main result of the paper can be achieved in a convenient and more general way without any additional assumptions on the covariance of the process noise except positive definiteness.

```
@article{diva2:379127,
author = {Chen, Tianshi},
title = {{Comments on "State estimation for linear systems with state equality constraints" [Automatica 43 (2007) 1363-1368] in AUTOMATICA, vol 46, issue 11, pp 1929-1932}},
journal = {Automatica},
year = {2010},
volume = {46},
number = {11},
pages = {1929--1932},
}
```

A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ^{18}O carbonate, which for freshwater influenced environments is hindered because the isotopic composition of the ambient water (related to salinity) affects the reconstructed temperature. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization to develop a temperature reconstruction model that is less sensitive to salinity variations. The motivation for using this type of model is twofold: Firstly, observed nonlinear relations between specific proxies and water temperature motivate the use of nonlinear models. Secondly, the use of multi-proxy models enables salinity related variations of a given temperature proxy to be explained by salinity-related information carried by a separate proxy. Our findings confirm that Mg/Ca is a powerful paleothermometer and highlight that reconstruction performance based on this proxy is improved significantly by combining its information with the information of other trace elements in multi-proxy models. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enabled a temperature reconstruction with a root mean squared error of ±2.19 °C for a salinity range between 15 and 32.

```
@article{diva2:375050,
author = {Bauwens, Maite and Ohlsson, Henrik and Barbe, Kurt and Beelaerts, Veerle and Dehairs, Frank and Schoukens, Johan},
title = {{A Nonlinear Multi-Proxy Model Based on Manifold Learning to Reconstruct Water Temperature from High Resolution Trace Element Profiles in Biogenic Carbonates}},
journal = {Geoscientific Model Development},
year = {2010},
volume = {3},
number = {3},
pages = {1105--1138},
}
```

The particle filter (PF) was introduced in 1993 as a numerical approximation to the nonlinear Bayesian filtering problem, and there is today a rather mature theory as well as a number of successful applications described in literature. This tutorial serves two purposes: to survey the part of the theory that is most important for applications and to survey a number of illustrative positioning applications from which conclusions relevant for the theory can be drawn. The theory part first surveys the nonlinear filtering problem and then describes the general PF algorithm in relation to classical solutions based on the extended Kalman filter (EKF) and the point mass filter (PMF). Tuning options, design alternatives, and user guidelines are described, and potential computational bottlenecks are identified and remedies suggested. Finally, the marginalized (or Rao-Blackwellized) PF is overviewed as a general framework for applying the PF to complex systems. The application part is more or less a stand-alone tutorial without equations that does not require any background knowledge in statistics or nonlinear filtering. It describes a number of related positioning applications where geographical information systems provide a nonlinear measurement and where it should be obvious that classical approaches based on Kalman filters (KFs) would have poor performance. All applications are based on real data and several of them come from real-time implementations. This part also provides complete code examples.

```
@article{diva2:360880,
author = {Gustafsson, Fredrik},
title = {{Particle Filter Theory and Practice with Positioning Applications}},
journal = {IEEE Aerospace and Electronic Systems Magazine},
year = {2010},
volume = {25},
number = {7},
pages = {53--81},
}
```

The main objective in this work is to compare different convex relaxations for Model Predictive Control (MPC) problems with mixed real valued and binary valued control signals. In the problem description considered, the objective function is quadratic, the dynamics are linear, and the inequality constraints on states and control signals are all linear. The relaxations are related theoretically and the quality of the bounds and the computational complexities are compared in numerical experiments. The investigated relaxations include the Quadratic Programming (QP) relaxation, the standard Semidefinite Programming (SDP) relaxation, and an equality constrained SDP relaxation. The equality constrained SDP relaxation appears to be new in the context of hybrid MPC and the result presented in this work indicates that it can be useful as an alternative relaxation, which is less computationally demanding than the ordinary SDP relaxation and which often gives a better bound than the bound from the QP relaxation. Furthermore, it is discussed how the result from the SDP relaxations can be used to generate suboptimal solutions to the control problem. Moreover, it is also shown that the equality constrained SDP relaxation is equivalent to a QP in an important special case.

```
@article{diva2:355801,
author = {Axehill, Daniel and Vandenberghe, Lieven and Hansson, Anders},
title = {{Convex Relaxations for Mixed Integer Predictive Control}},
journal = {Automatica},
year = {2010},
volume = {46},
number = {9},
pages = {1540--1545},
}
```

Detecting and isolating multiple faults is a computationally expensive task. It typically consists of computing a set of tests and then computing the diagnoses based on the test results. This paper describes FlexDx, a reconfigurable diagnosis framework which reduces the computational burden while retaining the isolation performance by only running a subset of all tests that is sufficient to find new conflicts. Tests in FlexDx are thresholded residuals used to indicate conflicts in the monitored system. Special attention is given to the issues introduced by a reconfigurable diagnosis framework. For example, tests are added and removed dynamically, tests are partially performed on historic data, and synchronous and asynchronous processing are combined. To handle these issues FlexDx has been implemented using DyKnow, a stream-based knowledge processing middleware framework. Concrete methods for each component in the FlexDx framework are presented. The complete approach is exemplified on a dynamic system which clearly illustrates the complexity of the problem and the computational gain of the proposed approach.

```
@article{diva2:354330,
author = {Krysander, Mattias and Heintz, Fredrik and Roll, Jacob and Frisk, Erik},
title = {{FlexDx:
A Reconfigurable Diagnosis Framework}},
journal = {Engineering applications of artificial intelligence},
year = {2010},
volume = {23},
number = {8},
pages = {1303--1313},
}
```

## Books

```
@book{diva2:484561,
editor = {Varga, Andras and Hansson, Anders and Puyou, Guilhem},
title = {{Optimization Based Clearance of Flight Control Laws - A Civil Aircraft Application}},
publisher = {Springer},
year = {2012},
address = {Berlin},
}
```

Sensor fusion deals with Merging information from two or more sensors. Elsewhere the area of statistical signal processing provides a powerful toolbox to attack bothering theoretical and practical problems. The objective of this book is to explain state of the art theory and algorithms into statistical sensor fusion, covering estimation, detection and non-linear filtering theory with applications to localisation, navigation and tracking problems. The book starts with a review of the theory on linear and non-linear estimation, with a focus on sensor network applications. Then, general non-linear filter theory is surveyed with a Particular attention to Different variants of the Kalman filter and the particle filter. Complexity and implementation issues are discussed in detail. Simultaneous localisation and mapping (SLAM) is distressed as a challenging application area of high-dimensional non-linear filtering problems. The book spans the whole range from mathematical foundations provided in Extensive Appendices, to real-world problems the covered in a party surveying standard sensors, motion models and applications in this field. All models and algorithms are available as object-oriented Matlab code with an Extensive data file library, and the examples, Which are richly distressed to illustrate the theory, are supplemented by fully reproducible Matlab code.

```
@book{diva2:489131,
author = {Gustafsson, Fredrik},
title = {{Statistical sensor fusion}},
publisher = {Studentlitteratur},
year = {2010},
address = {Lund},
}
```

This book provides signal processing exercises and can with advantage be used together with the text book Signal Processing by Fredrik Gustafsson, Lennart Ljung and Mille Millnert. The chapters of the books are aligned, which means that there are matching exercises to each theory chapter. The first part of the book treats classical digital signal processing based on transforms and filters, while model based digital processing is in focus in the second part. Some exercises are more theoretical and solved by hand, while others are intended for Matlab on a computer. The book material is inspired by real problems, and so are the exercises. This is emphasized by the use of data sets, both simulated and real. Most exercises have complete solutions, and a section with hints provides guidance to some exercises. Selected exercises also result in a Matlab function corresponding to specific signal processing algorithms. These functions are used to solve other exercises. Thereby, the reader gradually build up a signal processing toolbox during the studies of the material. The book homepage contains more information and links to access the matlab functions, data sets and examples used in the book. Main book Signal Processing

```
@book{diva2:488914,
author = {Gunnarsson, Fredrik and Gustafsson, Fredrik and Tjärnström, Fredrik},
title = {{Signal processing:
exercises}},
publisher = {Studentlitteratur},
year = {2010},
address = {Lund},
}
```

This book provides signal processing exercises and can with advantage be used together with the text book Signal Processing by Fredrik Gustafsson, Lennart Ljung and Mille Millnert. The chapters of the books are aligned, which means that there are matching exercises to each theory chapter. The first part of the book treats classical digital signal processing based on transforms and filters, while model based digital processing is in focus in the second part. Some exercises are more theoretical and solved by hand, while others are intended for Matlab on a computer. The book material is inspired by real problems, and so are the exercises. This is emphasized by the use of data sets, both simulated and real. Most exercises have complete solutions, and a section with hints provides guidance to some exercises. Selected exercises also result in a Matlab function corresponding to specific signal processing algorithms. These functions are used to solve other exercises. Thereby, the reader gradually build up a signal processing toolbox during the studies of the material. The book homepage contains more information and links to access the matlab functions, data sets and examples used in the book. Main book Signal Processing

```
@book{diva2:488887,
author = {Gustafsson, Fredrik and Ljung, Lennart and Millnert, Mille},
title = {{Signal processing}},
publisher = {Studentlitteratur},
year = {2010},
address = {Lund},
}
```

## Book chapters

In this chapter parallel implementations of hybrid MPC will be discussed. Different methods for achieving parallelism at different levels of the algorithms will be surveyed. It will be seen that there are many possible ways of obtaining parallelism for hybrid MPC, and it is by no means clear which possibilities that should be utilized to achieve the best possible performance. To answer this question is a challenge for future research.

```
@incollection{diva2:709563,
author = {Axehill, Daniel and Hansson, Anders},
title = {{Parallel implementation of hybrid MPC}},
booktitle = {Distributed Model Predictive Control Made Easy},
year = {2014},
pages = {375--392},
publisher = {Springer Netherlands},
}
```

The performance of all navigation and tracking algorithms for road-bound vehicles can be improved by utilizing the trajectory constraint imposed from the road network. We refer to this approach as road-assisted navigation and tracking. Further, we refer to the process of incorporating the road constraint into the standard filter algorithms by dynamic map matching. Basically, dynamic map matching can be done in three dierent ways: (1) as a virtual measurement, (2) as a state noise constraint, or (3) as a manifold estimation problem where the state space is reduced. Besides this basic choice of approach, we survey the field from various perspectives: which filter that is applied, which dynamic model that is used to describe the motion of the vehicle, and which sensors that are used and their corresponding sensor models. Various applications using real data are presented as illustrations.

```
@incollection{diva2:489649,
author = {Gustafsson, Fredrik and Orguner, Umut and Schön, Thomas B. and Skoglar, Per and Karlsson, G Rickard},
title = {{Navigation and Tracking of Road-Bound Vehicles}},
booktitle = {Handbook of Intelligent Vehicles},
year = {2012},
publisher = {Springer},
address = {London},
}
```

In this chapter the achievements of the COFCLUO project are summarized. The possible exploitation of the results is discussed. Finally, directions for future research are given.

```
@incollection{diva2:482326,
author = {Hansson, Anders and Menard, Philippe},
title = {{Concluding Remarks and Industrial Perspective}},
booktitle = {Optimization Based Clearance of Flight Control Laws},
year = {2012},
pages = {359--365},
publisher = {Springer Berlin/Heidelberg},
}
```

Results for stability analysis of the nonlinear rigid aircraft model and comfort and loads analysis of the integral aircraft model are presented in this chapter. The analysis is based on the theory for integral quadratic constraints and relies on linear fractional representations (LFRs) of the underlying closed-loop aircraft models. To alleviate the high computational demands associated with the usage of IQC based analysis to large order LFRs, two approaches have been employed aiming a trade-off between computational complexity and conservatism. First, the partitioning of the flight envelope in several smaller regions allows to use lower order LFRs in the analysis, and second, IQCs with lower computational demands have been used whenever possible. The obtained results illustrate the applicability of the IQCs based analysis techniques to solve highly complex analysis problems with an acceptable level of conservativeness.

```
@incollection{diva2:482319,
author = {Wallin, Ragnar and Khoshfetrat Pakazad, Sina and Hansson, Anders and Garuli, Andrea and Masi, Alfio},
title = {{Applications of IQC-Based Analysis Techniques for Clearance}},
booktitle = {Optimization Based Clearance of Flight Control Laws},
year = {2012},
pages = {277--297},
publisher = {Springer Berlin/Heidelberg},
}
```

This chapter presents the use of Integral Quadratic Constraints (IQCs) for solving flight control clearance problems. The theory of IQCs provides a powerful framework for the robustness analysis of control systems with respect to a very broad range of uncertainties and nonlinearities. The clearance criterion of robust stability with respect to parameter variations is addressed by employing the standard robust stability theorem of IQCs and by a suitable choice of an IQC for real parametric uncertainty. In addition, we use IQCs to solve two specific flight control clearance problems which are formulated as robust performance problems with respect to real parameter variations. These problems are the stability margins criterion and the comfort criterion with respect to turbulence which are formulated as robust H∞ and H2 problems respectively. The formulation of a flight control clearance problem using IQCs results in a convex optimization problem involving Linear Matrix Inequalities (LMIs) for which there exist efficient, numerical solvers. Even so, there exist limitations related to increased computational complexity in case of optimization problems resulting from the analysis of large systems.

```
@incollection{diva2:482233,
author = {Papageorgiou, Christos and Falkeborn, Rikard and Hansson, Anders},
title = {{IQC-Based Analysis Techniques for Clearance}},
booktitle = {Optimization Based Clearance of Flight Control Laws},
year = {2012},
pages = {179--201},
publisher = {Springer},
}
```

We describe the background and motivation of the research carried out within the COFCLUO project in developing and applying optimization techniques to the clearance of flight control laws for civil aircraft.

```
@incollection{diva2:482225,
author = {Hansson, Anders and Varga, Andreas},
title = {{Introduction}},
booktitle = {Optimization Based Clearance of Flight Control Laws},
year = {2012},
pages = {3--9},
publisher = {Springer Berlin/Heidelberg},
}
```

In this chapter parallel implementations of hybrid MPC will be discussed. Different methods for achieving parallelism at different levels of the algorithms will be surveyed. It will be seen that there are many possible ways of obtaining parallelism for hybrid MPC, and it is by no means clear which possibilities that should be utilized to achieve the best possible performance. To answer this question is a challenge for future research.

```
@incollection{diva2:475600,
author = {Axehill, Daniel and Hansson, Anders},
title = {{Towards Parallel Implementation of Hybrid MPC:
A Survey and Directions for Future Research}},
booktitle = {Distributed Decision Making and Control},
year = {2012},
pages = {313--338},
publisher = {Springer London},
}
```

Situational awareness is of paramount importance in all advanced driver assistance systems. Situational awareness can be split into the tasks of tracking moving vehicles and mapping stationary objects in the immediate surroundings of the vehicle as it moves. This chapter focuses on the map estimation problem. The map is constructed from sensor measurements from radars, lasers and/or cameras, with support from on-board sensors for compensating for the ego-motion.

Four different types of maps are discussed:

Feature-based maps are represented by a set of salient features, such as tree trunks, corners of buildings, lampposts and traffic signs.

Road maps make use of the fact that roads are highly structured, since they are built according to clearly specified road construction standards. This allows relatively simple and powerful models of the road to be employed.

Location-based maps consist of a grid, where the value of each element describes the property of the specific coordinate.

Finally, intensity-based maps can be considered as a continuous version of the location-based maps.

The aim is to provide a self-contained presentation of how these maps can be built from measurements. Real data from Swedish roads are used throughout the chapter to illustrate the methods.

```
@incollection{diva2:452068,
author = {Lundquist, Christian and Schön, Thomas and Gustafsson, Fredrik},
title = {{Situational Awareness and Road Prediction for Trajectory Control Applications}},
booktitle = {Handbook of Intelligent Vehicles},
year = {2012},
pages = {365--396},
publisher = {Springer London},
}
```

In many areas of human endeavor, the systems involved are not available for direct measurement. Instead, by combining mathematical models for a system's evolution with partial observations of its evolving state, we can make reasonable inferences about it. The increasing complexity of the modern world makes this analysis and synthesis of high-volume data an essential feature in many real-world problems. The celebrated Kalman-Bucy filter, designed for linear dynamical systems with linearly structured measurements, is the most famous Bayesian filter. Its generalizations to nonlinear systems and/or observations are collectively referred to as nonlinear filtering (NLF), an extension of the Bayesian framework to the estimation, prediction, and interpolation of nonlinear stochastic dynamics. NLF uses a stochastic model to make inferences about an evolving system and is a theoretically optimal algorithm.The breadth of its applications, firmly established and still emerging, is simply astounding. Early uses such as cryptography, tracking, and guidance were mostly of a military nature. Since then, the scope has exploded. It includes the study of global climate, estimating the state of the economy, identifying tumors using non-invasive methods, and much more.*The Oxford Handbook of Nonlinear Filtering* is the first comprehensive written resource for the subject. It contains classical and recent results and applications, with contributions from 58 authors. Collated into 10 parts, it covers the foundations of nonlinear filtering, connections to stochastic partial differential equations, stability and asymptotic analysis, estimation and control, approximation theory and numerical methods for solving the nonlinear filtering problem (including particle methods). It also contains a part dedicated to the application of nonlinear filtering to several problems in mathematical finance.

```
@incollection{diva2:489524,
author = {Schön, Thomas B. and Gustafsson, Fredrik and Karlsson, Rickard},
title = {{Particle Filter in Practice}},
booktitle = {The Oxford Handbook of Nonlinear Filtering},
year = {2011},
publisher = {Oxford University Press},
address = {Oxford, UK},
}
```

Within the class of nonlinear system models, the so-called *block-oriented models* have gained wide recognition and attention by the system identification and automatic control community. Typically, these models are constructed by joining linear dynamic system blocks with static nonlinear mappings in various forms of interconnection.

```
@incollection{diva2:652078,
author = {Wills, Adrian and Ljung, Lennart},
title = {{Wiener System Identification Using the Maximum Likelihood Method}},
booktitle = {Block-Oriented Nonlinear System Identification},
year = {2010},
pages = {89--110},
publisher = {Springer},
}
```

Block-oriented Nonlinear System Identification deals with an area of research that has been very active since the turn of the millennium. The book makes a pedagogical and cohesive presentation of the methods developed in that time. These include: iterative and over-parameterization techniques; stochastic and frequency approaches; support-vector-machine, subspace, and separable-least-squares methods; blind identification method; bounded-error method; and decoupling inputs approach.The identification methods are presented by authors who have either invented them or contributed significantly to their development. All the important issues e.g., input design, persistent excitation, and consistency analysis, are discussed. The practical relevance of block-oriented models is illustrated through biomedical/physiological system modelling. The book will be of major interest to all those who are concerned with nonlinear system identification whatever their activity areas. This is particularly the case for educators in electrical, mechanical, chemical and biomedical engineering and for practising engineers in process, aeronautic, aerospace, robotics and vehicles control. Block-oriented Nonlinear System Identification serves as a reference for active researchers, new comers, industrial and education practitioners and graduate students alike.

```
@incollection{diva2:378119,
author = {Enqvist, Martin},
title = {{Identification of Block-oriented Systems Using the Invariance Property}},
booktitle = {Block-Oriented Nonlinear System Identification},
year = {2010},
pages = {147--158},
publisher = {Springer London},
}
```

A new type of linear kernel smoother is derived and studied. The smoother, referred to as weight determination by manifold regularization, is the solution to a regularized least squares problem. The regularization avoids overfitting and can be used to express prior knowledge of an underlying smooth function. An interesting property ofthe kernel smoother is that it is well suited for systems govern by the semi-supervised smoothness assumption. Several examples are given to illustrate this property. We also discuss why these types of techniques can have a potential interest for the system identification community.

```
@incollection{diva2:360031,
author = {Ohlsson, Henrik and Ljung, Lennart},
title = {{Weight Determination by Manifold Regularization}},
booktitle = {Distributed Decision-Making and Control},
year = {2010},
pages = {195--214},
publisher = {Springer London},
}
```

## Conference papers

This paper proposes batch and sequential data-driven approaches to anomaly detection based on generalized likelihood ratio tests for a bias change. The procedure is divided into two steps. Assuming availability of a nominal dataset, a nonparametric density estimate is obtained in the first step, prior to the test. Second, the unknown bias change is estimated from test data. Based on the expectation maximization (EM) algorithm, batch and sequential maximum likelihood estimators of the bias change are derived for the case where the densit yestimate is given by a Gaussian mixture. Approximate asymptotic expressions for the probabilities of error are suggested based on available results. Simulations and real world experiments illustrate the approach.

```
@inproceedings{diva2:737667,
author = {Carvalho Bittencourt, Andr\'{e} and Schön, Thomas},
title = {{Data-Driven Anomaly Detection based on a Bias Change}},
booktitle = {In Proceedings of the 19th IFAC World Congress},
year = {2014},
}
```

Fault detection algorithms (FDAs) process data to generate a test quantity. Test quantities are used to determine presence of a fault in a monitored system, despite disturbances. Because only limited knowledge of the system can be embedded in an FDA, it is important to evaluate it in scenarios relevant in practice. In this paper, simulation based approaches are proposed in an attempt to determine: i) which disturbances affect the output of an FDA the most; ii) how to compare the performance of dierent FDAs; and iii) which combinations of fault change size and disturbances variations are allowed to achieve satisfactory performance. The ideas presented are inspired by the literature of design of experiments, surrogate models, sensitivity analysis and change detection. The approaches are illustrated for the problem of wear diagnosis in manipulators where three FDAs are considered. The application study reveals that disturbances caused by variations in temperature and payload mass error affect the FDAs the most. It is also shown how the size of these disturbances delimit the capacity of an FDA to relate to wear changes. Further comparison of the FDAs reveal which performs "best" in average.

```
@inproceedings{diva2:737661,
author = {Samuelsson, Andreas and Carvalho Bittencourt, Andr\'{e} and Saarinen, Kari and Sander Tavallaey, Shiva and Norrlöf, Mikael and Andersson, Hans and Gunnarsson, Svante},
title = {{Simulation based Evaluation of Fault Detection Algorithms:
Applications to Wear Diagnosis in Manipulators}},
booktitle = {Proceedings of the 19th IFAC World Congress},
year = {2014},
}
```

Before a sensor network can be used for target localization, the locations of the sensors need to be determined. We approach this calibration step by moving a source to distinct positions around the network. At each position, the range to each sensor is measured,and from these range measurements the sensor locations can be estimated by solving a nonlinear least squares (NLS) problem. Here we formulate the NLS problem and describe how to robustly initialize it by the use of multidimensional scaling. The method is evaluated on both simulations and real data from an acoustic sensor network. Withas few as six source positions, a robust calibration is demonstrated that gives a position error about the same size as the range error. In the acoustic example this RMSE is less than 40 cm.

```
@inproceedings{diva2:734113,
author = {Deleskog, Viktor and Habberstad, Hans and Hendeby, Gustaf and Lindgren, David and Wahlström, Niklas},
title = {{Robust NLS Sensor Localization using MDS Initialization}},
booktitle = {17th International Conference on Information Fusion},
year = {2014},
}
```

Nonlinear Kalman filter adaptations such as extended Kalman filters (EKF) or unscented Kalman filters (UKF) provide approximate solutions to state estimation problems in nonlinear models. The algorithms utilize mean values and covariance matrices to represent the probability densities in the otherwise intractable Bayesian filtering equations. As a consequence, their estimation performance can show significant dependence on the choice of state coordinates. The here considered problem of tracking maneuvering targets using coordinated turn (CT) models is one practically relevant example: The velocity in the target state can either be formulated in Cartesian or polar coordinates. We extend a previous study to a broader range of CT models that allow for changes in target speed and turn rate, and investigate UKF as well as EKF variants in terms of their performance and sensitivity to noise parameters. The results advocate for the use of polar CT models.

```
@inproceedings{diva2:734112,
author = {Roth, Michael and Hendeby, Gustaf and Gustafsson, Fredrik},
title = {{EKF/UKF Maneuvering Target Tracking using Coordinated Turn Models with Polar/Cartesian Velocity}},
booktitle = {17th International Conference on Information Fusion},
year = {2014},
}
```

The probabilistic hypothesis density (PHD) filter has grown in popularity during the last decade as a way to address the multi-target tracking problem. Several algorithms exist; for instance under linear-Gaussian assumptions, the Gaussian mixture PHD (GM-PHD) filter. This paper extends the GM-PHD filter to the common case with variable probability of detection throughout the tracking volume. This allows for more efficient utilization, e.g., in situations with distance dependent probability of detection or occluded regions. The proposed method avoids previous algorithmic pitfalls that can result in a not well-defined PHD. The method is illustrated and compared to the standard GM-PHD in a simplified multi-target tracking example as well asin a realistic nonlinear underwater sonar simulation application, both demonstrating the effectiveness of the proposed method.

```
@inproceedings{diva2:734107,
author = {Hendeby, Gustaf and Karlsson, Rickard},
title = {{Gaussian Mixture PHD Filtering with Variable Probability of Detection}},
booktitle = {17th International Conference on Information Fusion},
year = {2014},
}
```

The recent introduction of HDR video cameras has enabled the development of image based lighting techniques for rendering virtual objects illuminated with temporally varying real world illumination. A key challenge in this context is that rendering realistic objects illuminated with video environment maps is computationally demanding. In this work, we present a GPU based rendering system based on the NVIDIA OptiX framework, enabling real time raytracing of scenes illuminated with video environment maps. For this purpose, we explore and compare several Monte Carlo sampling approaches, including bidirectional importance sampling, multiple importance sampling and sequential Monte Carlo samplers. While previous work have focused on synthetic data and overly simple environment maps sequences, we have collected a set of real world dynamic environment map sequences using a state-of-art HDR video camera for evaluation and comparisons.

```
@inproceedings{diva2:726212,
author = {Kronander, Joel and Dahlin, Johan and Jönsson, Daniel and Kok, Manon and Schön, Thomas and Unger, Jonas},
title = {{Real-time video based lighting using GPU raytracing}},
booktitle = {Proceedings of the 22nd European Signal Processing Conference (EUSIPCO), 2014},
year = {2014},
publisher = {IEEE Signal Processing Society},
}
```

The Markov modulated (switching) state space is an importantmodel paradigm in statistical signal processing. In thisarticle, we specifically consider Markov modulated nonlinearstate-space models and address the online Bayesian inferenceproblem for such models. In particular, we propose a newRao-Blackwellized particle filter for the inference task whichis our main contribution here. A detailed description of theproblem and an algorithm is presented.

```
@inproceedings{diva2:723835,
author = {Saha, Saikat and Hendeby, Gustaf},
title = {{Rao-Blackwellized particle filter for Markov modulated nonlineardynamic systems}},
booktitle = {IEEE statistical signal processing workshop (SSP 2014), Gold Coast, Australia, 29 June -- 2 July 2014},
year = {2014},
publisher = {IEEE},
}
```

We consider an application of Bayesian signal processing tothe energy trading problem. In particular, we address theproblem of calibrating the Schwartz-Smith Model using theobserved electricity futures prices traded on the markets. Ascompared with the other financial markets, basic electricityderivatives such as futures are more complicated, as theseproducts are based not on the spot prices themselves but onthe arithmetic averages of the spot prices during the deliveryperiod. As a result, the (log) futures prices are no longeraffine function of the model factors and as such, an approachbased on Kalman filtering, to estimate the latent model factorsand the parameters seems meaningless. Here, we envisagea Bayesian approach using the particle marginal MetropolisHastings (PMMH) algorithm for this challenging estimationtask. We demonstrate the efficacy of our approach on simulateddata.

```
@inproceedings{diva2:723825,
author = {Saha, Saikat},
title = {{Bayesian calibration of the Schwartz-Smith Model adapted to the energy market}},
booktitle = {IEEE statistical signal processing workshop (SSP 2014), Gold Coast, Australia, 29 June -- 2 July 2014},
year = {2014},
pages = {556--559},
publisher = {IEEE},
}
```

```
@inproceedings{diva2:722121,
author = {Axelsson, Patrik and Axehill, Daniel and Glad, Torkel and Norrlöf, Mikael},
title = {{Iterative Learning Control - From a Controllability Point of View}},
booktitle = {Proceedings of Reglermöte 2014},
year = {2014},
}
```

```
@inproceedings{diva2:722012,
author = {Kronander, Joel and Schön, Thomas B. and Dahlin, Johan},
title = {{Backward sequential Monte Carlo for marginal smoothing}},
booktitle = {Proceedings of the 2014 IEEE Statistical Signal Processing Workshop},
year = {2014},
}
```

We propose an extended method for experiment design in nonlinear state space models. The proposed input design technique optimizes a scalar cost function of the information matrix, by computing the optimal stationary probability mass function (pmf) from which an input sequence is sampled. The feasible set of the stationary pmf is a polytope, allowing it to be expressed as a convex combination of its extreme points. The extreme points in the feasible set of pmf’s can be computed using graph theory. Therefore, the final information matrix can be approximated as a convex combination of the information matrices associated with each extreme point. For nonlinear systems, the information matrices for each extreme point can be computed by using particle methods. Numerical examples show that the proposed techniquecan be successfully employed for experiment design in nonlinear systems.

```
@inproceedings{diva2:718421,
author = {Valenzuela, P. E. and Dahlin, Johan and Rojas, C. R. and Schön, Thomas},
title = {{A graph/particle-based method for experiment design in nonlinear systems}},
booktitle = {19th IFAC World Congress, Cape Town, South Africa, August 24-29},
year = {2014},
}
```

We propose a novel method for maximum-likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate the value of the log-likelihood function at the current parameter iterate. Using these log-likelihood estimates, a surrogate objective function is created by utilizing a Gaussian process model. Finally, we use a heuristic procedure to obtain a revised parameter iterate, providing an automatic trade-off between exploration and exploitation of the surrogate model. The method is profiled on two state space models with good performance both considering accuracy and computational cost.

```
@inproceedings{diva2:718418,
author = {Dahlin, Johan and Lindsten, Fredrik},
title = {{Particle filter-based Gaussian process optimisation for parameter inference}},
booktitle = {19th IFAC World Congress, Cape Town, South Africa, August 24-29},
year = {2014},
}
```

_{∞}Synthesis Method for Control of Non-linear Flexible Joint Models", 19th IFAC World Congress, August 24-29, Cape Town, South Africa, 2014.

An H_{∞} synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a convex, yet conservative, LMI problem. The method is motivated by the assumption that the joint operates in a specific stiffness region of the non-linear spring most of the time, hence the performance requirements are only valid in that region. However, the controller must stabilise the system in all stiffness regions. The method is validated in simulations on a non-linear flexible joint model originating from an industrial robot.

```
@inproceedings{diva2:699051,
author = {Axelsson, Patrik and Pipeleers, Goele and Helmersson, Anders and Norrlöf, Mikael},
title = {{H$_{∞}$ Synthesis Method for Control of Non-linear Flexible Joint Models}},
booktitle = {19th IFAC World Congress, August 24-29, Cape Town, South Africa},
year = {2014},
}
```

_{∞}-Controller Design Methods Applied to One Joint of a Flexible Industrial Manipulator", 19th IFAC World Congress, August 24-29, Cape Town, South Africa, 2014.

Control of a flexible joint of an industrial manipulator using H_{∞} design methods is presented. The considered design methods are i) mixed-H_{∞} design, and ii) H_{∞} loop shaping design. Two different controller configurations are examined: one uses only the actuator position, while the other uses the actuator position and the acceleration of end-effector. The four resulting controllers are compared to a standard PID controller where only the actuator position is measured. The choices of the weighting functions are discussed in details. For the loop shaping design method, the acceleration measurement is required to improve the performance compared to the PID controller. For the mixed-H_{∞} method it is enough to have only the actuator position to get an improved performance. Model order reduction of the controllers is briefly discussed, which is important for implementation of the controllers in the robot control system.

```
@inproceedings{diva2:699043,
author = {Axelsson, Patrik and Helmersson, Anders and Norrlöf, Mikael},
title = {{H$_{∞}$-Controller Design Methods Applied to One Joint of a Flexible Industrial Manipulator}},
booktitle = {19th IFAC World Congress, August 24-29, Cape Town, South Africa},
year = {2014},
}
```

```
@inproceedings{diva2:664660,
author = {Heintz, Fredrik and Erlander Klein, Inger},
title = {{The Design of Sweden's First 5-year Computer Science and Software Engineering Program}},
booktitle = {Proceedings of the 45th ACM Technical Symposium on Computer Science Education (SIGCSE 2014)},
year = {2014},
}
```

The Swedish nuclear waste will be stored in copper canisters and kept isolated deep under ground for more than 100,000 years. To ensure reliable sealing of the canisters, friction stir welding is used. To repetitively produce high quality welds, it is vital to use automatic control of the process. This paper introduces a nonlinear model predictive controller for regulating both plunge depth and stir zone temperature, which has not been presented in literature before. Further, a nonlinear process model has been developed and used to evaluate the controller in simulations of the closed loop system. The controller is compared to a decentralized solution, and simulation results indicate that it is possible to achieve higher control performance using the nonlinear model predictive controller.

```
@inproceedings{diva2:714054,
author = {Nielsen, Isak and Garpinger, Olof and Cederqvist, Lars},
title = {{Simulation based Evaluation of a Nonlinear Model Predictive Controller for Friction Stir Welding of Nuclear Waste Canisters}},
booktitle = {2013 European Control Conference (ECC), July 17-19, 2013. Zurich, Switzerland.},
year = {2013},
series = {CONTROL CONFERENCE. EUROPEAN. 2013},
volume = {ECC 2013},
pages = {2074--2079},
publisher = {Institute of Electrical and Electronics Engineers ( IEEE )},
}
```

A Wiener model is a fairly simple, well known, and often used nonlinear block- oriented black-box model. A possible generalization of the class of Wiener models lies in the parallel Wiener model class. This paper presents a method to estimate the linear time-invariant blocks of such parallel Wiener models from input/output data only. The proposed estimation method combines the knowledge obtained by estimating the best linear approximation of a nonlinear system with the MAVE dimension reduction method to estimate the linear time- invariant blocks present in the model. The estimation of the static nonlinearity boils down to a standard static nonlinearity estimation problem starting from input-output data once the linear blocks are known.

```
@inproceedings{diva2:694125,
author = {Schoukens, Maarten and Lyzell, Christian and Enqvist, Martin},
title = {{Combining the best linear approximation and dimension reduction to identify the linear blocks of parallel Wiener systems}},
booktitle = {Proceedings of the 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing},
year = {2013},
pages = {372--377},
}
```

The performance and design of lateral stability systems in cars depend on the ratio between the height of the center of gravity and the wheel base. This ratio is car specific, but a roof load can affect this and decrease the stability margins. We investigate the use of vehicle roll dynamics to detect and estimate changes in the overall sprung mass as well as the load positioned on the roof. It is assumed that the vehicle is equipped with a lateral accelerometer and a roll gyro, and a second order physical model is derived. The parameters in this model are partly unknown, and here estimated with a greybox and an ARMAX approach. The changes in load distribution can be detected and the approach is supported by experimental data in a lab environment.

```
@inproceedings{diva2:694119,
author = {Sadeghi Reineh, Maryam and Enqvist, Martin and Gustafsson, Fredrik},
title = {{Detection of Roof Load for Automotive Safety Systems}},
booktitle = {Proceedings of the 52nd IEEE Conference on Decision and Control},
year = {2013},
pages = {2840--2845},
}
```

This paper considers the problem of how to estimate a model of the inverse of a system. The use of inverse systems can be found in many applications, such as feedforward control and power amplifier predistortion. The inverse model is here estimated with the purpose of using it in cascade with the system itself, as an inverter. A good inverse model in this setting would be one that, when used in series with the original system, reconstructs the original input. The goal here is to select suitable inputs, experimental conditions and loss functions to obtain a good input estimate. Both linear and nonlinear systems will be discussed.

For nonlinear systems, one way to obtain a linearizing prefilter is by Hirschorn’s algorithm. It is here shown how to extend this to the postdistortion case, and some formulations of how the pre- or postinverter could be estimated are also presented.

```
@inproceedings{diva2:694102,
author = {Jung, Ylva and Enqvist, Martin},
title = {{Estimating models of inverse systems}},
booktitle = {Proceedings of the 52nd IEEE Conference on Decision and Control},
year = {2013},
pages = {7143--7148},
}
```

We study the sequential identification problem for Bates stochastic volatility model, which is widely used as the model of a stock in finance. By using the exact simulation method, a particle filter for estimating stochastic volatility is constructed. The systems parameters are sequentially estimated with the aid of parallel filtering algorithm. To improve the estimation performance for unknown parameters, the new resampling procedure is proposed. Simulation studies for checking the feasibility of the developed scheme are demonstrated.

```
@inproceedings{diva2:693549,
author = {Aihara, Shin Ichi and Bagchi, Arunabha and Saha, Saikat},
title = {{Adaptive Filtering for Stochastic Volatility by Using Exact Sampling}},
booktitle = {10th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2013)},
year = {2013},
pages = {326--335},
}
```

The Bayesian Cramer Rao Bound (BCRB) is derived for nonlinear state space models with dependent process and measurement noise processes. It generalizes the previously BCRB for the case of dependent noise. Two different dependence structures appearing in literature are considered, leading to two different recursions for BCRB. The special cases of Gaussian noise, and linear models are presented separately. Simulations demonstrate that correct treatment of dependencies is important for both filtering algorithms and the BCRB.

```
@inproceedings{diva2:693539,
author = {Fritsche, Carsten and Saha, Saikat and Gustafsson, Fredrik},
title = {{Bayesian Cramer-Rao Bound for Nonlinear Filtering with Dependent Noise Processes}},
booktitle = {16th International Conference on Information Fusion (FUSION 2013)},
year = {2013},
pages = {797--804},
publisher = {IEEE},
}
```

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning in nonlinear nonparametric state-space models. We place a Gaussian process prior over the transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. However, to enable efficient inference, we marginalize over the dynamics of the model and instead infer directly the joint smoothing distribution through the use of specially tailored Particle Markov Chain Monte Carlo samplers. Once an approximation of the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. We make use of sparse Gaussian process models to greatly reduce the computational complexity of the approach.

```
@inproceedings{diva2:692906,
author = {Frigola, Roger and Lindsten, Fredrik and Schön, Thomas B. and Rasmussen, Carl E.},
title = {{Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC}},
booktitle = {Advances in Neural Information Processing Systems 26},
year = {2013},
}
```

A GM-PHD filter is used for pedestrian tracking in a crowdsurveillance application. The purpose is to keep track of thedifferent groups over time as well as to represent the shape ofthe groups and the number of people within the groups. In-put data to the GM-PHD filter are detections using a state ofthe art algorithm applied to video frames from the PETS 2012benchmark data. In a first step, the detections in the framesare converted from image coordinates to world coordinates.This implies that groups can be defined in physical units interms of distance in meters and speed differences in metersper second. The GM-PHD filter is a Bayesian framework thatdoes not form tracks of individuals. Its output is well suitedfor clustering of individuals into groups. The results demon-strate that the GM-PHD filter has the capability of estimatingthe correct number of groups with an accurate representationof their sizes and shapes.

```
@inproceedings{diva2:692900,
author = {Edman, Viktor and Maria, Andersson and Granström, Karl and Gustafsson, Fredrik},
title = {{Pedestrian Group Tracking Using the GM-PHD Filter}},
booktitle = {Proceedings of the 21st European Signal Processing Conference},
year = {2013},
}
```

```
@inproceedings{diva2:692896,
author = {Khoshfetrat Pakazad, Sina and Ohlsson, Henrik and Ljung, Lennart},
title = {{Sparse Control Using Sum-of-norms Regularized Model Predictive Control}},
booktitle = {52nd IEEE Conference on Decision and Control (CDC 2013), 10-13 December 2013, Firenze, Italy},
year = {2013},
publisher = {IEEE conference proceedings},
}
```

We consider a class of convex feasibility problems where the constraints that describe the feasible set are loosely coupled. These problems arise in robust stability analysis of large, weakly interconnected uncertain systems. To facilitate distributed implementation of robust stability analysis of such systems, we describe two algorithms based on decomposition and simultaneous projections. The first algorithm is a nonlinear variant of Cimmino's mean projection algorithm, but by taking the structure of the constraints into account, we can obtain a faster rate of convergence. The second algorithm is devised by applying the alternating direction method of multipliers to a convex minimization reformulation of the convex feasibility problem. We use numerical results to show that both algorithms require far less iterations than the accelerated nonlinear Cimmino algorithm.

```
@inproceedings{diva2:692893,
author = {Khoshfetrat Pakazad, Sina and S. Andersen, Martin and Hansson, Anders and Rantzer, Anders},
title = {{Decomposition and Projection Methods for Distributed Robustness Analysis of Interconnected Uncertain Systems}},
booktitle = {13th IFAC Symposium on Large Scale Complex Systems: Theory and Applications},
year = {2013},
pages = {194--199},
}
```

In optimization algorithms used for on-line Model Predictive Control (MPC), the main computational effort is spent while solving linear systems of equations to obtain search directions. Hence, it is of greatest interest to solve them efficiently, which commonly is performed using Riccati recursions or generic sparsity exploiting algorithms. The focus in this work is efficient search direction computation for active-set methods. In these methods, the system of equations to be solved in each iteration is only changed by a low-rank modification of the previous one. This highly structured change of the system of equations from one iteration to the next one is an important ingredient in the performance of active-set solvers. It seems very appealing to try to make a structured update of the Riccati factorization, which has not been presented in the literature so far. The main objective of this paper is to present such an algorithm for how to update the Riccati factorization in a structured way in an active-set solver. The result of the work is that the computational complexity of the step direction computation can be significantly reduced for problems with bound constraints on the control signal. This in turn has important implications for the computational performance of active-set solvers used for linear, nonlinear as well as hybrid MPC.

```
@inproceedings{diva2:689259,
author = {Nielsen, Isak and Ankelhed, Daniel and Axehill, Daniel},
title = {{Low-rank Modifications of Riccati Factorizations with Applications to Model Predictive Control}},
booktitle = {Proceedings of 52nd IEEE Conference on Decision and Control},
year = {2013},
pages = {3684--3690},
publisher = {IEEE conference proceedings},
}
```

An estimation-based iterative learning control (ILC) algorithm is applied to a realistic industrial manipulator model. By measuring the acceleration of the end-effector, the arm angular position accuracy is improved when the measurements are fused with motor angle observations. The estimation problem is formulated in a Bayesian estimation framework where three solutions are proposed: one using the extended Kalman filter (EKF), one using the unscented Kalman filter (UKF), and one using the particle filter (PF). The estimates are used in an ILC method to improve the accuracy for following a given reference trajectory. Since the ILC algorithm is repetitive no computational restrictions on the methods apply explicitly. In an extensive Monte Carlo simulation study it is shown that the PF method outperforms the other methods and that the ILC control law is substantially improved using the PF estimate.

```
@inproceedings{diva2:686628,
author = {Axelsson, Patrik and Karlsson, Rickard and Norrlöf, Mikael},
title = {{Estimation-based ILC using Particle Filter with Application to Industrial Manipulators}},
booktitle = {Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
year = {2013},
pages = {1740--1745},
}
```

This paper presents an approach for 6D pose estimation where MEMS inertial measurements are complemented with magnetometer measurements assuming that a model (map) of the magnetic field is known. The resulting estimation problem is solved using a Rao-Blackwellized particle filter. In our experimental study the magnetic field is generated by a magnetic coil giving rise to a magnetic field that we can model using analytical expressions. The experimental results show that accurate position estimates can be obtained in the vicinity of the coil, where the magnetic field is strong.

```
@inproceedings{diva2:680123,
author = {Kok, Manon and Wahlström, Niklas and Schön, Thomas and Gustafsson, Fredrik},
title = {{MEMS-based inertial navigation based on a magnetic field map}},
booktitle = {Proceedings of t\emph{he 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}},
year = {2013},
pages = {6466--6470},
}
```

Hösten 2013 startade Linköpings universitet den första civilingenjörsutbildningen i Mjukvaruteknik. Utbildningens mål är att bland annat att ge ett helhetsperspektiv på modern storskalig mjukvaruutveckling, ge en gedigen grund i datavetenskap och computational thinking samt främja entreprenörskap och innovation. Studenternas gensvar har varit över förväntan med över 600 sökande till de 30 platserna varav 134 förstahandssökande. Här presenterar vi programmets vision, mål, designprinciper samt det färdiga programmet. En viktig förebild är ACM/IEEE Computer Science Curricula som precis kommit i en ny uppdaterad version. Tre pedagogiska idéer vi har följt är (1) att använda projektkurser för att integrera teori och praktik samt ge erfarenhet i den vanligaste arbetsformen i näringslivet; (2) att undervisa i flera olika programspråk och flera olika programutvecklingsmetodiker för att ge en plattform att ta till sig det senaste på området; och (3) att införa en programsammanhållande kurs i ingenjörsprofessionalism i årskurs 1–3 som ger studenterna verktyg att reflektera över sitt eget lärande, att jobba i näringslivet samt sin professionella yrkesroll. Artikeln avslutas med en diskussion om viktiga aspekter som computational thinking och ACM/IEEE CS Curricula.

```
@inproceedings{diva2:664659,
author = {Heintz, Fredrik and Erlander Klein, Inger},
title = {{Civilingenjör i Mjukvaruteknik vid Linköpings universitet:
mål, design och erfarenheter}},
booktitle = {Proceedings of 4:de Utvecklingskonferensen för Sveriges ingenjörsutbildningar (UtvSvIng)},
year = {2013},
series = {UMINF},
volume = {13:21},
}
```

```
@inproceedings{diva2:661053,
author = {Ardeshiri, Tohid and Özkan, Emre},
title = {{An adaptive PHD filter for tracking with unknown sensor characteristics}},
booktitle = {Information Fusion (FUSION), 2013 16th International Conference on},
year = {2013},
}
```

Radar micro-Doppler signatures (MDS) of humans are created by movements of body parts, such as legs and arms. MDSs can be used in security applications to detect humans and classify their type and activity. Target association and tracking, which can facilitate the classification, become easier if it is possible to distinguish between human individuals by their MDSs. By this we mean to recognize the same individual in a short time frame but not to establish the identity of the individual. In this paper we perform a statistical experiment in which six test persons are able to distinguish between walking human individuals from their MDSs. From this we conclude that there is information in the MDSs of the humans to distinguish between different individuals, which also can be used by a machine. Based on the results of the best test persons we also discuss features in the MDSs that could be utilized to make this processing possible.

```
@inproceedings{diva2:652529,
author = {Björklund, Svante and Petersson, Henrik and Hendeby, Gustaf},
title = {{On distinguishing between human individuals in micro-Doppler signatures}},
booktitle = {14th International Radar Symposium (IRS)},
year = {2013},
pages = {865--870},
}
```

Physical activity monitoring has recently become an important topic in wearable computing, motivated by e.g. healthcare applications. However, new benchmark results show that the difficulty of the complex classification problems exceeds the potential of existing classifiers. Therefore, this paper proposes the ConfAdaBoost.M1 algorithm. The proposed algorithm is a variant of the AdaBoost.M1 that incorporates well established ideas for confidence based boosting. The method is compared to the most commonly used boosting methods using benchmark datasets from the UCI machine learning repository and it is also evaluated on an activity recognition and an intensity estimation problem, including a large number of physical activities from the recently released PAMAP2 dataset. The presented results indicate that the proposed ConfAdaBoost.M1 algorithm significantly improves the classification performance on most of the evaluated datasets, especially for larger and more complex classification tasks.

```
@inproceedings{diva2:648293,
author = {Reiss, Attila and Hendeby, Gustaf and Stricker, Didier},
title = {{Confidence-based multiclass AdaBoost for physical activity monitoring}},
booktitle = {ISWC '13: Proceedings of the 2013 International Symposium on Wearable Computers},
year = {2013},
pages = {13--20},
}
```

Calibration of ground sensor networks is a complex task in practice. To tackle the problem, we propose an approach based on simultaneous tracking of targets of opportunity and sparse estimation of the bias parameters. The evidence approximation method is used to get a sparse estimate of the bias parameters, and the method is here extended with a novel marginalization step where a state smoother is invoked. A simulation study shows that the non-zero bias parameters are detected and well estimated using only one target of opportunity passing by the network.

```
@inproceedings{diva2:647279,
author = {Syldatk, Marek and Gustafsson, Fredrik},
title = {{Simultaneous Tracking and Sparse Calibration in Ground Sensor Networks using Evidence Approximation}},
booktitle = {The 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 26-31, 2013},
year = {2013},
pages = {3108--3112},
publisher = {IEEE conference proceedings},
}
```

It is well-known that the motion of an acoustic source can be estimated from Doppler shift observations. It ishowever not obvious how to design a sensor network to efficiently deliver the localization service. In this work a rather simplistic motion model is proposed that is aimed at sensor networks with realistic numbers of sensor nodes. It is also described how to efficiently solve the associated least squares optimization problem by Gauss-Newton variable projection techniques, and how to initiate the numerical search from simple features extracted from the observed frequency series. The methods are demonstrated onreal data by determining the distance to a passing propellerdriven aircraft and by localizing an all-terrain vehicle. It is concluded that the processing components included are fairly mature for practical implementations in sensor networks.

```
@inproceedings{diva2:646335,
author = {Lindgren, David and Guldogan, Mehmet B. and Gustafsson, Fredrik and Habberstad, Hans and Hendeby, Gustaf},
title = {{Acoustic Source Localization in a Network of Doppler Shift Sensors}},
booktitle = {16th International Conference on Information Fusion},
year = {2013},
}
```

The monitoring of physical activities under realistic, everyday life conditions - thus while an individual follows his regular daily routine - is usually neglected or even completely ignored. Therefore, this paper investigates the development and evaluation of robust methods for everyday life scenarios, with focus on the task of aerobic activity recognition. Two important aspects of robustness are investigated: dealing with various (unknown) other activities and subject independency. Methods to handle these issues are proposed and compared, a thorough evaluation simulates usual everyday scenarios of the usage of activity recognition applications. Moreover, a new evaluation technique is introduced (leave-one-other-activity-out) to simulate when an activity recognition system is used while performing a previously unknown activity. Through applying the proposed methods it is possible to design a robust physical activity recognition system with the desired generalization characteristic.

```
@inproceedings{diva2:646275,
author = {Reiss, Attila and Hendeby, Gustaf and Stricker, Didier},
title = {{Towards Robust Activity Recognition for Everyday Life:
Methods and Evaluation}},
booktitle = {7th International Conference on Pervasive Computing Technologies for Healthcare (PervasiveHealth), 2013},
year = {2013},
pages = {25--32},
publisher = {IEEE},
}
```

This paper describes a competitive approach developed for an activity recognition challenge. The competition was defined on a new and publicly available dataset of human activities, recorded with smartphone sensors. This work investigates different feature sets for the activity recognition task of the competition. Moreover, the focus is also on the introduction of a new, confidence-based boosting algorithm called ConfAda- Boost.M1. Results show that the new classification method outperforms commonly used classifiers, such as decision trees or AdaBoost.M1.

```
@inproceedings{diva2:646274,
author = {Reiss, Attila and Hendeby, Gustaf and Stricker, Didier},
title = {{A Competitive Approach for Human Activity Recognition on Smartphones}},
booktitle = {ESANN 2013},
year = {2013},
pages = {455--460},
publisher = {ESANN},
}
```

This paper considers extended targets that have constant extension shapes, but generate measurements whose appearance can change abruptly. The problem is approached using multiple measurement models, where each model corresponds to a measurement appearance mode. Mode transitions are modeled as dependent on the extended target kinematic state, and a multiple model extended target PHD filter is used to handle multiple targets with multiple appearance modes. The extended target tracking is evaluated using real world data where a laser range sensor is used to track multiple bicycles.

```
@inproceedings{diva2:643726,
author = {Granström, Karl and Lundquist, Christian},
title = {{On the Use of Multiple Measurement Models for Extended Target Tracking}},
booktitle = {Proceedings of the 16th International Conference on Information Fusion},
year = {2013},
}
```

Unattended Ground Sensor Networks (UGSN) are be- coming increasingly popular for surveillance and situ- ational awareness applications. Acoustic sensors can be used in UGSN to detect and to classify targets, and these sensors are cost efficient, easy to deploy, and above all, non-jammable since they are passive. An array of acoustic sensors can detect multiple sound sources and determine the direction of arrival (DOA), and the network can deal with the multi-sensor multi- target tracking. This contribution focuses on DOA estimation of wideband sources, such as vehicles. We develop a coherent DOA estimation method by taking advantage of the spatial sparsity of the wideband acous- tic sources as a prior information, as an extension to the recently proposed SPICE method for narrowband sources. The method has been tested on both simulated data and field test data with different vehicles with very good performance compared to other state of the art methods.

```
@inproceedings{diva2:643286,
author = {Mathai, George and Jakobsson, A. and Gustafsson, Fredrik},
title = {{DIRECTION OF ARRIVAL ESTIMATION OF UNKNOWN NUMBER OF WIDEBAND SIGNALS IN UNATTENDED GROUND SENSOR NETWORKS}},
booktitle = {International Conference on Information Fusion 2013},
year = {2013},
pages = {1--6},
}
```

The mainstream approach to identication of linear discrete-time models is givenby parametric Prediction Error Methods (PEM). As a rule, the model complexity is unknownand model order selection (MOS) is a key ingredient of the estimation process. A dierentapproach to linear system identication has been recently proposed where impulse responsesare described in a Bayesian framework as zero-mean Gaussian processes. Their covariances aregiven by the so-called stable spline, TC or DC kernels that encode information on regularityand BIBO stability. In this paper, we show that these new kernel-based techniques lead alsoto a new eective MOS method for PEM. Furthermore, this paves the way to the design ofa new impulse response estimator that combines the regularized approaches and the classicalparametric PEM. Numerical experiments show that the performance of this technique is verysimilar to that of PEM equipped with an oracle which selects the best model order by knowingthe true impulse response.

```
@inproceedings{diva2:643260,
author = {Pillonetto, Gianluigi and Chen, Tianshi and Ljung, Lennart},
title = {{Kernel-based model order selection for linear system identification}},
booktitle = {Proc. 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP13},
year = {2013},
}
```

Estimation of unknown dynamics is what system identication is about and acore problem in adaptive control and adaptive signal processing. It has long been known thatregularization can be quite benecial for general inverse problems of which system identicationis an example. But only recently, partly under the inuence of machine learning, the use ofwell tuned regularization for estimating linear dynamical systems has been investigated moreseriously. In this presentation we review these new results and discuss what they may mean forthe theory and practice of dynamical model estimation in general.

```
@inproceedings{diva2:643258,
author = {Ljung, Lennart and Chen, Tianshi},
title = {{What can regularization offer for estimation of dynamical systems?}},
booktitle = {11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP13},
year = {2013},
publisher = {IFAC},
}
```

System Identification is about estimating models of dynamical systems from measured input-output data. Its traditional foundation is basic statistical techniques, such as maximum likelihood estimation and asymptotic analysis of bias and variance and the like. Maximum likelihood estimation relies on minimization of criterion functions that typically are non-convex, and may cause numerical search problems. Recent interest in identification algorithms has focused on techniques that are centered around convex formulations. This is partly the result of developments in machine learning and statistical learning theory. The development concerns issues of regularization for sparsity and for better tuned bias/variance trade-offs. It also involves the use of subspace methods as well as nuclear norms as proxies to rank constraints. A quite different route to convexity is to use algebraic techniques manipulate the model parameterizations. This article will illustrate all this recent development.

```
@inproceedings{diva2:643255,
author = {Ljung, Lennart and Chen, Tianshi},
title = {{Convexity Issues in System Identification}},
booktitle = {10th IEEE International Conference on Control \& Automation},
year = {2013},
}
```

We consider an indoor tracking system consisting of an inertial measurement unit (IMU) and a camera that detects markers in the environment. There are many camera based tracking systems described in literature and available commercially, and a few of them also has support from IMU. These are based on the best-effort principle, where the performance varies depending on the situation. In contrast to this, we start with a specification of the system performance, and the design isbased on an information theoretic approach, where specific user scenarios are defined. Precise models for the camera and IMU are derived for a fusion filter, and the theoretical Cramér-Rao lower bound and the Kalman filter performance are evaluated. In this study, we focus on examining the camera quality versus the marker density needed to get at least a one mm and one degree accuracy in tracking performance.

```
@inproceedings{diva2:643227,
author = {Nyqvist, Hanna and Gustafsson, Fredrik},
title = {{A High-Performance Tracking System based on Camera and IMU}},
booktitle = {2013 16th International Conference on Information Fusion},
year = {2013},
}
```

Model predictive control (MPC) is one of the most popular advanced control techniques and is used widely in industry. The main drawback with MPC is that it is fairly computationally expensive and this has so far limited its practical use for nonlinear systems.

To reduce the computational burden of nonlinear MPC, Feedback Linearization together with linear MPC has been used successfully to control nonlinear systems. The main drawback is that this results in an optimization problem with nonlinear constraints on the control signal.

In this paper we propose a method to handle the nonlinear constraints that arises using a set of dynamically generated local inner polytopic approximations. The main benefits of the proposed method is guaranteed recursive feasibility and convergence.

```
@inproceedings{diva2:643179,
author = {Simon, Daniel and Löfberg, Johan and Glad, Torkel},
title = {{Nonlinear Model Predictive Control using Feedback Linearization and Local Inner Convex Constraint Approximations}},
booktitle = {Proceedings of the 2013 European Control Conference},
year = {2013},
pages = {2056--2061},
}
```

We consider the filtering problem in linear state space models with heavy tailed process and measurement noise. Our work is based on Student's t distribution, for which we give a number of useful results. The derived filtering algorithm is a generalization of the ubiquitous Kalman filter, and reduces to it as special case. Both Kalman filter and the new algorithm are compared on a challenging tracking example where a maneuvering target is observed in clutter.

```
@inproceedings{diva2:626636,
author = {Roth, Michael and Ozkan, Emre and Gustafsson, Fredrik},
title = {{A student's t filter for heavy tailed process and measurement noise}},
booktitle = {Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
year = {2013},
pages = {5770--5774},
publisher = {IEEE conference proceedings},
}
```

Particle Markov Chain Monte Carlo (PMCMC) samplers allow for routine inference of parameters and states in challenging nonlinear problems. A common choice for the parameter proposal is a simple random walk sampler, which can scale poorly with the number of parameters.

In this paper, we propose to use log-likelihood gradients, i.e. the score, in the construction of the proposal, akin to the Langevin Monte Carlo method, but adapted to the PMCMC framework. This can be thought of as a way to guide a random walk proposal by using drift terms that are proportional to the score function. The method is successfully applied to a stochastic volatility model and the drift term exhibits intuitive behaviour.

```
@inproceedings{diva2:626579,
author = {Dahlin, Johan and Lindsten, Fredrik and Schön, Thomas},
title = {{Particle Metropolis Hastings using Langevin Dynamics}},
booktitle = {Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing},
year = {2013},
pages = {6308--6312},
publisher = {IEEE conference proceedings},
}
```

Particle smoothing is useful for offline state inference and parameter learning in nonlinear/non-Gaussian state-space models. However, many particle smoothers, such as the popular forward filter/backward simulator (FFBS), are plagued by a quadratic computational complexity in the number of particles. One approach to tackle this issue is to use rejection-sampling-based FFBS (RS-FFBS), which asymptotically reaches linear complexity. In practice, however, the constants can be quite large and the actual gain in computational time limited. In this contribution, we develop a hybrid method, governed by an adaptive stopping rule, in order to exploit the benefits, but avoid the drawbacks, of RS-FFBS. The resulting particle smoother is shown in a simulation study to be considerably more computationally efficient than both FFBS and RS-FFBS.

```
@inproceedings{diva2:624920,
author = {Taghavi, Ehsan and Lindsten, Fredrik and Svensson, Lennart and Schön, Thomas B.},
title = {{Adaptive stopping for fast particle smoothing}},
booktitle = {Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
year = {2013},
pages = {6293--6297},
}
```

We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction.

```
@inproceedings{diva2:624911,
author = {Lindsten, Fredrik and Bunch, Pete and Godsill, Simon J. and Schön, Thomas},
title = {{Rao-Blackwellized Particle Smoothers for Mixed Linear/Nonlinear State-Space Models}},
booktitle = {Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing},
year = {2013},
pages = {6288--6292},
publisher = {IEEE conference proceedings},
}
```

I present a novel method for maximum likelihood parameter estimation in nonlinear/non-Gaussian state-space models. It is an expectation maximization (EM) like method, which uses sequential Monte Carlo (SMC) for the intermediate state inference problem. Contrary to existing SMC-based EM algorithms, however, it makes efficient use of the simulated particles through the use of particle Markov chain Monte Carlo (PMCMC) theory. More precisely, the proposed method combines the efficient conditional particle filter with ancestor sampling (CPF-AS) with the stochastic approximation EM (SAEM) algorithm. This results in a procedure which does not rely on asymptotics in the number of particles for convergence, meaning that the method is very computationally competitive. Indeed, the method is evaluated in a simulation study, using a small number of particles with promising results.

```
@inproceedings{diva2:624904,
author = {Lindsten, Fredrik},
title = {{An Efficient Stochastic Approximation EM Algorithm using Conditional Particle Filters}},
booktitle = {Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing},
year = {2013},
pages = {6274--6278},
publisher = {IEEE conference proceedings},
}
```

Optimal estimation problems for general state space models do not typically admit a closed form solution. However, modern Monte Carlo methods have paved the way to solve such complex inference problems. Particle filters (PF) are a popular class of such Monte Carlo based Bayesian algorithms, which solve the estimation problems numerically in a sequential manner.

PF in general, assume a prior knowledge of the (process and observation) noise distributions involving the state space model, whereas the properties of the noise processes are often unknown for many practical problems. Furthermore, the unknown noise distributions may be state dependent or even non-stationary, which prevent the offline noise calibrations.

In this article, the unknown noises are assumed to be slowly varying in time. The article then proposes a hierarchical noise adaptive PF where a two tier PF is run, the top tier PF estimates the latent states from the streaming observations and the bottom tier PF estimates the noise statistics conditioned on the top tier PF output together with the observations. The estimates are statistically fused together for the inference purpose. In essence, it is an implementation of approximate Rao-Blackwellized PF, where the later is achieved through local Monte Carlo integration. This approach is very generic for different noise classes and importantly, it enhances the level of parallelism in PF implementations.

```
@inproceedings{diva2:614373,
author = {Saha, Saikat and Hendeby, Gustaf and Gustafsson, Fredrik},
title = {{Noise Adaptive Particle Filtering:
A Hierarchical Perspective}},
booktitle = {ISBA Regional Meeting and International Workshop/Conference on Bayesian Theory and Applications (IWCBTA), 6-10 January 2013, Varanasi, Uttar Pradesh, India},
year = {2013},
}
```

Starting from the electromagnetic theory, we derive a Bayesian nonparametric model allowing for joint estimation of the magnetic field and the magnetic sources in complex environments. The model is a Gaussian process which exploits the divergence- and curl-free properties of the magnetic field by combining well-known model components in a novel manner. The model is estimated using magnetometer measurements and spatial information implicitly provided by the sensor. The model and the associated estimator are validated on both simulated and real world experimental data producing Bayesian nonparametric maps of magnetized objects.

```
@inproceedings{diva2:606538,
author = {Wahlström, Niklas and Kok, Manon and Schön, Thomas B. and Gustafsson, Fredrik},
title = {{Modeling Magnetic Fields using Gaussian Processes}},
booktitle = {2013 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)},
year = {2013},
pages = {3522--3526},
publisher = {IEEE conference proceedings},
}
```

Many RGB-D sensors, e.g. the Microsoft Kinect, use rolling shutter cameras. Such cameras produce geometrically distorted images when the sensor is moving. To mitigate these rolling shutter distortions we propose a method that uses an attached gyroscope to rectify the depth scans. We also present a simple scheme to calibrate the relative pose and time synchronization between the gyro and a rolling shutter RGB-D sensor. We examine the effectiveness of our rectification scheme by coupling it with the the Kinect Fusion algorithm. By comparing Kinect Fusion models obtained from raw sensor scans and from rectified scans, we demonstrate improvement for three classes of sensor motion: panning motions causes slant distortions, and tilt motions cause vertically elongated or compressed objects. For wobble we also observe a loss of detail, compared to the reconstruction using rectified depth scans. As our method relies on gyroscope readings, the amount of computations required is negligible compared to the cost of running Kinect Fusion.

```
@inproceedings{diva2:603474,
author = {Ovr\'{e}n, Hannes and Forss\'{e}n, Per-Erik and Törnqvist, David},
title = {{Why Would I Want a Gyroscope on my RGB-D Sensor?}},
booktitle = {IEEE Workshop on Robot Vision 2013, Clearwater Beach, Florida, USA, January 16-17, 2013},
year = {2013},
}
```

This contribution aims to enrich the recently introduced kernel-based regularization method for linear system identification. Instead of a single kernel, we use multiple kernels, which can be instances of any existing kernels for the impulse response estimation of linear systems. We also introduce a new class of kernels constructed based on output error (OE) model estimates. In this way, a more flexible and richer representation of the kernel is obtained. Due to this representation the associated hyper-parameter estimation problem has two good features. First, it is a difference of convex functions programming (DCP) problem. While it is still nonconvex, it can be transformed into a sequence of convex optimization problems with majorization minimization (MM) algorithms and a local minima can thus be found iteratively. Second, it leads to sparse hyper-parameters and thus sparse multiple kernels. This feature shows the kernel-based regularization method with multiple kernels has the potential to tackle various problems of finding sparse solutions in linear system identification.

```
@inproceedings{diva2:688527,
author = {Chen, Tianshi and Ljung, Lennart and Andersen, Martin and Chiuso, Alessandro and Carli, Francesca and Pillonetto, Gianluigi},
title = {{Sparse multiple kernels for impulse response estimation with majorization minimization algorithms}},
booktitle = {Decision and Control (CDC), 2012},
year = {2012},
pages = {1500--1505},
publisher = {IEEE},
}
```

We present a subspace system identification method based on weighted nuclear norm approximation. The weight matrices used in the nuclear norm minimization are the same weights as used in standard subspace identification methods. We show that the inclusion of the weights improves the performance in terms of fit on validation data. Experimental results from randomly generated examples as well as from the Daisy benchmark collection are reported. The key to an efficient implementation is the use of the alternating direction method of multipliers to solve the optimization problem.

```
@inproceedings{diva2:688522,
author = {Hansson, Anders and Liu, Zhang and Vandenberghe, Lieven},
title = {{Subspace System Identification via Weighted Nuclear Norm Optimization in 2012 IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), vol , issue , pp 3439-3444}},
booktitle = {IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC)},
year = {2012},
pages = {3439--3444},
publisher = {IEEE; 1998},
}
```

[No abstract available]

```
@inproceedings{diva2:665660,
author = {Gustafsson, Fredrik},
title = {{Geolocation: Maps, measurements and methods}},
booktitle = {IET Conference Publications},
year = {2012},
series = {IET Conference Publications},
pages = {1--48},
}
```

In this paper, we analyze the performance of the Gaussian mixture probability hypothesis density (GM-PHD) filter in tracking multiple non-cooperative targets using a passive sensor network. Non-cooperative transmissions from illuminators of opportunity like GSM base stations, FM radio transmitters or digital broadcasters are exploited by non-directional separately located Doppler measuring sensors. Clutter, missed detections and multi-static Doppler variances are incorporated into a realistic multi-target scenario. Simulation results show that the GM-PHD filter successfully tracks multiple targets using only Doppler shift measurements in a passive multi-static scenario.

```
@inproceedings{diva2:665598,
author = {Burak Guldogan, Mehmet and Orguner, Umut and Gustafsson, Fredrik},
title = {{Gaussian mixture PHD filter for multi-target tracking using passive doppler-only measurements}},
booktitle = {IET Conference Publications},
year = {2012},
series = {IET Conference Publications},
pages = {1--6},
publisher = {IEEE conference proceedings},
}
```

```
@inproceedings{diva2:661056,
author = {Ardeshiri, Tohid and Orguner, Umut and Lundquist, Christian and Schön, Thomas},
title = {{On mixture reduction for multiple target tracking}},
booktitle = {Information Fusion (FUSION), 2012 15th International Conference on},
year = {2012},
}
```

We compare dead-reckoning of underwater vehicles based on inertial sensors and kinematic models on one hand, and control inputs and hydrodynamic model on the other hand. Both can be used in an inertial navigation system to provide relative motion and absolute orientation of the vehicle. The combination of them is particularly useful for robust navigation in the case of missing data from the crucial doppler log speedometer. As a concrete result, we demonstrate that the performance critical doppler log can be replaced with longitudinal dynamics in the case of missing data, based on field test data of a remotely operated vehicle.

```
@inproceedings{diva2:647988,
author = {Skoglund, Martin A. and Jönsson, Kenny and Fredrik, Gustafsson},
title = {{Modeling and Sensor Fusion of a Remotely Operated Underwater Vehicle}},
booktitle = {Proceedings of the 15th International Conference on Information Fusion (FUSION), 2012},
year = {2012},
pages = {947--954},
publisher = {IEEE},
}
```

Target tracking in ground sensor networks requires an accurate calibration of sensor positions and orientations, as well as sensor offsets and scale errors. We present a calibration algorithm based on the EM (expectation maximization) algorithm, where the particle filter is used for target tracking and a non-linear least squares estimator is used for estimation of the calibration parameters. The proposed algorithm is very simple to use in practice, since no ground truth of the target position and time synchronization are needed. In that way, opportunistic targets can also be used for calibration. For road-bound targets, a road-constrained particle filter is used to increase the performance. Tests on real data shows that a sensor position accuracy of a couple of meters is obtained from only one passing target.

```
@inproceedings{diva2:643465,
author = {Syldatk, Marek and Gustafsson, Fredrik and Sviestins, Egils},
title = {{Expectation Maximization Algorithm for Calibration of Ground Sensor Networks using a Road Constrained Particle Filter}},
booktitle = {15th International Conference on Information Fusion (FUSION), 2012},
year = {2012},
pages = {771--778},
publisher = {IEEE},
}
```

Many extremist groups and terrorists use the Web for various purposes such as exchanging and reinforcing their beliefs, making monitoring and analysis of discussion boards an important task for intelligence analysts in order to detect individuals that might pose a threat towards society. In this work we focus on how to automatically analyze discussion boards in an effective manner. More specifically, we propose a method for fusing several alias (entity) matching techniques, that can be used to identify authors with multiple aliases. This is one part of a larger system, where the aim is to provide the analyst with a list of potential extremist worth investigating further.

```
@inproceedings{diva2:642357,
author = {Dahlin, Johan and Johansson, Fredrik and Kaati, Lisa and Martenson, Christian and Svenson, Pontus},
title = {{Combining Entity Matching Techniques for Detecting Extremist Behavior on Discussion Boards}},
booktitle = {Advances in Social Networks Analysis and Mining (ASONAM), 2012},
year = {2012},
pages = {850--857},
publisher = {IEEE},
}
```

FIR (finite impulse response) model is widely used in tackling the problem of the impulse response estimation with quantized measurements. Its use is, however, limited, in the case when a high order FIR model is required to capture a slowly decaying impulse response. This is because the high variance for high order FIR models would override the low bias and thus lead to large MSE (mean square error). In this contribution, we apply the recently introduced regularized FIR model approach to the problem of the impulse response estimation with binary measurements. We show by Monte Carlo simulations that the proposed approach can yield both better accuracy and better robustness than a recently introduced FIR model based approach.

```
@inproceedings{diva2:636489,
author = {Chen, Tianshi and Ljung, Lennart and Zhao, Yanlong},
title = {{Impulse Response Estimation with Binary Measurements:
A Regularized FIR Model}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {113--118},
}
```

Version 8.0 of MATLAB's System Identification toolbox is released with version R2012a of MATLAB in the spring of 2012. This release presents a re-engineered implementation of the code using the new MATLAB object-oriented programming. Two main features are (1) that the toolbox commands and plots are seamlessly integrated with the other MATLAB toolboxes that deal with linear dynamic systems and (2) several new features and model objects. The toolbox now supports multi-input--multi-output (MIMO) systems across all model objects, and more emphasis is placed on continuous-time models. Also a new model object, IDTF covers MIMO transfer function models in both continuous and discrete time.

```
@inproceedings{diva2:636485,
author = {Ljung, Lennart and Singh, Rajiv},
title = {{Version 8 of the MatLab System Identification Toolbox}},
booktitle = {Proceedings of the 16th IFAC Symposium on Sytem Identification},
year = {2012},
pages = {1826--1831},
}
```

In the presence of frequent inlet flow upsets, tuning of averaging level controllers is typically quite complicated since not only the size of the individual steps but also the time in between the subsequent steps need to considered. One structured way to achieve optimal filtering for such a case is to use Robust Model Predictive Control. The robust MPC controller is, however, quite computationally demanding and not easy to implement. In this paper two linear controllers, which mimic the behavior of the robust MPC, are proposed. Tuning guidelines to avoid violation of the tank level constraints as well as to achieve optimal filtering are presented.

```
@inproceedings{diva2:636479,
author = {Rosander, Peter and Isaksson, Alf and Löfberg, Johan and Forsman, Krister},
title = {{Practical Control of Surge Tanks Suﬀering from Frequent Inlet Flow Upsets}},
booktitle = {Proceedings of the 2nd IFAC Conference on Advances in PID Control},
year = {2012},
pages = {258--263},
}
```

Frequent inlet ﬂow changes, especially in the same direction, typically cause problems for averaging level controllers. To obtain optimal ﬂow ﬁltering while being robust towards future inlet ﬂow upsets closed loop robust MPC was used. Its performance and robustness is analyzed and compared to the optimal averaging level controller. The knowledge gained from the robust MPC exercise is also used to propose a robustiﬁcation of the optimal controller. Both the analysis and the simulation results show that the robust controller obtains comparable ﬂow ﬁltering as the optimal controller even when inlet ﬂow changes are sparse while handling frequent upsets considerably better

```
@inproceedings{diva2:636475,
author = {Rosander, Peter and Isaksson, Alf and Löfberg, Johan and Forsman, Krister},
title = {{Performance Analysis of Robust Averaging Level Control}},
booktitle = {Proceedings of the 2012 Conference on Chemical Process Control},
year = {2012},
}
```

Support processes in industrial energy systems, such as heating, ventilation and cooling systems, are important processes in industrial premises as they are related to energy cost, product quality as well as the indoor environment.

In the vehicle production process the paint shop is the most energy intensive part, and about 75% of the energy is used in the ovens and spray booths. The spray booth line, which includes paint application and the oven, uses large quantities of air in order to keep the air quality in an optimal range to achieve the desired paint quality. The approach used in paint shops has up to now been to keep as much of steady state conditions as possible to avoid paint defects due to disturbances in the balance. This means that these high air flows are used also at low and non production hours. There is thus a large potential to increase energy efficiency by controlling the air flow and heating without losing the critical balances. This paper will present an initial post-implementation evaluation of the energy efficiency potential and experiences after running this type of system. CFD has been used to investigate the control strategy.

```
@inproceedings{diva2:628477,
author = {Rohdin, Patrik and Johansson, Magnus and Löfberg, Johan and Ottosson, Mattias},
title = {{Energy efficient process ventilation in paint shops in the car industry:
experiences and an evaluation of a full scale implementation at Saab Automobile in Sweden}},
booktitle = {The 10th International Conference on Industrial Ventilation, Paris, France, 17-19 September 2012},
year = {2012},
}
```

The estimation of nonlinear models can be a challenging problem, in particular when the number of available data points is small or when the dimension of the regressor space is high. To meet these challenges, several dimension reduction methods have been proposed in the literature, where a majority of the methods are based on the framework of inverse regression. This allows for the use of standard tools when analyzing the statistical properties of an approach and often enables computationally efficient implementations. The main limitation of the inverse regression approach to dimension reduction is the dependence on a design criterion which restricts the possible distributions of the regressors. This limitation can be avoided by using a forward approach, which will be the topic of this paper. One drawback with the forward approach to dimension reduction is the need to solve nonconvex optimization problems. In this paper, a reformulation of a well established dimension reduction method is presented, which reveals the structure of the optimization problem, and a convex relaxation is derived.

```
@inproceedings{diva2:623916,
author = {Lyzell, Christian and Andersen, Martin and Enqvist, Martin},
title = {{A Convex Relaxation of a Dimension Reduction Problem using the Nuclear Norm}},
booktitle = {Proceedings of the 51st IEEE Conference on Decision and Control},
year = {2012},
pages = {2852--2857},
}
```

The concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like *sliced inverse regression* (SIR) and *directional regression* (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear dynamical systems will be discussed. In particular, it will be shown that the inverse regression methods can be used for identification of systems of the Wiener class, that is, systems consisting of a number of parallel linear subsystems followed by a static multiple-input single-output nonlinearity. For a particular class of input signals, including Gaussian signals, the inverse regression approach makes it possible to estimate the linear subsystems without knowing or estimating the nonlinearity.

```
@inproceedings{diva2:623906,
author = {Lyzell, Christian and Enqvist, Martin},
title = {{Inverse Regression for the Wiener Class of Systems}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {476--481},
}
```

The estimation of nonlinear functions can be challenging when the number of independent variables is high. This difficulty may, in certain cases, be reduced by first projecting the independent variables on a lower dimensional subspace before estimating the nonlinearity. In this paper, a statistical nonparametric dimension reduction method called *sliced inverse regression* is presented and a consistency analysis for dynamically dependent variables is given. The straightforward system identification application is the estimation of the number of linear subsystems in a Wiener class system and their corresponding impulse response.

```
@inproceedings{diva2:623903,
author = {Lyzell, Christian and Enqvist, Martin},
title = {{Sliced Inverse Regression for the Identification of Dynamical Systems}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {1575--1580},
}
```

Here we deal with the choice of the sampling rate in nonlinear system identification applications. In particular, we focus on the effect of the sampling rate when the prediction-error method is used. On one hand, a high sampling rate is advantageous since it enables the measurement of high-frequent nonlinear components in the output signal of the system without aliasing. However, a high sampling rate might also make it harder to realize that the system is nonlinear, since the nonlinearities cannot be detected in the residuals from a linear model in some cases. Here, this phenomenon is illustrated in a couple of numerical examples and a way to avoid it is proposed.

```
@inproceedings{diva2:623899,
author = {Escobar, Jesica and Enqvist, Martin},
title = {{On the Detection of Nonlinearities in Sampled Data}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {1587--1592},
}
```

Performing tests on complicated systems can be very expensive and having a good model that describes the true system well can significantly reduce cost. This is certainly true for testing of a highly maneuverable fighter aircraft. A real-time method could be useful during testing to help in the decision process for safety reasons and for monitoring the amount of excitation in the collected data, and thus making good post-flight model identification possible. Here, an existing frequency domain method is described and improvements, using the correct finite Fourier transformation of the system equations together with an Instrumental Variable approach to handle atmospheric turbulence as system noise, are suggested. Results from simulations as well as real flight tests are presented.

```
@inproceedings{diva2:623871,
author = {Larsson, Roger and Enqvist, Martin},
title = {{Sequential Aerodynamic Model Parameter Identification}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {1413--1418},
}
```

This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.

```
@inproceedings{diva2:614859,
author = {Andersen, Martin and Hansson, Anders and Khoshfetrat Pakazad, Sina and Rantzer, Anders},
title = {{Distributed Robust Stability Analysis of Interconnected Uncertain Systems}},
booktitle = {Proceedings of the 51st IEEE Conference on Decision and Control},
year = {2012},
pages = {1548--1553},
}
```

A common assumption when proving stability of linear MPC algorithms for tracking applications is to assume that the desired setpoint is located far into the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severely limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modifications that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allows a setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints is used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile fighter aircraft is given.

```
@inproceedings{diva2:608012,
author = {Simon, Daniel and Löfberg, Johan and Glad, Torkel},
title = {{Reference Tracking MPC using Terminal Set Scaling}},
booktitle = {Proceedings of the 51st IEEE Conference on Decision and Control},
year = {2012},
pages = {4543--4548},
publisher = {IEEE conference proceedings},
}
```

State estimation of a flexible industrial manipulator is presented using experimental data. The problem is formulated in a Bayesian framework where the extended Kalman filter and particle filter are used. The filters use the joint positions on the motor side of the gearboxes as well as the acceleration at the end-effector as measurements and estimates the corresponding joint angles on the arm side of the gearboxes. The techniques are verified on a state of the art industrial robot, and it is shown that the use of the acceleration at the end-effector improves the estimates significantly.

```
@inproceedings{diva2:606589,
author = {Axelsson, Patrik and Karlsson, Rickard and Norrlöf, Mikael},
title = {{Bayesian Methods for Estimating Tool Position of an Industrial Manipulator}},
booktitle = {Proceedings of Reglermöte 2012},
year = {2012},
}
```

Change detection has traditionally been seen as a centralized problem. Many change detection problems are however distributed in nature and the need for distributed change detection algorithms is therefore significant. In this paper a distributed change detection algorithm is proposed. The change detection problem is first formulated as a convex optimization problem and then solved distributively with the alternating direction method of multipliers (ADMM). To further reduce the computational burden on each sensor, a homotopy solution is also derived. The proposed method have interesting connections with Lasso and compressed sensing and the theory developed for these methods are therefore directly applicable.

```
@inproceedings{diva2:606307,
author = {Ohlsson, Henrik and Chen, Tianshi and Khoshfetrat Pakazad, Sina and Ljung, Lennart and Sastry, Shankar},
title = {{Distributed Change Detection}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {77--82},
}
```

We present a novel identification framework that enables the use of first-order methods when estimating model parameters near a periodic orbit of a hybrid dynamical system. The proposed method reduces the space of initial conditions to a smooth manifold that contains the hybrid dynamics near the periodic orbit while maintaining the parametric dependence of the original hybrid model. First-order methods apply on this subsystem to minimize average prediction error, thus identifying parameters for the original hybrid system. We implement the technique and provide simulation results for a hybrid model relevant to terrestrial locomotion.

```
@inproceedings{diva2:606306,
author = {Burden, Sam and Ohlsson, Henrik and Sastry, Shankar},
title = {{Parameter Identification Near Periodic Orbits of Hybrid Dynamical Systems}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {1197--1202},
}
```

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear program, namely, l1-minimization, guarantees recovery of sparse parameter signals even when the system is underdetermined. In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted. Using a lifting technique, we show that even though the phase information is missing, the sparse signal can be recovered exactly by solving a semidefinite program when the sampling rate is sufficiently high. This is an interesting finding since the exact solutions to both sparse signal recovery and phase retrieval are combinatorial. The results extend the type of applications that compressive sensing can be applied to those where only output magnitudes can be observed. We demonstrate the accuracy of the algorithms through extensive simulation and a practical experiment.

```
@inproceedings{diva2:606304,
author = {Ohlsson, Henrik and Yang, Allen and Dong, Roy and Sastry, Shankar},
title = {{Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {89--94},
}
```

While compressive sensing (CS) has been one of the most vibrant research fields in the past few years, most development only applies to linear models. This limits its application in many areas where CS could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique – CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation.

```
@inproceedings{diva2:606301,
author = {Ohlsson, Henrik and Yang, Allen and Dong, Roy and Sastry, Shankar},
title = {{CPRL:
An Extension of Compressive Sensing to the Phase Retrieval Problem}},
booktitle = {Proceedings of the 26th Conference on Advances in Neural Information Processing Systems},
year = {2012},
pages = {1376--1384},
}
```

In this paper, multi-objective optimization is applied to the hot rolling process. It is modeled mostly using first principle models considering, for instance, the mass balance (or mass flow rate), the tensions in the material, the power requirements, the thermal field, and the microstructure of the material.

Two optimization formulations are considered. In the first case, both the grain size and the power consumption in the rolling process are minimized. It is shown that the result from a single-objective optimization formulation, i.e., where only one of the two objectives are considered, yields control schedules with poor performance for the other objective. Furthermore, the differences between optimal control schedules for different objectives are compared and analyzed. The second case is a design optimization problem where the optimal positioning of cooling pipes is considered. This study shows how the MOO framework can be used to systematically choose a good cooling pipe setup.

The two studies shows that MOO can be a helpful tool when designing and running hot rolling processes. Furthermore, navigation among the Pareto optimal solutions is very useful when the user wants to learn how the control variables interact with the process.

```
@inproceedings{diva2:606277,
author = {Sjöberg, Johan and Lindkvist, Simon and Linder, Jonas and Daneryd, Anders},
title = {{Interactive Multiobjective Optimization for the Hot Rolling Process}},
booktitle = {Proceedings of 51st IEEE Conference on Decision and Control\emph{}},
year = {2012},
pages = {7030--7036},
}
```

Many studies in target localization and tracking use GPS measurements as ground truth. These GPS locations might be in conflict with computed estimates in applications where road network information is available (and employed in the estimation procedure). This paper proposes to use particle methods to generate on-road trajectories that can be used as improved ground truth for such road constrained estimation schemes. A bootstrap particle filter and three different particle smoothers are utilized to obtain kinematic target state estimates. The particle smoothers require important adjustments for their implementation in the resulting hybrid state space. The performances of the presented methods are compared on challenging real data obtained from an urban area.

Although particle filters and smoothers can be applied to general localization problems, with arbitrary sensors, we concentrate on GPS measurements, motivated by an application in cellular network systems.

```
@inproceedings{diva2:606190,
author = {Roth, Michael and Gustafsson, Fredrik and Orguner, Umut},
title = {{On-road Trajectory Generation from GPS Data: A Particle Filtering/Smoothing Application}},
booktitle = {2012 15th International Conference on Information Fusion},
year = {2012},
pages = {779--786},
publisher = {IEEE},
}
```

We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward and backward sweeps as in PG-BS, however, we achieve the same effect in a single forward sweep. We apply the PG-AS framework to the challenging class of non-Markovian state-space models. We develop a truncation strategy of these models that is applicable in principle to any backward-simulation-based method, but which is particularly well suited to the PG-AS framework. In particular, as we show in a simulation study, PG-AS can yield an order-of-magnitude improved accuracy relative to PG-BS due to its robustness to the truncation error. Several application examples are discussed, including Rao-Blackwellized particle smoothing and inference in degenerate state-space models.

```
@inproceedings{diva2:605133,
author = {Lindsten, Fredrik and Jordan, Michael I. and Schön, Thomas},
title = {{Ancestor Sampling for Particle Gibbs}},
booktitle = {Proceedings of the 26th Conference on Neural Information Processing Systems},
year = {2012},
}
```

This paper considers a Bayesian approach to linear system identification. One motivation is the advantage of the minimum mean square error of the associated conditional mean estimate. A further motivation is the error quantifications afforded by the posterior density which are not reliant on asymptotic in data length derivations. To compute these posterior quantities, this paper derives and illustrates a Gibbs sampling approach, which is a randomized algorithm in the family of Markov chain Monte Carlo methods. We provide details on a numerically robust implementation of the Gibbs sampler. In a numerical example, the proposed method is illustrated to give good convergence properties without requiring any user tuning.

```
@inproceedings{diva2:605130,
author = {Wills, Adrian and Schön, Thomas and Lindsten, Fredrik and Ninness, Brett},
title = {{Estimation of Linear Systems using a Gibbs Sampler}},
booktitle = {Proceedings\emph{ of the 16th IFAC Symposium on System Identification}},
year = {2012},
pages = {203--208},
}
```

The theory and the applications of the marginalized particle filter (MPF) have attracted much research attention during the last decade. However, the existing MPF framework does not cover dependent process and measurement noises. This dependency is perhaps more common in practice than is acknowledged in the literature. In this article, we propose a general framework for MPF, covering both cases of dependent and independent noises. As a consequence, MPF with independent noises is a special case of this general framework. The treatment of dependency always provides `extra' information to the state estimation tasks. This beneficial effect is shown through a numerical example.

```
@inproceedings{diva2:589540,
author = {Saha, Saikat and Gustafsson, Fredrik},
title = {{Marginalized Particle Filter for Dependent Gaussian Noise Processes}},
booktitle = {Proceedings of the 2012 IEEE Aerospace Conference},
year = {2012},
}
```

A sensor fusion method for state estimation of a flexible industrial robot is presented. By measuring the acceleration at the end-effector, the accuracy of the arm angular position is improved significantly when these measurements are fused with motor angle observation. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; one using the extended Kalman filter (EKF) and one using the particle filter (PF). The technique is verified on experiments on the ABB IRB4600 robot, where the accelerometer method is showing a significant better dynamic performance, even when model errors are present.

```
@inproceedings{diva2:589538,
author = {Axelsson, Patrik and Karlsson, Rickard and Norrlöf, Mikael},
title = {{Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods}},
booktitle = {Proceedings of the 2012 IEEE International Conference on Robotics and Automation},
year = {2012},
pages = {5234--5239},
}
```

Measurements from magnetometers and inertial sensors (accelerometers and gyroscopes) can be combined to give 3D orientation estimates. In order to obtain accurate orientation estimates it is imperative that the magnetometer and inertial sensor axes are aligned and that the magnetometer is properly calibrated for both sensor errors as well as presence of magnetic distortions. In this work we derive an easy-to-use calibration algorithm that can be used to calibrate a combination of a magnetometer and inertial sensors. The algorithm compensates for any static magnetic distortions created by the sensor plat- form, magnetometer sensor errors and determines the alignment between the magnetometer and the inertial sensor axes. The resulting calibration procedure does not require any additional hardware. We make use of probabilistic models and obtain the calibration algorithm as the solution to a maximum likelihood problem. The efficacy of the proposed algorithm is illustrated using experimental data collected from a sensor unit placed in a magnetically disturbed environment onboard a jet aircraft.

```
@inproceedings{diva2:573843,
author = {Kok, Manon and Hol, Jeroen and Schön, Thomas and Gustafsson, Fredrik and Luinge, Henk},
title = {{Calibration of a magnetometer in combination with inertial sensors}},
booktitle = {Proceedings of the 15th International Conference on Information Fusion (FUSION)},
year = {2012},
pages = {787--793},
publisher = {IEEE conference proceedings},
}
```

We present an approach for computing the heading direction of avehicle by processing measurements from a 2-axis magnetometer rapidly. The proposed method relies on a non-linear transformation of the measurement data comprising only two inner products. Deterministic analysis of the signal model shows how the heading direction is contained in the signal and the proposed estimator is analyzed in terms of its statistical properties. Experimental verification indicates that good performance is achieved under the presence of saturation, measurement noise, and near field effects.

```
@inproceedings{diva2:573816,
author = {Wahlström, Niklas and Hostettler, Roland and Gustafsson, Fredrik and Birk, Wolfgang},
title = {{Rapid Classification of Vehicle Heading Direction with Two-Axis Magnetometer}},
booktitle = {Acoustics, Speech and Signal Processing (ICASSP), 2012},
year = {2012},
pages = {3385--3388},
publisher = {IEEE},
}
```

A male common swift Apus apus was equipped witha light logger on August 5, 2010, and again captured in his nest 298 days later. The data stored in the light logger enables analysis of the fascinating travel it made in this time period. The state of the art algorithm for geolocation based on light loggers consists in computing first sunrise and sunset from thelogged data, which are then converted to midday (gives longitude) and day length (gives latitude). This approach has singularities at the spring and fall equinoxes, and gives a bias for fast day transitions in the east-west direction. We derive a flexible particle filter solution, where sunset and sunrise are processed in separately measurement updates, and where the motion model has two modes, one for migration and one for stationary long time visits, which are designed to fit the flying pattern of the swift. This approach circumvents the aforementioned problems with singularity and bias, and provides realistic confidence bounds on the geolocation as well as an estimate of the migration mode.

```
@inproceedings{diva2:573801,
author = {Wahlström, Niklas and Gustafsson, Fredrik and Åkesson, Susanne},
title = {{A Voyage to Africa by Mr Swift}},
booktitle = {Proceedings of the 15th International Conference on Information Fusion},
year = {2012},
pages = {808--815},
publisher = {IEEE conference proceedings},
}
```

Airborne surveillance systems equipped with a vision/infrared camera require good knowledge about the position and orientation of the camera for successful tracking of ground targets. In particular, this is essential when incorporating prior information, like road maps, that is expressed relative a global reference system. Usually, it is possible to obtain good positioning with inertial/satellite navigation systems, but estimating the orientation is generally more difficult. It might be possible to use SLAM (Simultaneous Localization and Mapping) or image registration approaches to support the navigation system, but not always since such approaches require stable features in the images. In this paper the problem of simultaneous orientation error estimation and road target tracking is considered by assuming that the target is constrained to a known road network. A particle filter approach is proposed and it is shown that the result of this filter is close to the performance of the ideal case where the orientation error is perfectly known. However, the performance depends on how informative the road path is and in rare cases the orientation error is unobservable.

```
@inproceedings{diva2:570672,
author = {Skoglar, Per and Törnqvist, David},
title = {{Simultaneous Camera Orientation Estimation and Road Target Tracking}},
booktitle = {Proceedings of the 15th International Conference on Information Fusion},
year = {2012},
pages = {802--807},
publisher = {IEEE},
}
```

*", 15th International Conference on Information Fusion (FUSION), 2012, Proceeding, 114-120, 2012.*

Sequential Monte Carlo (SMC), or Particle Filters(PF), approximate the posterior distribution in nonlinear ﬁlteringarbitrarily well, but the problem how to compute a state estimateis not always straightforward. For multimodal posteriors, themaximum a posteriori (MAP) estimate is a logical choice, butit is not readily available from the SMC output. In principle,the MAP can be obtained by maximizing the posterior density obtained e.g. by the particle based approximation of theChapman-Kolmogorov equation. However, this posterior is amixture distribution with many local maxima, which makes theoptimization problem very hard. We suggest an algorithm forestimating the MAP using the global optimization principle ofPincus and subsequently outline the frameworks for estimatingthe ﬁlter and marginal smoother MAP of a dynamical systemfrom the SMC output.

```
@inproceedings{diva2:543905,
author = {Saha, Saikat and Gustafsson, Fredrik},
title = {{Importance Sampling Applied to Pincus Maximization for Particle Filter MAP Estimation\emph{ }}},
booktitle = {15th International Conference on Information Fusion (FUSION), 2012, Proceeding},
year = {2012},
pages = {114--120},
publisher = {International Society of Information Fusion (ISIF)},
}
```

We study the identification problem for Bates stochastic volatility model, which is widely used as the model of a stock in finance. By using the exact simulation method, a particle filter for estimating stochastic volatility and its systems parameters is constructed. Simulation studies for checking the feasibility of the developed scheme are demonstrated.

```
@inproceedings{diva2:543910,
author = {Aihara, ShinIchi and Bagch, Arunabha and Saha, Saikat},
title = {{Identification of Bates Stochastic Volatility Model by Using Non-Central Chi-Square Random Generation Method}},
booktitle = {Proceedings of the 37th IEEE International Conference on Acoustics, Speech, and Signal Processing},
year = {2012},
pages = {3905--3908},
}
```

This paper presents an algorithm for reduction of Gaussian inverse Wishart mixtures. Sums of an arbitrary number of mixture components are approximated with single components by analytically minimizing the Kullback-Leibler divergence. The Kullback-Leibler difference is used as a criterion for deciding whether or not two components should be merged, and a simple reduction algorithm is given. The reduction algorithm is tested in simulation examples in both one and two dimensions. The results presented in the paper are useful in extended target tracking using the random matrix framework.

```
@inproceedings{diva2:557428,
author = {Granström, Karl and Orguner, Umut},
title = {{On the Reduction of Gaussian inverse Wishart Mixtures}},
booktitle = {Proceedings of the International Conference on Information Fusion (FUSION)},
year = {2012},
pages = {2162--2169},
publisher = {IEEE Press},
}
```

In Gilholm et al.'s extended target model, the number of measurements generated by a target is Poisson distributed with measurement rate γ. Practical use of this extended target model in multiple extended target tracking algorithms requires a good estimate of γ. In this paper, we first give a Bayesian recursion for estimating γ using the well-known conjugate prior Gamma-distribution. In multiple extended target tracking, consideration of different measurement set associations to a single target makes Gamma-mixtures arise naturally. This causes a need for mixture reduction, and we consider the reduction of Gamma-mixtures by means of merging. Analytical minimization of the Kullback-Leibler divergence is used to compute the single Gamma distribution that best approximates a weighted sum of Gamma distributions. Results from simulations show the merits of the presented multiple target measurement-rate estimator. The Bayesian recursion and presented reduction algorithm have important implications for multiple extended target tracking, e.g. using the implementations of the extended target PHD filter.

```
@inproceedings{diva2:557427,
author = {Granström, Karl and Orguner, Umut},
title = {{Estimation and Maintenance of Measurement Rates for Multiple Extended Target Tracking}},
booktitle = {Proceedings of the International Conference on Information Fusion (FUSION)},
year = {2012},
pages = {2170--2176},
publisher = {IEEE Press},
}
```

We consider measurements from possibly zero-mean stochastic processes in a nonlinear filtering framework. This is a challenging problem, since it is only the second order properties of the measurements that bear information about the unknown state vector. The covariance function of the measurements can have both spatial and temporal correlation that depend on the state. Recently, a solution to this problem was presented for the case of Gaussian processes. We here extend the theory to Student's t processes. We illustrate the state observability by a simple but still realistic simulation example.

```
@inproceedings{diva2:543913,
author = {Saha, Saikat and Orguner, Umut and Gustafsson, Fredrik},
title = {{Nonlinear Filtering based on Observations from Student's T Processes}},
booktitle = {Proceedings of the 2012 IEEE Aerospace Conference},
year = {2012},
}
```

A novel method to find the orientation and position of a triaxial accelerometer mounted on a six degrees-of-freedom industrial robot is proposed and evaluated on experimental data. The method consists of two consecutive steps, where the first is to estimate the orientation of the accelerometer from static experiments. In the second step the accelerometer position relative to the robot base is identified using accelerometer readings when the accelerometer moves in a circular path and where the accelerometer orientation is kept constant in a path fixed coordinate system. Once the accelerometer position and orientation are identified it is possible to use the accelerometer in robot model parameter identification and in advanced control solutions. Compared to previous methods, the accelerometer position estimation is completely new, whereas the orientation is found using an analytical solution to the optimisation problem. Previous methods use a parameterisation where the optimisation uses an iterative solver.

```
@inproceedings{diva2:552577,
author = {Axelsson, Patrik and Norrlöf, Mikael},
title = {{Method to Estimate the Position and Orientation of a Triaxial Accelerometer Mounted to an Industrial Manipulator}},
booktitle = {Proceedings of the 10th IFAC Symposium on Robot Control},
year = {2012},
pages = {283--288},
}
```

Experimental evaluations for path estimation are performed on an ABB IRB4600 robot. Different observers using Bayesian techniques with different estimation models are proposed. The estimated paths are compared to the true path measured by a laser tracking system. There is no significant difference in performance between the six observers. Instead, execution time, model complexities and implementation issues have to be considered when choosing the method.

```
@inproceedings{diva2:552576,
author = {Axelsson, Patrik},
title = {{Evaluation of Six Different Sensor Fusion Methods for an Industrial Robot using Experimental Data}},
booktitle = {Proceedings of the 10th IFAC Symposium on Robot Control},
year = {2012},
pages = {126--132},
}
```

It is described how set membership identification and model rejection for polynomial models can be described using polynomial inequalities and inequations. Using difference algebra methods these problems can be reduced to a form based on so called autoreduced sets. It is shown that these descriptions generalize state space descriptions. It is also discussed how special forms of autoreduced sets can make calculations based on interval methods easier to implement.

```
@inproceedings{diva2:551556,
author = {Glad, Torkel},
title = {{Dealing with Inequalities in Polynomial Models}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {936--940},
}
```

The particle filter (PF) has emerged as a powerful tool for solving nonlinear and/or non-Gaussian filtering problems. When some of the states enter the model linearly, this can be exploited by using particles only for the "nonlinear" states and employing conditional Kalman filters for the "linear" states; this leads to the Rao-Blackwellised particle filter (RBPF). However, it is well known that the PF fails when the state of the model contains some static parameter. This is true also for the RBPF, even if the static states are marginalised analytically by a Kalman filter. The reason is that the posterior density of the static states is computed conditioned on the nonlinear particle trajectories, which are bound to degenerate over time. To circumvent this problem, we propose a method for targeting the posterior parameter density, conditioned on just the current nonlinear state. This results in an RBPF-like method, capable of recursive identification of nonlinear dynamical models with affine parameter dependencies.

```
@inproceedings{diva2:551267,
author = {Lindsten, Fredrik and Schön, Thomas B. and Svensson, Lennart},
title = {{A non-degenerate Rao-Blackwellised particle filter for estimating static parameters in dynamical models}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
}
```

We consider a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process (GP) model for the static nonlinearity. The GP model is a flexible model that can describe different types of nonlinearities while avoiding making strong assumptions such as monotonicity. We derive an inferential method based on recent advances in Monte Carlo statistical methods, known as Particle Markov Chain Monte Carlo (PMCMC). The idea underlying PMCMC is to use a particle filter (PF) to generate a sample state trajectory in a Markov chain Monte Carlo sampler. We use a recently proposed PMCMC sampler, denoted particle Gibbs with backward simulation, which has been shown to be efficient even when we use very few particles in the PF. The resulting method is used in a simulation study to identify two different Wiener systems with non-invertible nonlinearities.

```
@inproceedings{diva2:551263,
author = {Lindsten, Fredrik and Schön, Thomas B. and Jordan, Michael I.},
title = {{A Semiparametric Bayesian Approach to Wiener System Identification}},
booktitle = {Proceedings of the 16th IFAC Symposium on System Identification},
year = {2012},
pages = {1137--1142},
}
```

The particle Gibbs (PG) sampler was introduced in [Andrieu et al. (2010)] as a way to incorporate a particle filter (PF) in a Markov chain Monte Carlo (MCMC) sampler. The resulting method was shown to be an efficient tool for joint Bayesian parameter and state inference in nonlinear, non-Gaussian state-space models. However, the mixing of the PG kernel can be very poor when there is severe degeneracy in the PF. Hence, the success of the PG sampler heavily relies on the, often unrealistic, assumption that we can implement a PF without suffering from any considerate degeneracy. However, as pointed out by Whiteley in the discussion following [Andrieu et al. (2010)], the mixing can be improved by adding a backward simulation step to the PG sampler. Here, we investigate this further, derive an explicit PG sampler with backward simulation (denoted PG-BSi) and show that this indeed is a valid MCMC method. Furthermore, we show in a numerical example that backward simulation can lead to a considerable increase in performance over the standard PG sampler.

```
@inproceedings{diva2:551257,
author = {Lindsten, Fredrik and Schön, Thomas},
title = {{On the Use of Backward Simulation in the Particle Gibbs Sampler}},
booktitle = {Proceedings of the 37th IEEE International Conference on Acoustics, Speech, and Signal Processing},
year = {2012},
series = {Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing},
pages = {3845--3848},
publisher = {IEEE},
}
```

Gaussian innovations are the typical choice in most ARX models but using other distributions such as the Student's t could be useful. We demonstrate that this choice of distribution for the innovations provides an increased robustness to data anomalies, such as outliers and missing observations. We consider these models in a Bayesian setting and perform inference using numerical procedures based on Markov Chain Monte Carlo methods. These models include automatic order determination by two alternative methods, based on a parametric model order and a sparseness prior, respectively. The methods and the advantage of our choice of innovations are illustrated in three numerical studies using both simulated data and real EEG data.

```
@inproceedings{diva2:551244,
author = {Dahlin, Johan and Lindsten, Fredrik and Schön, Thomas Bo and Wills, Adrian George},
title = {{Hierarchical Bayesian approaches for robust inference in ARX models}},
booktitle = {Proceedings from the 16th IFAC Symposium on System Identification, 2012},
year = {2012},
series = {IFAC papers online},
volume = {2012},
pages = {131--136},
}
```

A Design-Build-Test (DBT) project course in electronics is presented. The course was developed during the first years of the CDIO Initiative, and it has been given successfully for almost ten years within two engineering programs at Linköping University. More than 2000 students have passed the course, and it is considered to be one of the most popular and also demanding courses within these programs. The key factors that have contributed to the success of the course are:

- Clearly defined learning outcomes.
- A suitable and well working course organization.
- A systematic method for project management.
- Challenging project tasks of sufficient complexity.
- Laboratory workspaces with modern equipment and high availability.

The aim of the paper is to describe these key factors in more detail based on the experiences that have been gained during the almost ten years the course has been given.

```
@inproceedings{diva2:543787,
author = {Svensson, Tomas and Gunnarsson, Svante},
title = {{Teaching Project Courses in Large Scale Using Industry Like Methods - Experiences After Ten Years}},
booktitle = {8th International CDIO Conference, Brisbane, AustraliaJuly 1-4},
year = {2012},
}
```

The global positioning system (GPS) is a Global Navigation Satellite System (GNSS) uses a constellation of between 24 and 32 Medium Earth Orbit satellites that transmit precise microwave signals, which enable GPS receivers to determine their current location, the time, and their velocity [1]. Initially, the GPS was developed for military applications, but very quickly became the most used technology in positioning even for end-user applications run by individuals with no technical skills. GPS reading are used also as reference points for many positioning techniques such as the techniques that depend on the transmitted electromagnetic signal to determine the position of the transmitter or the receiver, due to their superior accuracy comparing to such techniques. But how accurate are those readings, and how to obtain accurate reference points starting from raw GPS observations even when they are corrupted with errors. In this paper, a practical study about GPS positioning is provided. Generating the ground-truth reference points depending on GPS observations is also provided and discussed in details.

```
@inproceedings{diva2:663675,
author = {Bshara, M. and Orguner, Umut and Gustafsson, Fredrik and L. Van, Biesen},
title = {{GPS positioning and groung-truth reference points generation}},
booktitle = {Joint IMEKO TC11-TC19-TC20 Int. Symp. Metrological Infrastructure, Environmental and Energy Measurement and Int. Symp. of Energy Agencies of Mediterranean Countries, IMEKO-MI 2011},
year = {2011},
series = {Joint IMEKO TC11-TC19-TC20 Int. Symp. Metrological Infrastructure, Environmental and Energy Measurement and Int. Symp. of Energy Agencies of Mediterranean Countries, IMEKO-MI 2011},
pages = {111--116},
publisher = {Curran Associates, Incorporated, 2011},
}
```

This paper deals with the issue of estimating the parameters in a continuous-time nonlinear dynamical model from sampled data. We focus on the issue of bias-variance trade-offs. In particular, we show that the bias error can be significantly reduced by using a particular form of sampled data model based on truncated Taylor series. This model retains the conceptual simplicity of models based on Euler integration but has much improved accuracy as a function of the sampled period.

```
@inproceedings{diva2:636448,
author = {Cassasco, Diego S. and Ljung, Lennart and Goodwin, Graham C. and Agüero, Juan C.},
title = {{On the Accuracy of Parameter Estimation for Continuous Time Nonlinear Systems from Sampled Data}},
booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control},
year = {2011},
pages = {4308--4311},
}
```

The identification of multiple affine subspaces from a set of data is of interest in fields such as system identification, data compression, image processing and signal processing and in the literature referred to as subspace clustering. If the origin of each sample would be known, the problem would be trivially solved by applying principal component analysis to samples originated from the same subspace. Now, not knowing what samples that originates from what subspace, the problem becomes considerably more difficult. We present a novel convex formulation for subspace clustering. The proposed method takes the shape of a least-squares problem with sum-of-norms regularization over optimization parameter differences, a generalization of the ℓ1-regularization. The regularization constant is used to trade off fit and the identified number of affine subspaces.

```
@inproceedings{diva2:636445,
author = {Ohlsson, Henrik and Ljung, Lennart},
title = {{A Convex Approach to Subspace Clustering}},
booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control},
year = {2011},
pages = {1467--1472},
}
```

In this companion paper, the choice of kernels for estimating the impulse response of linear stable systems is considered from a classical, “frequentist”, point of view. The kernel determines the regularization matrix in a regularized least squares estimate of an FIR model. The quality is assessed from a mean square error (MSE) perspective, and measures and algorithms for optimizing the MSE are discussed. The ideas are tested on the same data bank as used in Part I of the companion papers. The resulting findings and conclusions in the two papers are very similar despite the different perspectives.

```
@inproceedings{diva2:636442,
author = {Chen, Tianshi and Ohlsson, Henrik and Goodwin, Graham C. and Ljung, Lennart},
title = {{Kernel Selection in Linear System Identification:
Part II: A Classical Perspective}},
booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control},
year = {2011},
pages = {4326--4331},
}
```

Segmentation of time series data is of interest in many applications, as for example in change detection and fault detection. In the area of convex optimization, the sum-of-norms regularization has recently proven useful for segmentation. Proposed formulations handle linear models, like ARX models, but cannot handle nonlinear models. To handle nonlinear dynamics, we propose integrating the sum-of-norms regularization with a least squares support vector machine (LS-SVM) core model. The proposed formulation takes the form of a convex optimization problem with the regularization constant trading off the fit and the number of segments.

```
@inproceedings{diva2:636436,
author = {Falck, Tillmann and Ohlsson, Henrik and Ljung, Lennart and Suykens, Johan A.K. and De Moor, Bart},
title = {{Segmentation of Time Series from Nonlinear Dynamical Systems}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {13209--13214},
}
```

This paper develops and illustrates methods for the identiﬁcation of Wiener model structures. These techniques are capable of accommodating the “blind” situation where the input excitation to the linear block is not observed. Furthermore, the algorithm developed here can accommodate a nonlinearity which need not be invertible, and may also be multivariable. Central to these developments is the employment of the Expectation Maximisation (EM) method for computing maximum likelihood estimates, and the use of a new approach to particle smoothing to eﬃciently compute stochastic expectations in the presence of nonlinearities.

```
@inproceedings{diva2:636431,
author = {Wills, Adrian and Schön, Thomas and Ljung, Lennart and Ninness, Brett},
title = {{Blind Identification of Wiener Models}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {5597--5602},
}
```

Performing experiments for system identication is often a time-consuming task which may also interfere with the process operation. With memory prices going down, it is more and more common that years of process data are stored (without compression) in a history database. The rationale for this work is that in such stored data there must already be intervals informative enough for system identication. Therefore, the goal of this project was to find an algorithm that searches and marks intervals suitable for process identication (rather than performing completely automatic system identication). For each loop, 4 stored variables are required; setpoint, manipulated variable, process output and mode of the controller.

The proposed method requires a minimum of knowledge of the process and is implemented in a simple and ecient recursive algorithm. The essential features of the method are the search for excitation of the input and output, followed by the estimation of a Laguerre model combined with a chi-square test to check that at least one estimated parameter is statistically signicant. The use of Laguerre models is crucial to handle processes with deadtime without explicit delay estimation. The method was tested on three years of data from more than 200 control loops. It was able to find all intervals in which known identication experiments were performed as well as many other useful intervals in closed/open loop operation.

```
@inproceedings{diva2:636424,
author = {Peretzki, Daniel and Isaksson, Alf and Carvalho Bittencourt, Andr\'{e} and Forsman, Krister},
title = {{Data Mining of Historic Data for Process Identification}},
booktitle = {Proceedings of the 2011 AIChE Annual Meeting},
year = {2011},
pages = {1027--1033},
publisher = {American Institute of Chemical Engineers},
}
```

```
@inproceedings{diva2:636422,
author = {Carvalho Bittencourt, Andr\'{e} and Saarinen, Kari and Sander-Tavallaey, Shiva},
title = {{A method for Monitoring of Systems that operate in a Repetitive Manner:
Application to Wear Monitoring of an Industrial Robot}},
booktitle = {Proceedings of the 2011 PAPYRUS Workshop on Fault Diagnosis and Fault Tolerand Control in Large Scale Processing Industries},
year = {2011},
}
```

Frequent inlet ﬂow changes typically cause problems for averaging level controllers. For a frequently changing inlet ﬂow the upsets do not occur when the system is in steady state and the tank level at its set-point. For this reason the tuning of the level controller gets quite complicated, since not only the size of the upsets but also the time in between them relative to the hold up of the tank have to be considered. One way to obtain optimal ﬂow ﬁltering while directly accounting for future inlet ﬂow upsets is to use closed-loop robust MPC, as proposed here. The behavior of the robust MPC controller differs from earlier proposed level controllers as it does not return the tank level to a ﬁxed set-point following an inlet ﬂow upset. Guidelines on the tuning of the controller is presented and its performance is compared to that of a previously proposed MPC approach.

```
@inproceedings{diva2:636420,
author = {Rosander, Peter and Isaksson, Alf and Löfberg, Johan and Forsman, Krister},
title = {{Robust Averaging Level Control}},
booktitle = {Proceedings of the 2011 AIChE Annual Meeting},
year = {2011},
}
```

Three approaches of iterative learning control (ILC) applied to a Gantry-Tau parallel kinematic robot are studied; ILC algorithms using 1) measured motor angles, 2) tool-position estimates, and for evaluation purposes, 3) measured tool position. The approaches are compared experimentally, with the tool performance evaluated using external sensors. It is concluded that the tool performance can be improved using tool-position estimates in the ILC algorithm, compared to when using motor-angle measurements. Applying ILC algorithms to a system following trajectories with so-called lead-in/lead-out is also considered in the paper.

```
@inproceedings{diva2:636246,
author = {Wall\'{e}n, Johanna and Dressler, Isolde and Robertsson, Anders and Norrlöf, Mikael and Gunnarsson, Svante},
title = {{Observer-based ILC Applied to the Gantry-Tau Parallel Kinematic Robot}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {992--998},
publisher = {IFAC},
}
```

This paper is concerned with vehicle motion estimation. The problem is formulated as a sensor fusion problem, where the vehicle motion is estimated based on the information from a far infrared camera, inertial sensors and the vehicle speed. This information is already present in premium cars. We are concerned with the off-line situation and the approach taken is to formulate the problem as a nonlinear least squares problem. In order to illustrate the performance of the proposed method experiments on rural roads in Sweden during night time driving have been performed. The results clearly indicates the efficacy of the approach.

```
@inproceedings{diva2:433349,
author = {Nilsson, Emil and Lundquist, Christian and Schön, Thomas and Forslund, David and Roll, Jacob},
title = {{Vehicle Motion Estimation Using an Infrared Camera}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {12952--12957},
publisher = {Elsevier},
}
```

Systems today often consist of logic switches working besides continuous physical systems. The demand for novel hybrid system identification algorithms is therefore of growing interest and essential for the development of control algorithms for this type of systems. An important type of hybrid systems is piecewise affine systems. The identification of piecewise affine systems is here tackled by overparametrizing and assigning a regressor-parameter to each of the observations. The regressor parameters are forced to be the same if that not causes a major increase in the fit term. The formulation takes the shape of a least-squares problem with sum-of-norms regularization over regressor parameter differences, a generalization of l1-regularization. The regularization constant is used to trade off fit and the number of partitions of the model.

```
@inproceedings{diva2:360026,
author = {Ohlsson, Henrik and Ljung, Lennart},
title = {{Identification of Piecewise Affine Systems Using Sum-of-Norms Regularization}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {6640--6645},
}
```

Controller synthesis for linear parameter varying (LPV) systems has received a lot of attention from the control community. This is mainly motivated by the wide range of non-linear dynamical systems that can be approximated by LPV-systems. In this paper a novel method is presented that, by only using local state space models as data, tries to solve the problem of finding a linear parameter varying output-feedback controller. The method uses non-linear programming and a quasi-Newton framework to solve the problem. The great advantages with the proposed method is that it is possible to impose structure in the controller and that you do not need an lpv-model, only state space models for different values of the scheduling parameters. Finally an example is presented to show the potential of the method.

```
@inproceedings{diva2:606338,
author = {Petersson, Daniel and Löfberg, Johan},
title = {{LPV H2-Controller Synthesis using Nonlinear Programming}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {6692--6696},
}
```

The robust H_{2} norm plays an important role in analysis and design in many fields. However, for many practical applications, design and analysis is based on finite frequency range. In this paper we review the concept of the robust finite frequency H_{2} norm, and we provide an algorithmic method for calculating an upper bound for the mentioned quantity.

```
@inproceedings{diva2:567590,
author = {Khoshfetrat Pakazad, Sina and Hansson, Anders and Garulli, Andrea},
title = {{On the Calculation of the Robust Finite Frequency H2 Norm}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {3360--3365},
}
```

This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has already been derived by Mahler and a Gaussian mixture implementation has been proposed recently. This work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers to achieve better estimation performance. A Gaussian mixture implementation is described. The early results using real data from a laser sensor confirm that the sensitivity of the number of targets in the extended target PHD filter can be avoided with the added flexibility of the extended target CPHD filter.

```
@inproceedings{diva2:557436,
author = {Orguner, Umut and Lundquist, Christian and Granström, Karl},
title = {{Extended Target Tracking with a Cardinalized Probability Hypothesis Density Filter}},
booktitle = {Proceedings of 2011 International Conference on Information Fusion (FUSION)},
year = {2011},
}
```

Particle filters (PFs) have shown to be very potent tools for state estimation in nonlinear and/or non-Gaussian state-space models. For certain models, containing a conditionally tractable substructure (typically conditionally linear Gaussian or with finite support), it is possible to exploit this structure in order to obtain more accurate estimates. This has become known as Rao-Blackwellised particle filtering (RBPF). However, since the RBPF is typically more computationally demanding than the standard PF per particle, it is not always beneficial to resort to Rao-Blackwellisation. For the same computational effort, a standard PF with an increased number of particles, which would also increase the accuracy, could be used instead. In this paper, we have analysed the asymptotic variance of the RBPF and provide an explicit expression for the obtained variance reduction. This expression could be used to make an efficient discrimination of when to apply Rao-Blackwellisation, and when not to.

```
@inproceedings{diva2:551250,
author = {Lindsten, Fredrik and Schön, Thomas and Olsson, Jimmy},
title = {{An Explicit Variance Reduction Expression for the Rao-Blackwellised Particle Filter}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {11979--11984},
}
```

We present a system that rectifies and stabilizes video sequences on mobile devices with rolling-shutter cameras. The system corrects for rolling-shutter distortions using measurements from accelerometer and gyroscope sensors, and a 3D rotational distortion model. In order to obtain a stabilized video, and at the same time keep most content in view, we propose an adaptive low-pass filter algorithm to obtain the output camera trajectory. The accuracy of the orientation estimates has been evaluated experimentally using ground truth data from a motion capture system. We have conducted a user study, where the output from our system, implemented in iOS, has been compared to that of three other applications, as well as to the uncorrected video. The study shows that users prefer our sensor-based system.

```
@inproceedings{diva2:525241,
author = {Hanning, Gustav and Forslöw, Nicklas and Forss\'{e}n, Per-Erik and Ringaby, Erik and Törnqvist, David and Callmer, Jonas},
title = {{Stabilizing Cell Phone Video using Inertial Measurement Sensors}},
booktitle = {The Second IEEE International Workshop on Mobile Vision},
year = {2011},
address = {Barcelona Spain},
}
```

The choice of proposal distribution in the particle filter is one of the most important design choices, and also one of the trickiest one to implement. There are basically three main options: the prior, the likelihood and the optimal proposal that combines the prior and the likelihood. The optimal proposal however, can not be obtained in most cases. The prior proposal is although easy to implement, it does not incorporate the information available otherwise from the recent observation. The prior may thus work fine for low signal to noise ratio (SNR), where the recent observation does not carry much information. However, defining the critical value of the SNR is not that obvious. On the other hand, the likelihood as a proposal always includes the information from the recent observation, but it requires that the measurement dimension is at least equal to the state dimension. We here formalize the problem, and point out an approach based on down-sampling the model. One main advantage of down-sampling is that it can decrease the problem of particle degeneracy.

```
@inproceedings{diva2:512107,
author = {Gustafsson, Fredrik and Saha, Saikat and Orguner, Umut},
title = {{The Benefits of Down-Sampling in the Particle Filter}},
booktitle = {Proceedings of the 14th International Conference on Information Fusion},
year = {2011},
}
```

We consider a class of non-linear filtering problems, where the observation model is given by a Gaussian process rather than the common non-linear function of the state and measurement noise. The new observation model can be considered as a generalization of the standard one with correlated measurement noise in both time and space. We propose a particle filter based approach with a measurement update step that requires a memory of past observations which can be truncated using a moving window to obtain a finite-dimensional filter with arbitrarily good accuracy. The validity of the conceptual solution is proved via simulations on a one dimensional tracking problem and implementation issues are discussed.

```
@inproceedings{diva2:512104,
author = {Gustafsson, Fredrik and Saha, Saikat and Orguner, Umut},
title = {{Non-Linear Filtering based on Observations from Gaussian Processes}},
booktitle = {Proceedings of the 2011 IEEE Aerospace Conference},
year = {2011},
}
```

For linear and Gaussian systems, fault detection over a batch of data is well-studied, and analytical solutions exist in a stochastic framework. The parity space approach handles additive faults and can be shown to be equivalent to estimating the state trajectory and then removing its influence on the output sequence. Multiplicative faults in linear systems can be handled using parameter estimation methods, such as the EM-algorithm in combination with the Kalman smoother. For nonlinear and non-Gaussian systems, we propose to estimate the state trajectory and the faults over the data batch using a particle smoother and the EM-algorithm. The result is a generic fault detection and isolation scheme that applies to arbitrary nonlinear and non-Gaussian systems, where the faults are monitored over a sliding window.

```
@inproceedings{diva2:512100,
author = {Törnqvist, David and Saha, Saikat and Gustafsson, Fredrik},
title = {{Fault Detection using Nonlinear Parameter Estimation}},
booktitle = {Proceedings of the 2011 IEEE Aerospace Conference},
year = {2011},
}
```

The second order extended Kalman filter (EKF2) is based on a second order Taylor expansion of a nonlinear system, in contrast to the more common (first order) extended Kalman filter (EKF1). Despite a solid theoretical ground for its approximation, it is seldom used in applications, where the EKF and the unscented Kalman filter (UKF) are the standard algorithms. One reason for this might be the requirement for analytical Jacobian and Hessian of the system equations, and the high complexity that scales with the state order $n_x$ as $n_x^5$. We propose a numerical algorithm which is based on an extended set of sigma points (compared to the UKF) that needs neither Jacobian nor Hessian (or numerical approximations of these). Further, it scales as $n_x^4$, which is an order of magnitude better than the EKF2 algorithm presented in literature.

```
@inproceedings{diva2:511843,
author = {Roth, Michael and Gustafsson, Fredrik},
title = {{An Efficient Implementation of the Second Order Extended Kalman Filter}},
booktitle = {Proceedings of the 14th International Conference on Information Fusion (FUSION), 2011},
year = {2011},
publisher = {IEEE},
}
```

With the electromagnetic theory as basis, we present a sensor model for three-axis magnetometers suitable for localization and tracking applications. The model depends on a physical magnetic dipole model of the target and its relative position to the sensor. Furthermore, the dependency between the magnetic dipole and the target orientation has been modeled enabling tracking of a maneuvering target. Due to multimodality, a bank of Extended Kalman Filters is proposed for tracking road vehicles. Results from field test data indicate excellent tracking of target position.

```
@inproceedings{diva2:471285,
author = {Wahlström, Niklas and Callmer, Jonas and Gustafsson, Fredrik},
title = {{Single Target Tracking using Vector Magnetometers}},
booktitle = {Acoustics, Speech and Signal Processing (ICASSP), 2011},
year = {2011},
series = {IEEE International Conference on Acoustics, Speech and Signal Processing. Proceedings},
pages = {4332--4335},
publisher = {IEEE},
}
```

We present a novel clustering method, formulated as a convex optimization problem. The method is based on over-parameterization and uses a sum-of-norms (SON) regularization to control the trade-off between the model fit and the number of clusters. Hence, the number of clusters can be automatically adapted to best describe the data, and need not to be specified a priori. We apply SON clustering to cluster the particles in a particle filter, an application where the number of clusters is often unknown and time varying, making SON clustering an attractive alternative.

```
@inproceedings{diva2:506576,
author = {Lindsten, Fredrik and Ohlsson, Henrik and Ljung, Lennart},
title = {{Clustering using Sum-of-Norms Regularization:
With Application to Particle Filter Output Computation}},
booktitle = {Proceedings of the 2011 IEEE Statistical Signal Processing Workshop},
year = {2011},
pages = {201--204},
}
```

The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed and an existing convex optimization formulation of the problem is extended to include new types of constraints. The new constraints are speed dependent and can be motivated from physical modeling of the motors and the drive system. It is shown how the speed dependent constraints should be added in order to keep the convexity of the overall problem. A method to, conservatively, approximate the linear speed dependent constraints by a convex constraint is also proposed. A numerical example proves versatility of the extension proposed in this paper.

```
@inproceedings{diva2:475993,
author = {Ardeshiri, Tohid and Norrlöf, Mikael and Löfberg, Johan and Hansson, Anders},
title = {{Convex Optimization Approach for Time-Optimal Path Tracking of Robots with Speed Dependent Constraints}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {14648--14653},
publisher = {IFAC},
}
```

The paper deals with the problem of active fault detection and control for multiple models. It is assumed that a fault detector is given and the goal is to design an input signal generator such that detection and control aims are achieved. Since these two aim are conflicting, it is necessary to express a desired compromise between them. The paper investigates three formulations that allow for respecting both competing aims. In the first formulation both aims are combined into a single criterion. In other two formulations, one aim is reflected in the criterion and the other aim is enforced as a constraint.

```
@inproceedings{diva2:475612,
author = {Siroky, Jan and Simandl, Miroslav and Axehill, Daniel and Puncochar, Ivo},
title = {{An Optimization Approach to Resolve the Competing Aims of Active Fault Detection and Control}},
booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control},
year = {2011},
pages = {3712--3717},
}
```

In this paper we describe a procedure for computation of optimal and suboptimal explicit MPC controllers for hybrid systems. This procedure is based on a parametric branch and bound approach, which allows the user to specify a state-dependent suboptimality tolerance. Depending on the choice of the tolerance, an optimal solution can be sought for, a merely feasible solution can be sought for, a certain suboptimality can be enforced, or a priori stability guarantees can be given. Moreover, the proposed procedure does not require that the computation of the optimal solution is tractable.

```
@inproceedings{diva2:475606,
author = {Axehill, Daniel and Besselmann, Thomas and Raimondo, Davide and Morari, Manfred},
title = {{Suboptimal Explicit Hybrid MPC via Branch and Bound}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {10281--10286},
}
```

Saab Aeronautics has chosen Modelica and Dymola as part of the means for model based system engineering (MBSE). This paper will point out why a considerable effort has been made to migrate models from other simulation tools to Dymola. The paper also shows how the models and tools are used, experiences gained from usage in an industrial context as well as some remaining trouble spots.

```
@inproceedings{diva2:473646,
author = {Lind, Ingela and Andersson, Henric},
title = {{Model Based Systems Engineering for Aircraft Systems -- How does Modelica Based Tools Fit?}},
booktitle = {Proceedings of the 8$^{th}$ International Modelica Conference, March 20th-22nd, Technical Univeristy, Dresden, Germany},
year = {2011},
series = {Linköping Electronic Conference Proceedings},
volume = {63},
pages = {856--864},
publisher = {Linköping University Electronic Press},
address = {Linköping},
}
```

In this study, we investigate online Bayesian estimation of the measurement noise density of a given state space model using particle filters and Dirichlet process mixtures. Dirichlet processes are widely used in statistics for nonparametric density estimation. In the proposed method, the unknown noise is modeled as a Gaussian mixture with unknown number of components. The joint estimation of the state and the noise density is done via particle filters. Furthermore, the number of components and the noise statistics are allowed to vary in time. An extension of the method for the estimation of time varying noise characteristics is also introduced.

```
@inproceedings{diva2:471284,
author = {Özkan, Emre and Saha, Saikat and Gustafsson, Fredrik and Smidl, Vaclav},
title = {{Non-Parametric Bayesian Measurement Noise Density Estimation in Non-Linear Filtering}},
booktitle = {Acoustics, Speech and Signal Processing (ICASSP), 2011},
year = {2011},
series = {IEEE International Conference on Acoustics, Speech and Signal Processing. Proceedings},
pages = {5924--5927},
publisher = {IEEE},
}
```

Monitoring and tracking human activities around restricted areas is an important issue in security and surveillance applications. The movement of different parts of the human body generates unique micro-Doppler features which can be extracted effectively using joint time-frequency analysis. In this paper, we describe the simultaneous tracking of both location and micro-Doppler features of a human using particle filters (PF). The results obtained using the data from a 77 GHz radar prove the successful usage of particle filters in tracking micro-Doppler features of the human gait.

```
@inproceedings{diva2:471281,
author = {Guldogan, Mehmet Burak and Gustafsson, Fredrik and Orguner, Umut and Björklund, Svante and Petersson, H. and Nezirovic, A.},
title = {{Human gait parameter estimation based on micro-doppler signatures using particle filters}},
booktitle = {Acoustics, Speech and Signal Processing (ICASSP), 2011},
year = {2011},
series = {IEEE International Conference on Acoustics, Speech and Signal Processing. Proceedings},
pages = {5940--5943},
publisher = {IEEE},
}
```

High-precision estimation of vehicle tire radii is considered, based on measurements on individual wheel speeds and absolute position from a global navigation satellite system (GNSS). The wheel speed measurements are subject to noise with time-varying covariance that depends mainly on the road surface. The novelty lies in a Bayesian approach to estimate online the time-varying radii and noise parameters using a marginalized particle filter, where no model approximations are needed such as in previously proposed algorithms based on the extended Kalman filter. Field tests show that the absolute radius can be estimated with millimeter accuracy, while the relative wheel radius on one axle is estimated with submillimeter accuracy.

```
@inproceedings{diva2:464340,
author = {Özkan, Emre and Lundquist, Christian and Gustafsson, Fredrik},
title = {{A Bayesian Approach to Jointly Estimate Tire Radii and Vehicle Trajectory}},
booktitle = {Proceedings of the International IEEE Conference on Intelligent Transportation Systems},
year = {2011},
pages = {1--6},
publisher = {IEEE conference proceedings},
address = {Washington DC, USA},
}
```

The performance of a non-linear filter hinges in the end on the accuracy of the assumed non-linear model of the process. In particular, the process noise covariance Q is hard to get by physical modeling and dedicated system identification experiments. We propose a variant of the expectation maximization (EM) algorithm which iteratively estimates the unobserved state sequence and Q based on the observations of the process. The extended Kalman smoother (EKS) is the instrument to find the unobserved state sequence. Our contribution fills a gap in literature, where previously only the linear Kalman smoother and particle smoother have been applied. The algorithm will be important for future industrial robots with more flexible structures, where the particle smoother cannot be applied due to the high state dimension. The proposed method is compared to two alternative methods on a simulated robot.

```
@inproceedings{diva2:458439,
author = {Axelsson, Patrik and Orguner, Umut and Gustafsson, Fredrik and Norrlöf, Mikael},
title = {{ML Estimation of Process Noise Variance in Dynamic Systems}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2011},
pages = {5609--5614},
}
```

This paper studies the accuracy of the estimated eyepoint of an Optical See-Through Head-Mounted Display (OST HMD) calibrated using the Single Point Active Alignment Method (SPAAM). Quantitative evaluation of calibration procedures for OST HMDs is complicated as it is currently not possible to share the subject’s view. Temporarily replacing the subject’s eye with a camera during the calibration or evaluation stage has been proposed, but the uncertainty of a correct eyepoint estimation remains. In the experiment reported in this paper, subjects were used for all stages of calibration and the results were verified with a 3D measurement device. The nine participants constructed 25 visual alignments per calibration after which the estimated pinhole camera model was decomposed into its intrinsic and extrinsic parameters using two common methods. Unique to this experiment, compared to previous evaluations, is the measurement device used to cup the subject’s eyeball. It measures the eyepoint location relative to the head tracker, thereby establishing the calibration accuracy of the estimated eyepoint location. As the results on accuracy are expressed as individual pinhole camera parameters, rather than a compounded registration error, this paper complements previously published work on parameter variance as the former denotes bias and the latter represents noise. Results indicate that the calibrated eyepoint is on average 5 cm away from its measured location and exhibits a vertical bias which potentially causes dipvergence for stereoscopic vision for objects located further away than 5.6 m. Lastly, this paper closes with a discussion on the suitability of the traditional pinhole camera model for OST HMD calibration.

```
@inproceedings{diva2:456340,
author = {Axholt, Magnus and Skoglund, Martin A. and O'Connell, Stephen D. and Cooper, Matthew D. and Ellis, Stephen R. and Ynnerman, Anders},
title = {{Accuracy of Eyepoint Estimation in Optical See-Through Head-Mounted Displays Using the Single Point Active Alignment Method}},
booktitle = {IEEE Virtual Reality Conference 2012, Orange County (CA), USA},
year = {2011},
}
```

This paper considers tracking of extended targets using data from laser range sensors. Two types of extended target shapes are considered, rectangular and elliptical, and a method to compute predicted measurements and corresponding innovation covariances is suggested. The proposed method can easily be integrated into any tracking framework that relies on the use of an extended Kalman filter. Here, it is used together with a recently proposed Gaussian mixture probability hypothesis density (GM-PHD) filter for extended target tracking, which enables estimation of not only position, orientation, and size of the extended targets, but also estimation of extended target type (i.e. rectangular or elliptical). In both simulations and experiments using laser data, the versatility of the proposed tracking framework is shown. In addition, a simple measure to evaluate the extended target tracking results is suggested.

```
@inproceedings{diva2:434601,
author = {Granström, Karl and Lundquist, Christian and Orguner, Umut},
title = {{Tracking Rectangular and Elliptical Extended Targets Using Laser Measurements}},
booktitle = {Proceedings of the 14th International Conference on Information Fusion},
year = {2011},
pages = {592--599},
}
```

This paper presents a framework for tracking extended targets which give rise to a structured set of measurements per each scan. The concept of a measurement generating point (MGP) which is defined on the boundary of each target is introduced. The tracking framework contains an hybrid statespace where MGP:s and the measurements are modeled by random finite sets and target states by random vectors. The target states are assumed to be partitioned into linear and nonlinear components and a Rao-Blackwellized particle filter is used for their estimation. For each state particle, a probability hypothesis density (PHD) filter is utilized for estimating the conditional set of MGP:s given the target states. The PHD kept for each particle serves as a useful means to represent information in the set of measurements about the target states. The early results obtained show promising performance with stable target following capability and reasonable shape estimates.

```
@inproceedings{diva2:433343,
author = {Lundquist, Christian and Granström, Karl and Orguner, Umut},
title = {{Estimating the Shape of Targets with a PHD Filter}},
booktitle = {Proceedings of the 14th International Conference on Information Fusion},
year = {2011},
}
```

A new approach to track bicycles from imagery sensor data is proposed. It is based on detecting ellipsoids in the images, and treat these pair-wise using a dynamic bicycle model. One important application area is in automotive collision avoidance systems, where no dedicated systems for bicyclists yet exist and where very few theoretical studies have been published.

Possible conflicts can be predicted from the position and velocity state in the model, but also from the steering wheel articulation and roll angle that indicate yaw changes before the velocity vector changes. An algorithm is proposed which consists of an ellipsoid detection and estimation algorithm and a particle filter.

A simulation study of three critical single target scenarios is presented, and the algorithm is shown to produce excellent state estimates. An experiment using a stationary camera and the particle filter for state estimation is performed and has shown encouraging results.

```
@inproceedings{diva2:430910,
author = {Ardeshiri, Tohid and Larsson, Fredrik and Gustafsson, Fredrik and Schön, Thomas B. and Felsberg, Michael},
title = {{Bicycle Tracking Using Ellipse Extraction}},
booktitle = {Proceedings of the 14thInternational Conference on Information Fusion, 2011},
year = {2011},
pages = {1--8},
publisher = {IEEE},
}
```

In this paper we present a solution to the simultaneous localisation and mapping (SLAM) problem using a camera and inertial sensors. Our approach is based on the maximum a posteriori (MAP) estimate of the complete SLAM problem. The resulting problem is posed in a nonlinear least-squares framework which we solve with the Gauss-Newton method. The proposed algorithm is evaluated on experimental data using a sensor platform mounted on an industrial robot. In this way, accurate ground truth is available, and the results are encouraging.

```
@inproceedings{diva2:421456,
author = {Sjanic, Zoran and Skoglund, Martin A. and Schön, Thomas B. and Gustafsson, Fredrik},
title = {{A Nonlinear Least-Squares Approach to the SLAM Problem}},
booktitle = {Proceedings of the 18th IFAC World Congress, 2011},
year = {2011},
}
```

Synthetic Aperture Radar (SAR) equipment is an all-weather radar imaging system that can be used to create high resolution images of the scene by utilising the movement of the flying platform. It is therefore essential to accurately estimate the platform's trajectory in order to get good and focused images. Recently, both real time applications and smaller and cheaper platforms have been considered. This, in turn, leads to unfocused images since cheaper platforms, in general, have navigation systems with poorer performance. At the same time the radar data contain information about the platform's motion that can be used to estimate the trajectory andget more focused images. Here, a method of utilising the phase gradient of the SAR data in a sensor fusion framework is presented. The method is illustrated on a simulated example with promising results. At the end a discussion about the obtained results and future work is covered.

```
@inproceedings{diva2:416751,
author = {Sjanic, Zoran and Gustafsson, Fredrik},
title = {{Navigation and SAR Auto-focusing Based on the Phase Gradient Approach}},
booktitle = {Proceedings of the 14th International Conference on Information Fusion (FUSION), 2011},
year = {2011},
pages = {1--8},
publisher = {IEEE conference proceedings},
}
```

The parameter estimation variance of the Single Point Active Alignment Method (SPAAM) is studied through an experiment where 11 subjects are instructed to create alignments using an Optical See-Through Head Mounted Display (OSTHMD) such that three separate correspondence point distributions are acquired. Modeling the OSTHMD and the subject's dominant eye as a pinhole camera, findings show that a correspondence point distribution well distributed along the user's line of sight yields less variant parameter estimates. The estimated eye point location is studied in particular detail. Thefindings of the experiment are complemented with simulated datawhich show that image plane orientation is sensitive to the numberof correspondence points. The simulated data also illustrates someinteresting properties on the numerical stability of the calibrationproblem as a function of alignment noise, number of correspondencepoints, and correspondence point distribution.

```
@inproceedings{diva2:408445,
author = {Axholt, Magnus and Skoglund, Martin and O'Connell, Stephen and Cooper, Matthew and Ellis, Stephen and Ynnerman, Anders},
title = {{Parameter Estimation Variance of the Single Point Active Alignment Method in Optical See-Through Head Mounted Display Calibration}},
booktitle = {Proceedings of the IEEE Virtual Reality Conference},
year = {2011},
series = {IEEE Virtual Reality Conference},
pages = {27--24},
publisher = {IEEE},
address = {Piscataway, NJ, USA},
}
```

Shooter localization in a wireless network of geographically distributed microphones is studied. The arrival time of both the acoustic muzzle blast (MB) from the gunfire and the ballistic shock wave (SW) from the bullet can be registered by the microphone nodes and considered as measurements. To relax the requirements on accurate node clocks, the approach to base the localization on the time difference of MB and SW at each sensor is analyzed. Cramér-Rao lower bound analysis indicates how a lower bound of the root mean square error depends on the synchronization error for different approaches to use the measurements. The localization problem is formulated in a separable nonlinear least squares framework. A simplified ballistic model with only one, assumed unknown, parameter is used. Results from field trials with different types of ammunition demonstrate excellent results using the MB-SW difference for both the position and the aiming angle of the shooter.

```
@inproceedings{diva2:663759,
author = {Lindgren, D. and Gustafsson, Fredrik and Habberstad, H.},
title = {{Microphone networks for shooter localization:
}},
booktitle = {in INFORMATIK 2010 - Service Science - Neue Perspektiven fur die Informatik, Beitrage der 40. Jahrestagung der Gesellschaft fur Informatik e.V. (GI), vol 2},
year = {2010},
series = {INFORMATIK 2010 - Service Science - Neue Perspektiven fur die Informatik, Beitrage der 40. Jahrestagung der Gesellschaft fur Informatik e.V. (GI)},
pages = {831--837},
}
```

This paper addresses the issue of the practical implementation of Model Predictive Controllers (MPC) to processes with short sampling times. Given an explicit solution to an MPC problem, the main idea is to approximate the optimal control law defined over state space regions by a single polynomial of pre-specified degree which, when applied as a state-feedback, guarantees closed-loop stability, constraint satisfaction, and a bounded performance decay. It is shown how to search for such a polynomial by solving a single linear program.

```
@inproceedings{diva2:636218,
author = {Kvasnica, Michal and Löfberg, Johan and Herceg, Martin and C̆irka, L'ubos and Fikar, Miroslav},
title = {{Low-Complexity Polynomial Approximation of Explicit MPC via Linear Programming}},
booktitle = {Proceedings of the 2010 American Control Conference},
year = {2010},
pages = {4713--4718},
}
```

This paper presents a new robustified data-driven fault detection approach, connected to closed-loop subspace identification. Although data-driven detection methods have recently been reported in the literature, attention has not yet been given to a robust solution coping with identification errors. The key idea of this paper is to analytically quantify the effect of the identification errors on the residual generator of a new data-driven detection approach, namely FICSI. The comparisons of the proposed robust FICSI detection scheme with both its nominal counterpart and the nominal data-driven PSA solutions have verified the effectiveness of accounting the identification errors in improving the performance of the data-driven detection scheme.

```
@inproceedings{diva2:636214,
author = {Dong, Jianfei and Verhaegen, Michael and Gustafsson, Fredrik},
title = {{Data Driven Fault Detection with Robustness to Uncertain Parameters Identified in Closed Loop}},
booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control},
year = {2010},
pages = {750--755},
}
```

This paper presents an integrity monitoring method for tight integration of an Inertial Measurement Unit (IMU) and a GPS receiver. The method is applied to data from a Maxus sounding rocket used for microgravity research. It is crucial to determine the rocket position during launch to ensure a safe landing location. Today, the navigation relies on IMU integration only. Involving a GPS receiver enhances the position accuracy but there is a need for protection against faulty satellite range measurements. Monitoring over a sequence of the measurements gives higher confidence to the tests.

```
@inproceedings{diva2:636210,
author = {Törnqvist, David and Helmersson, Anders and Gustafsson, Fredrik},
title = {{Window Based GPS Integrity Test using Tight GPS/IMU Integration Applied to a Sounding Rocket}},
booktitle = {Proceedings of the 2010 IEEE Aerospace Conference},
year = {2010},
}
```

A framework for Iterative Learning Control (ILC) is derived when the ILC algorithm is based on estimates from an observer. Under the assumption that the ILC input converges to a bounded signal, a general expression for the asymptotic error of the controlled variable is given. The asymptotic error is then discussed when the ILC algorithm is based on different errors and it is exempliﬁed by an ILC algorithm applied to a ﬂexible two-mass model of a robot joint.

```
@inproceedings{diva2:636165,
author = {Wall\'{e}n, Johanna and Norrlöf, Mikael and Gunnarsson, Svante},
title = {{A Framework for Analysis of Observer-Based ILC}},
booktitle = {Proceedings of Reglermöte 2010},
year = {2010},
}
```

System Identification for linear systems and models is a well established and mature topic. Identifying nonlinear models is a much more rich and demanding problem area. In this presentation some major approaches and concepts for that are outlined.

```
@inproceedings{diva2:636157,
author = {Ljung, Lennart},
title = {{Approaches to Identification of Nonlinear Systems}},
booktitle = {Proceedings of the 29th Chinese Control Conference},
year = {2010},
}
```

This paper summarizes previous work on tool position estimation on industrial manipulators, and emphasize the problems that must be taken care of in order to get a satisfied result. The acceleration of the robot tool, measured by an accelerometer, together with measurements of motor angles are used. The states are estimated with an extended Kalman filter. A method for tuning the covariance matrices for the noise, used in the observer, is suggested. The work has been focused on a robot with two degrees of freedom.

```
@inproceedings{diva2:606591,
author = {Axelsson, Patrik and Norrlöf, Mikael and Wernholt, Erik and Gustafsson, Fredrik},
title = {{Extended Kalman Filter Applied to Industrial Manipulators}},
booktitle = {Proceedings of Reglermöte 2010},
year = {2010},
}
```

The particle filter provides a general solution to the nonlinear filtering problem with arbitrarily accuracy. However, the curse of dimensionality prevents its application in cases where the state dimensionality is high. Further, estimation of stationary parameters is a known challenge in a particle filter framework. We suggest a marginalization approach for the case of unknown noise distribution parameters that avoid both aforementioned problem. First, the standard approach of augmenting the state vector with sensor offsets and scale factors is avoided, so the state dimension is not increased. Second, the mean and covariance of both process and measurement noises are represented with parametric distributions, whose statistics are updated adaptively and analytically using the concept of conjugate prior distributions. The resulting marginalized particle filter is applied to and illustrated with a standard example from literature.

```
@inproceedings{diva2:512129,
author = {Saha, Saikat and Özkan, Emre and Gustafsson, Fredrik and Smidl, Vaclav},
title = {{Marginalized Particle Filters for Bayesian Estimation of Gaussian Noise Parameters}},
booktitle = {Proceedings of the 13th Conference on Information Fusion},
year = {2010},
}
```

The theory and applications of the particle filter (PF) have developed tremendously during the past two decades. However, there appear to be no version of the PF readily applicable to the case of dependent process and measurement noise. This is in contrast to the Kalman filter, where the case of correlated noise is a standard modification. Further, the fact that sampling continuous time models give dependent noise processes is an often neglected fact in literature. We derive the optimal proposal distribution in the PF for general and Gaussian noise processes, respectively. The main result is a modified prediction step. It is demonstrated that the original Bootstrap particle filter gets a particular simple and explicit form for dependent Gaussian noise. Finally, the practical importance of dependent noise is motivated in terms of sampling of continuous time models.

```
@inproceedings{diva2:512125,
author = {Gustafsson, Fredrik and Saha, Saikat},
title = {{Particle Filtering with Dependent Noise}},
booktitle = {Proceedings of the 13th Conference on Information Fusion},
year = {2010},
}
```

Situation awareness for vehicular safety and autonomy functions includes knowledge of the drivable area. This area is normally constrained between stationary road-side objects as guard-rails, curbs, ditches and vegetation. We consider these as extended objects modeled by polynomials along the road, and propose an algorithm to track each polynomial based on noisy range and bearing detections, typically from a radar. A straightforward Kalman filter formulation of the problem suffers from the errors-in-variables (EIV) problem in that the noise enters the system model. We propose an EIV modification of the Kalman filter and demonstrates its usefulness using radar data from public roads.

```
@inproceedings{diva2:374824,
author = {Lundquist, Christian and Orguner, Umut and Gustafsson, Fredrik},
title = {{Estimating Polynomial Structures from Radar Data}},
booktitle = {Proceedings of the 13th International Conference on Information Fusion},
year = {2010},
address = {Edinburgh, Scotland},
}
```

This work is concerned with the problem of multi-sensor multi-target tracking of stationary road side objects, i.e. guard rails and parked vehicles, in the context of automotive active safety systems. Advanced active safety applications, such as collision avoidance by steering, rely on obtaining a detailed map of the surrounding infrastructure to accurately assess the situation. Here, this map consists of the position of objects, represented by a random finite set (RFS) of multi-target states and we propose to describe the map as the spatial stationary object intensity. This intensity is the first order moment of a multi-target RFS representing the position of stationary objects and it is calculated using a Gaussian mixture probability hypothesis density (GM-PHD) filter.

```
@inproceedings{diva2:374832,
author = {Lundquist, Christian and Danielsson, Lars and Gustafsson, Fredrik},
title = {{Random Set Based Road Mapping using Radar Measurements}},
booktitle = {Proceedings of the 18th European Signal Processing Conference},
year = {2010},
pages = {219--223},
}
```

Reducing the overhead required for tracing mobile devices is one of the major aspects in the study of mobility management of a cellular network. The Long Term Evolution (LTE) systems give a more flexible configuration of Tracking Area (TA) design by means of Tracking Area List (TAL). Being a novel concept, TAL goes beyond the capability of the conventional TA approach. Although TAL is expected to be able to reduce the overall signaling overhead by overcoming a couple of major limitations of the conventional TA concept, how to apply TAL in large scale networks, remains unexplored. In this paper, we present a novel approach for allocating and assigning TA lists. The approach does not require any data other than what is needed for conventional TA design. We present numerical results to illustrate the approach for a realistic network of Lisbon city. The experiments demonstrate the ability of TAL in reducing the signaling overhead compared to the conventional TA concept.

```
@inproceedings{diva2:426588,
author = {Modarres Razavi, Sara and Yuan, Di and Gunnarsson, Fredrik and Moe, Johan},
title = {{Exploiting Tracking Area List for Improving Signaling Overhead in LTE}},
booktitle = {Proceedings of IEEE 71st Vehicular Technology Conference (VTC 2010-Spring)},
year = {2010},
series = {Vehicular Technology Conference},
volume = {CFP10VTC},
pages = {1--5},
publisher = {IEEE},
}
```

Reducing the signaling overhead for tracing user equipment (UE), while maintaining the improved performance over time despite the changes in UE location and mobility patterns, is a challenging issue in the area of mobility management. Flexibility and automatic reconfiguration are two significant features in Long Term Evolution (LTE) systems. The Tracking Area List (TAL) is a novel concept in LTE systems, which allows a more flexible configurations, expecting to reduce the overall signaling overhead. In this paper, we first present a ”rule of thumb” method to allocate and assign TALs for a network. The easily applied approach does not require any data other than what is available for conventional TA design. Second we compare the performance of an optimum conventional TA design with the suggested TAL design for a large scale network in Lisbon, Portugal. A thorough computation is done to make a justified evaluation. We follow the comparison during specific time intervals for one complete day, and we illustrate the performance of reconfiguration for each approach. The results clearly demonstrate the ability of dynamic TAL in reducing the signaling overhead and maintaining a good performance due to reconfiguration compared to the conventional TA design.

```
@inproceedings{diva2:426584,
author = {Modarres Razavi, Sara and Yuan, Di and Gunnarsson, Fredrik and Moe, Johan},
title = {{Dynamic Tracking Area List configuration and performance evaluation in LTE}},
booktitle = {IEEE GLOBECOM Workshops (GC Wkshps), 6-10 December, Miami, USA},
year = {2010},
publisher = {IEEE},
}
```

The primary contribution of this paper is an algorithm capable of identifying parameters in certain mixed linear/nonlinear state-space models, containing conditionally linear Gaussian substructures. More specifically, we employ the standard maximum likelihood framework and derive an expectation maximization type algorithm. This involves a nonlinear smoothing problem for the state variables, which for the conditionally linear Gaussian system can be efficiently solved using a so called Rao-Blackwellized particle smoother (RBPS). As a secondary contribution of this paper we extend an existing RBPS to be able to handle the fully interconnected model under study.

```
@inproceedings{diva2:380236,
author = {Lindsten, Fredrik and Schön, Thomas},
title = {{Identification of Mixed Linear/Nonlinear State-Space Models}},
booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control},
year = {2010},
pages = {6377--6382},
}
```

A UAV navigation system relying on GPS is vulnerable to signal failure, making a drift free backup system necessary. We introduce a vision based geo-referencing system that uses pre-existing maps to reduce the long term drift. The system classifies an image according to its environmental content and thereafter matches it to an environmentally classified map over the operational area. This map matching provides a measurement of the absolute location of the UAV, that can easily be incorporated into a sensor fusion framework. Experiments show that the geo-referencing system reduces the long term drift in UAV navigation, enhancing the ability of the UAV to navigate accurately over large areas without the use of GPS.

```
@inproceedings{diva2:380787,
author = {Lindsten, Fredrik and Callmer, Jonas and Ohlsson, Henrik and Törnqvist, David and Schön, Thomas and Gustafsson, Fredrik},
title = {{Geo-Referencing for UAV Navigation using Environmental Classification}},
booktitle = {Proceedings of the 2010 IEEE International Conference on Robotics and Automation},
year = {2010},
pages = {1420--1425},
}
```

In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested sub-problems and then handles the two nested sub-problems using PFs. The DPF has an advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and thus can be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results from a numerical example indicates that the DPF has a potential to achieve the same level of performance as the regular PF, in a shorter execution time.

```
@inproceedings{diva2:380831,
author = {Chen, Tianshi and Schön, Thomas and Ohlsson, Henrik and Ljung, Lennart},
title = {{Decentralization of Particle Filters Using Arbitrary State Decomposition}},
booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control},
year = {2010},
pages = {7383--7388},
}
```

The expectation maximisation (EM) algorithm has proven to be effective for a range of identification problems. Unfortunately, the way in which the EM algorithm has previously been applied has proven unsuitable for the commonly employed innovations form model structure. This paper addresses this problem, and presents a previously unexamined method of EM algorithm employment. The results are profiled, which indicate that a hybrid EM/gradient-search technique may in some cases outperform either a pure EM or a pure gradient-based search approach.

```
@inproceedings{diva2:380830,
author = {Wills, Adrian and Schön, Thomas and Ninness, Brett},
title = {{Estimating State-Space Models in Innovations Form using the Expectation Maximisation Algorithm}},
booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control},
year = {2010},
pages = {5524--5529},
}
```

This paper presents a novel approach to the estimation of a general class of dynamic nonlinear system models. The main contribution is the use of a tool from mathematical statistics, known as Fishers’ identity, to establish how so-called “particle smoothing” methods may be employed to compute gradients of maximum-likelihood and associated prediction error cost criteria.

```
@inproceedings{diva2:380819,
author = {Ninness, Brett and Wills, Adrian and Schön, Thomas},
title = {{Estimation of General Nonlinear State-Space Systems}},
booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control},
year = {2010},
pages = {6371--6376},
}
```

An example of how entrepreneurship can be integrated into Design-Build-Test (DBT) project courses is presented. The example is taken from the engineering program Applied Physics and Electrical Engineering at Linköping University, where entrepreneurship has been introduced in ten different DBT project courses related to the specializations of the program. The purpose of the entrepreneurship part is that the students shall acquire knowledge and abilities within the general area of entrepreneurship with particular focus on business planning for new ventures. The organization and execution of the entrepreneurship activities are described in detail together with a summary of the experiences from the first year. The results of the entrepreneurship activities within the project courses are positive and will be further developed, with emphasis on the connections between project ideas and technical contents of the courses.

```
@inproceedings{diva2:377286,
author = {Gunnarsson, Svante and Klofsten, Magnus and Bergek, Anna},
title = {{Integrating Entrepreneurship in DBT Project Courses at Linköping University}},
booktitle = {Proceedings of the 6th International CDIO Conference},
year = {2010},
}
```

Starting from Maxwell's equations, we derive a sensor model for three-axis magnetometers suitable for localization and tracking applications. The model depends on the relative position between the sensor and the target, and a physical magnetic multipole model of the target. Both point targets (far-field) and extended target (near-field) models are provided. The models are validated on data taken from various road vehicles. The suitability of magnetometers for tracking is analyzed in terms of local observability and Cramér Rao lower bound as a function of the sensor positions in a two sensor scenario. Results from field test data indicate excellent tracking of position and velocity of the target, as well as identification of the magnetic target model suitable for target classification.

```
@inproceedings{diva2:379471,
author = {Wahlström, Niklas and Callmer, Jonas and Gustafsson, Fredrik},
title = {{Magnetometers for Tracking Metallic Targets}},
booktitle = {Proceedings of 13th International Conference on Information Fusion},
year = {2010},
}
```

We consider stand still detection for indoor localization based on observations from a foot-mounted inertial measurement unit (IMU). The main contribution is a statistical framework for stand-still detection, which is a fundamental step in zero velocity update (ZUPT) to reduce the drift from cubic to linear in time. First, the observations are transformed to a test statistic having non-central chi-square distribution during zero velocity. Second, a hidden Markov model is used to describe the mode switching between stand still, walking, running, crawling and other possible movements. The resulting algorithm computes the probability of being in each mode, and it is easily extendable to a dynamic navigation framework where map information can be included. Results of first mode probability estimation, second map matching without ZUPT and third step length estimation with ZUPT are provided.

```
@inproceedings{diva2:379362,
author = {Callmer, Jonas and Törnqvist, David and Gustafsson, Fredrik},
title = {{Probabilistic Stand Still Detection using Foot Mounted IMU}},
booktitle = {Proceedings of the 13th International Conference on Information Fusion},
year = {2010},
}
```

Synthetic Aperture Radar (SAR) equipment is an all-weather radar imaging system that can create high resolution images by means of utilising the movement of the ﬂying platform. Accurate knowledge of the ﬂown trajectory is essential in order to get focused images. Recently SAR systems are becoming more used on smaller and cheaper ﬂying platforms like Unmanned Aerial Vehicles (UAV). Since UAVs in general have navigation systems with poorer performance than manned aircraft, the resulting images will inevitably be unfocused. At the same time, the unfocused images carry the information about the platforms trajectory that can be utilised. Here a way of using SAR images and their focus measure in a sensor fusion framework in order to simultaneously obtain both improved images and trajectory estimate is presented. The method is illustrated on a simple simulated example with promising results. Finally a discussion about the results and future work is given.

```
@inproceedings{diva2:374840,
author = {Sjanic, Zoran and Gustafsson, Fredrik},
title = {{Simultaneous Navigation and SAR Auto-Focusing}},
booktitle = {Proceedings of 13th International Conference on Information Fusion},
year = {2010},
}
```

When designing robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.

The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities.

The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method performs slightly better.

```
@inproceedings{diva2:378133,
author = {Ankelhed, Daniel and Helmersson, Anders and Hansson, Anders},
title = {{A Primal-Dual Method for Low Order H-Infinity Controller Synthesis}},
booktitle = {Proceedings of Reglermöte 2010},
year = {2010},
address = {Lund},
}
```

Finite-frequency H2 analysis is relevant to a number of problems in which a priori information is available on the frequency domain of interest. This paper addresses the problem of analyzing robust finite-frequency H2 performance of systems with structured uncertainties. An upper bound on this measure is provided by exploiting convex optimization tools for robustness analysis and the notion of finite-frequency Gramians. An application to a comfort analysis problem for an aircraft aeroelastic model is presented.

```
@inproceedings{diva2:377988,
author = {Wallin, Ragnar and Masi, Alfio and Garulli, Andrea and Hansson, Anders},
title = {{Robust Finite-Frequency H2 Analysis}},
booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control},
year = {2010},
pages = {6876--6881},
}
```

Many control related problems can be cast as semidefinite programs but, even though there exist polynomial time algorithms and good publicly available solvers, the time it takes to solve these problems can be long. Something many of these problems have in common, is that some of the variables enter as matrix valued variables. This leads to a low-rank structure in the basis matrices which can be exploited when forming the Newton equations. In this paper, we describe how this can be done, and show how our code can be used when using SDPT3. The idea behind this is old and is implemented in LMI Lab, but we show that when using a modern algorithm, the computational time can be reduced. Finally, we describe how the modeling language YALMIP is changed in such a way that our code can be interfaced using standard YALMIP commands, which greatly simplifies for the user.

```
@inproceedings{diva2:377915,
author = {Falkeborg, Rikard and Löfberg, Johan and Hansson, Anders},
title = {{Low-Rank Exploitation in Semidefinite Programming for Control}},
booktitle = {Proceedings of Reglermöte 2010},
year = {2010},
}
```

Direct Torque Control (DTC) is considered as one of the latest and most efficient techniques that can be used for the speed and/or position tracking control problem of induction motor drives. However, the main drawbacks of classical DTC are the variable switching frequency that could exceed the maximum allowable switching frequency of inverters and also the ripples it has over the current and torque, especially at low speed tracking. It has been shown that applying Model Predictive Control (MPC) to a Linear Induction Motor (LIM) leads to a much better speed tracking performance. MPC provides the optimal 3-phase primary voltages necessary for speed tracking using a Pulse Width Modulation (PWM) inverter. The main inherent drawbacks of the MPC strategy are its high switching frequency and also its heavy computational load which makes it inapplicable in real-time. This paper presents a new analytical approach based on the MPC strategy. The new analytical approach controls directly the inverter switches. Hence the PWM inverter is not needed. It computes the optimal position transitions sequence of the inverter switches to track the speed reference trajectory. The proposed analytical nonlinear MPC controller includes an integral action to reduce the steady state error. The proposed controller admits real-time implementation. Simulation results show that the new analytical approach has good tracking properties at the same time as it reduces the average inverter switching frequency by 93 % as compared to classical DTC.

```
@inproceedings{diva2:377907,
author = {Hansson, Anders and Thomas, Jean},
title = {{Speed Tracking of Linear Induction Motor:
an Analytical Nonlinear Model Predictive Controller}},
booktitle = {Proceedings of the 2010 IEEE International Conference on Control Applications},
year = {2010},
pages = {1939--1944},
}
```

Many control related problems can be cast as semidefinite programs but, even though there exist polynomial time algorithms and good publicly available solvers, the time it takes to solve these problems can be long. Something many of these problems have in common, is that some of the variables enter as matrix valued variables. This leads to a low-rank structure in the basis matrices which can be exploited when forming the Newton equations. In this paper, we describe how this can be done, and show how our code can be used when using SDPT3. The idea behind this is old and is implemented in LMI Lab, but we show that when using a modern algorithm, the computational time can be reduced. Finally, we describe how the modeling language YALMIP is changed in such a way that our code can be interfaced using standard YALMIP commands, which greatly simplifies for the user.

```
@inproceedings{diva2:377904,
author = {Falkeborn, Rikard and Löfberg, Johan and Hansson, Anders},
title = {{Low-Rank Exploitation in Semidefinite Programming for Control}},
booktitle = {Proceedings of the 2010 IEEE International Symposium on Computer-Aided Control System Design},
year = {2010},
pages = {24--28},
}
```

This paper presents a combined Point Mass Filter (PMF) and Particle Filter (PF), which utilizes the support of the PMF and the high particle density in the PF close to the current estimate. The result is a filter robust to unexpected process events but still with low error covariance. This filter is especially useful for target tracking applications, where target maneuvers suddenly can change unpredictably.

```
@inproceedings{diva2:376437,
author = {Orguner, Umut and Skoglar, Per and Törnqvist, David and Gustafsson, Fredrik},
title = {{Combined Point Mass and Particle Filter for Target Tracking}},
booktitle = {Proceedings of the 2010 IEEE Aerospace Conference},
year = {2010},
}
```

This paper presents a method to achieve multi target tracking using acoustic power measurements obtained from an acoustic sensor network. We first present a novel concept called emitted power density (EPD) which is an aggregate information state that holds the emitted power distribution of all targets in the scene over the target state space. It is possible to find prediction and measurement update formulas for an EPD which is conceptually similar to a probability hypothesis density (PHD). We propose a Gaussian process based representation for making the related EPD updates using Kalman filter formulas. These updates constitute a recursive EPD-filter which is based on the discretization of the position component of the target state space. The results are illustrated on a real data scenario where experiments are done with two targets constrained to a road segment.

```
@inproceedings{diva2:376434,
author = {Orguner, Umut and Gustafsson, Fredrik},
title = {{Multi Target Tracking with Acoustic Power Measurements using Emitted Power Density}},
booktitle = {Proceedings of the 13th International Conference on Information Fusion},
year = {2010},
}
```

This paper investigates the problem of propagation delayed measurements in a particle filtering scenario. Based on implicit constraints specified by target dynamics and physics rules of signal propagation, authors apply the ideas that were first proposed in their previous work to the case of particle filters. Unlike the deterministic sampling based approach called propagation delayed measurement filter (PDMF) in their previous work, the new algorithm proposed here (called as PDM particle filter (PDM-PF)) has the potential to be used with general nonlinear models. This advantage and the estimation results of PDM-PF are illustrated in a challenging target tracking scenario by making comparisons to PDMF along with some other alternative particle filters.

```
@inproceedings{diva2:376425,
author = {Orguner, Umut and Gustafsson, Fredrik},
title = {{Particle Filtering with Propagation Delayed Measurements}},
booktitle = {Proceedings of the 2010 IEEE Aerospace Conference},
year = {2010},
pages = {1--9},
}
```

This paper presents a new solution to the loop closing problem for 3D point clouds. Loop closing is the problem of detecting the return to a previously visited location, and constitutes an important part of the solution to the Simultaneous Localisation and Mapping (SLAM) problem. It is important to achieve a low level of false alarms, since closing a false loop can have disastrous effects in a SLAM algorithm. In this work, the point clouds are described using features, which efficiently reduces the dimension of the data by a factor of 300 or more. The machine learning algorithm AdaBoost is used to learn a classifier from the features. All features are invariant to rotation, resulting in a classifier that is invariant to rotation. The presented method does neither rely on the discretisation of 3D space, nor on the extraction of lines, corners or planes. The classifier is extensively evaluated on publicly available outdoor and indoor data, and is shown to be able to robustly and accurately determine whether a pair of point clouds is from the same location or not. Experiments show detection rates of 63% for outdoor and 53% for indoor data at a false alarm rate of 0%. Furthermore, the classifier is shown to generalise well when trained on outdoor data and tested on indoor data in a SLAM experiment.

```
@inproceedings{diva2:375007,
author = {Granström, Karl and Schön, Thomas},
title = {{Learning to Close the Loop from 3D Point Clouds}},
booktitle = {Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems},
year = {2010},
pages = {2089--2095},
}
```

In extended target tracking, targets potentially produce more than one measurement per time step. Multiple extended targets are therefore usually hard to track, due to the resulting complex data association. The main contribution of this paper is the implementation of a Probability Hypothesis Density (PHD) filter for tracking of multiple extended targets. A general modification of the PHD filter to handle extended targets has been presented recently by Mahler, and the novelty in this work lies in the realisation of a Gaussian mixture PHD filter for extended targets. Furthermore, we propose a method to easily partition the measurements into a number of subsets, each of which is supposed to contain measurements that all stem from the same source. The method is illustrated in simulation examples, and the advantage of the implemented extended target PHD filter is shown in a comparison with a standard PHD filter.

```
@inproceedings{diva2:374864,
author = {Granström, Karl and Lundquist, Christian and Orguner, Umut},
title = {{A Gaussian Mixture PHD Filter for Extended Target Tracking}},
booktitle = {Proceedings of the 13th International Conference on Information Fusion},
year = {2010},
}
```

Friction is the result of complex interactions between contacting surfaces in a nanoscale perspective. Depending on the application, the different models available are more or less suitable. Available static friction models are typically considered to be dependent only on relative speed of interacting surfaces. However, it is known that friction can be affected by other factors than speed. In this paper, static friction in robot joints is studied with respect to changes in joint angle, load torque and temperature. The effects of these variables are analyzed by means of experiments on a standard industrial robot. Justified by their significance, load torque and temperature are included in an extended static friction model. The proposed model is validated in a wide operating range, reducing the average error a factor of 6 when compared to a standard static friction model.

```
@inproceedings{diva2:375128,
author = {Carvalho Bittencourt, Andr\'{e} and Wernholt, Erik and Sander-Tavallaey, Shiva and Brogårdh, Torgny},
title = {{An Extended Friction Model to capture Load and Temperature effects in Robot Joints}},
booktitle = {Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems},
year = {2010},
pages = {6161--6167},
}
```

The main contribution of this work is a novel calibration method to determine the clock parameters of the UWB receivers as well as their 3D positions. It exclusively uses time-of-arrival measurements, thereby removing the need for the typically labor-intensive and time-consuming process of surveying the receiver positions. Experiments show that the method is capable of accurately calibrating a UWB setup within minutes.

```
@inproceedings{diva2:375040,
author = {Hol, Jeroen D and Schön, Thomas and Gustafsson, Fredrik},
title = {{Ultra-Wideband Calibration for Indoor Positioning}},
booktitle = {Proceedings of the 2010 IEEE International Conference on Ultra-Wideband},
year = {2010},
}
```

The presence of abrupt changes, such as impulsive disturbances and load disturbances, make state estimation considerably more difficult than the standard setting with Gaussian process noise. Nevertheless, this type of disturbances is commonly occurring in applications which makes it an important problem. An abrupt change often introduces a jump in the state and the problem is therefore readily treated by change detection techniques. In this paper, we take a rather different approach. The state smoothing problem for linear state space models is here formulated as a least-squares problem with sum-of-norms regularization, a generalization of the ℓ1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade off fit and the number of jumps.

```
@inproceedings{diva2:375029,
author = {Ohlsson, Henrik and Gustafsson, Fredrik and Ljung, Lennart and Boyd, Stephen},
title = {{State Smoothing by Sum-of-Norms Regularization}},
booktitle = {Proceedings of the 49th Conference on Decision and Control},
year = {2010},
pages = {2880--2885},
}
```

In this paper we present a regularization of an H_{2}-minimization based LPV-model generation algorithm. Our goal is to take care of uncertainties in the data, and obtain more robust models when we have few data. We give an interpretation of the regularization, which shows that the regularization has connections to robust optimization and worst-case approaches. We present how to effectively calculate the original cost function and its gradient, and extend these ideas to the regularized cost function and its gradient. A few examples, illustrating effects of both uncertain and few data, are finally presented to show the validity of the regularization.

```
@inproceedings{diva2:375026,
author = {Petersson, Daniel and Löfberg, Johan},
title = {{Robust Generation of LPV State-Space Models using a Regularized H2-Cost}},
booktitle = {Proceedings of the 2010 IEEE International Symposium on Computer-Aided Control System Design},
year = {2010},
pages = {1170--1175},
}
```

Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements.We formulate a classical regularization approach, focused on ﬁnite impulse response (FIR) models, and ﬁnd that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression.

```
@inproceedings{diva2:360030,
author = {Chen, Tianshi and Ohlsson, Henrik and Ljung, Lennart},
title = {{On the Estimation of Transfer Functions, Regularizations and Gaussian Processes -- Revisited}},
booktitle = {Proceedings of the 18th IFAC World Congress},
year = {2010},
pages = {2303--2308},
}
```

Many tracking problems are split into two sub-problems, first a smooth reference trajectory is generated that meet the control design objectives, and then a closed loop control system is designed to follow this reference trajectory as well as possible. Applications of this kind include (autonomous) vehicle navigation systems and robotics. Typically, a spline model is used for trajectory generation and another physical and dynamical model is used for the control design. Here we propose a direct approach where the dynamical model is used to generate a control signal that takes the state trajectory through the waypoints specified in the design goals. The strength of the proposed formulation is the methodology to obtain a control signal with compact representation and that changes only when needed, something often wanted in tracking. The formulation takes the shape of a constrained least-squares problem with sum-of-norms regularization, a generalization of the ℓ1-regularization. The formulation also gives a tool to, e.g. in model predictive control, prevent chatter in the input signal, and also select the most suitable instances for applying the control inputs.

```
@inproceedings{diva2:360023,
author = {Ohlsson, Henrik and Gustafsson, Fredrik and Ljung, Lennart and Boyd, Stephen},
title = {{Trajectory Generation Using Sum-of-Norms Regularization}},
booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control},
year = {2010},
pages = {540--545},
}
```

In aircraft development, it is crucial to understand and evaluate behaviour, performance, safety and other aspects of subsystems before and after they are physically available for testing. Simulation models are used to gain knowledge in order to make decisions at all development stages.

This paper describes the development of Saab Gripen´s vehicle systems and some methods and challenges related to uncertainties in test and model data. The ability to handle uncertain information and lack of information is the key to success in early design. The vehicle systems comprise fuel, environment control system (ECS), hydraulic, auxiliary power, escape, electrical power and landing gear system.

```
@inproceedings{diva2:358781,
author = {Steinkellner, Sören and Andersson, Henric and Gavel, Hampus and Lind, Ingela and Krus, Petter},
title = {{Modeling and Simulation of Saab Gripens Vehicle Systems, Challenges in Processes and Data Uncertainties}},
booktitle = {27th Congress of the International Councilof the Aeronautical Sciences, ICAS2010, September 19-24, Nice, France},
year = {2010},
}
```

A common computer vision task is navigation and mapping. Many indoor navigation tasks require depth knowledge of flat, unstructured surfaces (walls, floor, ceiling). With passive illumination only, this is an ill-posed problem. Inspired by small children using a torchlight, we use a spotlight for active illumination. Using our torchlight approach, depth and orientation estimation of unstructured, flat surfaces boils down to estimation of ellipse parameters. The extraction of ellipses is very robust and requires little computational effort.

```
@inproceedings{diva2:358053,
author = {Felsberg, Michael and Larsson, Fredrik and Wang, Han and Ynnerman, Anders and Schön, Thomas},
title = {{Torchlight Navigation}},
booktitle = {Proceedings of the 20th International Conferenceon Pattern Recognition},
year = {2010},
series = {International Conference on Pattern Recognition},
pages = {302--306},
}
```

The correct spatial registration between virtual and real objects in optical see-through augmented reality implies accurate estimates of the user’s eyepoint relative to the location and orientation of the display surface. A common approach is to estimate the display parameters through a calibration procedure involving a subjective alignment exercise. Human postural sway and targeting precision contribute to imprecise alignments, which in turn adversely affect the display parameter estimation resulting in registration errors between virtual and real objects. The technique commonly used has its origin incomputer vision, and calibrates stationary cameras using hundreds of correspondence points collected instantaneously in one video frame where precision is limited only by pixel quantization and image blur. Subsequently the input noise level is several order of magnitudes greater when a human operator manually collects correspondence points one by one. This paper investigates the effect of human alignment noise on view parameter estimation in an optical see-through head mounted display to determine how well astandard camera calibration method performs at greater noise levels than documented in computer vision literature. Through Monte-Carlo simulations we show that it is particularly difficult to estimate the user’s eyepoint in depth, but that a greater distribution of correspondence points in depth help mitigate the effects of human alignment noise.

```
@inproceedings{diva2:356619,
author = {Axholt, Magnus and Skoglund, Martin and Peterson, Stephen and Cooper, Matthew and Schön, Thomas and Gustafsson, Fredrik and Ynnerman, Anders and Ellis, Stephen},
title = {{Optical See-Through Head Mounted Display:
Direct Linear Transformation Calibration Robustness in the Presence of User Alignment Noise}},
booktitle = {Proceedings of the 54th Annual Meeting of the Human Factors and Ergonomics Society},
year = {2010},
}
```

## Theses

In this thesis, we consider the problem of estimating position and orientation (6D pose) using inertial sensors (accelerometers and gyroscopes). Inertial sensors provide information about the change in position and orientation at high sampling rates. However, they suffer from integration drift and hence need to be supplemented with additional sensors. To combine information from the inertial sensors with information from other sensors we use probabilistic models, both for sensor fusion and for sensor calibration.

Inertial sensors can be supplemented with magnetometers, which are typically used to provide heading information. This relies on the assumption that the measured magnetic field is equal to a constant local magnetic field and that the magnetometer is properly calibrated. However, the presence of metallic objects in the vicinity of the sensor will make the first assumption invalid. If the metallic object is rigidly attached to the sensor, the magnetometer can be calibrated for the presence of this magnetic disturbance. Afterwards, the measurements can be used for heading estimation as if the disturbance was not present. We present a practical magnetometer calibration algorithm that is experimentally shown to lead to improved heading estimates. An alternative approach is to exploit the presence of magnetic disturbances in indoor environments by using them as a source of position information. We show that in the vicinity of a magnetic coil it is possible to obtain accurate position estimates using inertial sensors, magnetometers and knowledge of the magnetic field induced by the coil.

We also consider the problem of estimating a human body’s 6D pose. For this, multiple inertial sensors are placed on the body. Information from the inertial sensors is combined using a biomechanical model which represents the human body as consisting of connected body segments. We solve this problem using an optimization-based approach and show that accurate 6D pose estimates are obtained. These estimates accurately represent the relative position and orientation of the human body, i.e. the shape of the body is accurately represented but the absolute position can not be determined.

To estimate absolute position of the body, we consider the problem of indoor positioning using time of arrival measurements from an ultra-wideband (uwb) system in combination with inertial measurements. Our algorithm uses a tightlycoupled sensor fusion approach and is shown to lead to accurate position and orientation estimates. To be able to obtain position information from the uwb measurements, it is imperative that accurate estimates of the receivers’ positions and clock offsets are known. Hence, we also present an easy-to-use algorithm to calibrate the uwb system. It is based on a maximum likelihood formulation and represents the uwb measurements assuming a heavy-tailed asymmetric noise distribution to account for measurement outliers.

```
@phdthesis{diva2:719206,
author = {Kok, Manon},
title = {{Probabilistic modeling for positioning applications using inertial sensors}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1656}},
year = {2014},
address = {Sweden},
}
```

Nonlinear state space models (SSMs) are a useful class of models to describe many different kinds of systems. Some examples of its applications are to model; the volatility in financial markets, the number of infected persons during an influenza epidemic and the annual number of major earthquakes around the world. In this thesis, we are concerned with state inference, parameter inference and input design for nonlinear SSMs based on sequential *Monte Carlo* (SMC) methods.

The state inference problem consists of estimating some latent variable that is not directly observable in the output from the system. The parameter inference problem is concerned with fitting a pre-specified model structure to the observed output from the system. In input design, we are interested in constructing an input to the system, which maximises the information that is available about the parameters in the system output. All of these problems are analytically intractable for nonlinear SSMs. Instead, we make use of SMC to approximate the solution to the state inference problem and to solve the input design problem. Furthermore, we make use of *Markov chain Monte Carlo* (MCMC) and Bayesian optimisation (BO) to solve the parameter inference problem.

In this thesis, we propose new methods for parameter inference in SSMs using both Bayesian and maximum likelihood inference. More specifically, we propose a new proposal for the particle Metropolis-Hastings algorithm, which includes gradient and Hessian information about the target distribution. We demonstrate that the use of this proposal can reduce the length of the burn-in phase and improve the mixing of the Markov chain.

Furthermore, we develop a novel parameter inference method based on the combination of BO and SMC. We demonstrate that this method requires a relatively small amount of samples from the analytically intractable likelihood, which are computationally costly to obtain. Therefore, it could be a good alternative to other optimisation based parameter inference methods. The proposed BO and SMC combination is also extended for parameter inference in nonlinear SSMs with intractable likelihoods using approximate Bayesian computations. This method is used for parameter inference in a stochastic volatility model with -stable returns using real-world financial data.

Finally, we develop a novel method for input design in nonlinear SSMs which makes use of SMC methods to estimate the expected information matrix. This information is used in combination with graph theory and convex optimisation to estimate optimal inputs with amplitude constraints. We also consider parameter estimation in ARX models with Student-t innovations and unknown model orders. Two different algorithms are used for this inference: reversible Jump Markov chain Monte Carlo and Gibbs sampling with sparseness priors. These methods are used to model real-world EEG data with promising results.

```
@phdthesis{diva2:718460,
author = {Dahlin, Johan},
title = {{Sequential Monte Carlo for inference in nonlinear state space models}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1652}},
year = {2014},
address = {Sweden},
}
```

One of the main tasks for an industrial robot is to move the end-effector in a predefined path with a specified velocity and acceleration. Different applications have different requirements of the performance. For some applications it is essential that the tracking error is extremely small, whereas other applications require a time optimal tracking. Independent of the application, the controller is a crucial part of the robot system. The most common controller configuration uses only measurements of the motor angular positions and velocities, instead of the position and velocity of the end-effector. The development of new cost optimised robots has introduced unwanted flexibilities in the joints and the links. The consequence is that it is no longer possible to get the desired performance and robustness by only measuring the motor angular positions.

This thesis investigates if it is possible to estimate the end-effector position using Bayesian estimation methods for state estimation, here represented by the extended Kalman filter and the particle filter. The arm-side information is provided by an accelerometer mounted at the end-effector. The measurements consist of the motor angular positions and the acceleration of the end-effector. In a simulation study on a realistic flexible industrial robot, the angular position performance is shown to be close to the fundamental Cramér-Rao lower bound. The methods are also verified in experiments on an ABB IRB4600 robot, where the dynamic performance of the position for the end-effector is significantly improved. There is no significant difference in performance between the different methods. Instead, execution time, model complexities and implementation issues have to be considered when choosing the method. The estimation performance depends strongly on the tuning of the filters and the accuracy of the models that are used. Therefore, a method for estimating the process noise covariance matrix is proposed. Moreover, sampling methods are analysed and a low-complexity analytical solution for the continuous-time update in the Kalman filter, that does not involve oversampling, is proposed.

The thesis also investigates two types of control problems. First, the norm-optimal iterative learning control (ILC) algorithm for linear systems is extended to an estimation-based norm-optimal ILC algorithm where the controlled variables are not directly available as measurements. The algorithm can also be applied to non-linear systems. The objective function in the optimisation problem is modified to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. Second, H_{∞} controllers are designed and analysed on a linear four-mass flexible joint model. It is shown that the control performance can be increased, without adding new measurements, compared to previous controllers. Measuring the end-effector acceleration increases the control performance even more. A non-linear model has to be used to describe the behaviour of a real flexible joint. An H_{∞}-synthesis method for control of a flexible joint, with non-linear spring characteristic, is therefore proposed.

```
@phdthesis{diva2:706015,
author = {Axelsson, Patrik},
title = {{Sensor Fusion and Control Applied to Industrial Manipulators}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1585}},
year = {2014},
address = {Sweden},
}
```

Aircraft are dynamic systems that naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems are becoming increasingly important as the performance and complexity of the controlled systems is constantly increasing. It is especially important in the design of control systems for fighter aircraft. These require maximum control performance in order to have the upper hand in a dogfight or when they have to outmaneuver an enemy missile. Therefore pilots often maneuver the aircraft very close to the limit of what it is capable of, and an automatic system (called flight envelope protection system) against violating the restrictions is a necessity.

In other application areas, nonlinear optimal control methods have been successfully used to solve this but in the aeronautical industry, these methods have not yet been established. One of the more popular methods that are well suited to handle constraints is Model Predictive Control (MPC) and it is used extensively in areas such as the process industry and the refinery industry. Model predictive control means in practice that the control system iteratively solves an advanced optimization problem based on a prediction of the aircraft's future movements in order to calculate the optimal control signal. The aircraft's operating limitations will then be constraints in the optimization problem.

In this thesis, we explore model predictive control and derive two fast, low complexity algorithms, one for guaranteed stability and feasibility of nonlinear systems and one for reference tracking for linear systems. In reference tracking model predictive control for linear systems we build on the dual mode formulation of MPC and our goal is to make minimal changes to this framework, in order to develop a reference tracking algorithm with guaranteed stability and low complexity suitable for implementation in real time safety critical systems.

To reduce the computational burden of nonlinear model predictive control several methods to approximate the nonlinear constraints have been proposed in the literature, many working in an ad hoc fashion, resulting in conservatism, or worse, inability to guarantee recursive feasibility. Also several methods work in an iterative manner which can be quit time consuming making them inappropriate for fast real time applications. In this thesis we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefits of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence.

```
@phdthesis{diva2:690771,
author = {Simon, Daniel},
title = {{Model Predictive Control in Flight Control Design:
Stability and Reference Tracking}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1642}},
year = {2014},
address = {Sweden},
}
```

Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods.Particular emphasis is placed on the combination of SMC and MCMC in so called particle MCMC algorithms. These algorithms rely on SMC for generating samples from the often highly autocorrelated state-trajectory. A specific particle MCMC algorithm, referred to as particle Gibbs with ancestor sampling (PGAS), is suggested. By making use of backward sampling ideas, albeit implemented in a forward-only fashion, PGAS enjoys good mixing even when using seemingly few particles in the underlying SMC sampler. This results in a computationally competitive particle MCMC algorithm. As illustrated in this thesis, PGAS is a useful tool for both Bayesian and frequentistic parameter inference as well as for state smoothing. The PGAS sampler is successfully applied to the classical problem of Wiener system identification, and it is also used for inference in the challenging class of non-Markovian latent variable models.Many nonlinear models encountered in practice contain some tractable substructure. As a second problem considered in this thesis, we develop Monte Carlo methods capable of exploiting such substructures to obtain more accurate estimators than what is provided otherwise. For the filtering problem, this can be done by using the well known Rao-Blackwellized particle filter (RBPF). The RBPF is analysed in terms of asymptotic variance, resulting in an expression for the performance gain offered by Rao-Blackwellization. Furthermore, a Rao-Blackwellized particle smoother is derived, capable of addressing the smoothing problem in so called mixed linear/nonlinear state-space models. The idea of Rao-Blackwellization is also used to develop an online algorithm for Bayesian parameter inference in nonlinear state-space models with affine parameter dependencies.

```
@phdthesis{diva2:654644,
author = {Lindsten, Fredrik},
title = {{Particle filters and Markov chains for learning of dynamical systems}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1530}},
year = {2013},
address = {Sweden},
}
```

Small and medium sized Unmanned Aerial Vehicles (UAV) are today used in military missions, and will in the future find many new application areas such as surveillance for exploration and security. To enable all these foreseen applications, the UAV's have to be cheap and of low weight, which restrict the sensors that can be used for navigation and surveillance. This thesis investigates several aspects of how fusion of navigation and imaging sensors can improve both tasks at a level that would require much more expensive sensors with the traditional approach of separating the navigation system from the applications. The core idea is that vision sensors can support the navigation system by providing odometric information of the motion, while the navigation system can support the vision algorithms, used to map the surrounding environment, to be more efficient. The unified framework for this kind of approach is called Simultaneous Localisation and Mapping (SLAM) and it will be applied here to inertial sensors, radar and optical camera.

Synthetic Aperture Radar (SAR) uses a radar and the motion of the UAV to provide an image of the microwave reflectivity of the ground. SAR images are a good complement to optical images, giving an all-weather surveillance capability, but they require an accurate navigation system to be focused which is not the case with typical UAV sensors. However, by using the inertial sensors, measuring UAV's motion, and information from the SAR images, measuring how image quality depends on the UAV's motion, both higher navigation accuracy and, consequently, more focused images can be obtained. The fusion of these sensors can be performed in both batch and sequential form. For the first approach, we propose an optimisation formulation of the navigation and focusing problem while the second one results in a filtering approach. For the optimisation method the measurement of the focus in processed SAR images is performed with the image entropy and with an image matching approach, where SAR images are matched to the map of the area. In the proposed filtering method the motion information is estimated from the raw radar data and it corresponds to the time derivative of the range between UAV and the imaged scene, which can be related to the motion of the UAV.

Another imaging sensor that has been exploited in this framework is an ordinary optical camera. Similar to the SAR case, camera images and inertial sensors can also be used to support the navigation estimate and simultaneously build a three-dimensional map of the observed environment, so called inertial/visual SLAM. Also here, the problem is posed in optimisation framework leading to batch Maximum Likelihood (ML) estimate of the navigation parameters and the map. The ML problem is solved in both the straight-forward way, resulting in nonlinear least squares where both map and navigation parameters are considered as parameters, and with the Expectation-Maximisation (EM) approach. In the EM approach, all unknown variables are split into two sets, hidden variables and actual parameters, and in this case the map is considered as parameters and the navigation states are seen as hidden variables. This split enables the total problem to be solved computationally cheaper then the original ML formulation. Both optimisation problems mentioned above are nonlinear and non-convex requiring good initial solution in order to obtain good parameter estimate. For this purpose a method for initialisation of inertial/visual SLAM is devised where the conditional linear structure of the problem is used to obtain the initial estimate of the parameters. The benefits and performance improvements of the methods are illustrated on both simulated and real data.

```
@phdthesis{diva2:646587,
author = {Sjanic, Zoran},
title = {{Navigation and Mapping for Aerial Vehicles Based on Inertial and Imaging Sensors}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1533}},
year = {2013},
address = {Sweden},
}
```

This thesis is on filtering in state space models. First, we examine approximate Kalman filters for nonlinear systems, where the optimal Bayesian filtering recursions cannot be solved exactly. These algorithms rely on the computation of certain expected values. Second, the problem of filtering in linear systems that are subject to heavy-tailed process and measurement noise is addressed.

Expected values of nonlinearly transformed random vectors are an essential ingredient in any Kalman filter for nonlinear systems, because of the required joint mean vector and joint covariance of the predicted state and measurement. The problem of computing expected values, however, goes beyond the filtering context. Insights into the underlying integrals and useful simplification schemes are given for elliptically contoured distributions, which include the Gaussian and Student’s t distribution. Furthermore, a number of computation schemes are discussed. The focus is on methods that allow for simple implementation and that have an assessable computational cost. Covered are basic Monte Carlo integration, deterministic integration rules and the unscented transformation, and schemes that rely on approximation of involved nonlinearities via Taylor polynomials or interpolation. All methods come with realistic accuracy statements, and are compared on two instructive examples.

Heavy-tailed process and measurement noise in state space models can be accounted for by utilizing Student’s t distribution. Based on the expressions forconditioning and marginalization of t random variables, a compact filtering algorithm for linear systems is derived. The algorithm exhibits some similarities with the Kalman filter, but involves nonlinear processing of the measurements in form of a squared residual in one update equation. The derived filter is compared to state-of-the-art filtering algorithms on a challenging target tracking example, and outperforms all but one optimal filter that knows the exact instances at which outliers occur.

The presented material is embedded into a coherent thesis, with a concise introduction to the Bayesian filtering and state estimation problems; an extensive survey of available filtering algorithms that includes the Kalman filter, Kalman filters for nonlinear systems, and the particle filter; and an appendix that provides the required probability theory basis.

```
@phdthesis{diva2:648389,
author = {Roth, Michael},
title = {{Kalman Filters for Nonlinear Systems and Heavy-Tailed Noise}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1613}},
year = {2013},
address = {Sweden},
}
```

*H*-Optimal Modeling and Control", Linköping Studies in Science and Technology. Dissertations, No. 1528, 2013.

_{2}Mathematical models of physical systems are pervasive in engineering. These models can be used to analyze properties of the system, to simulate the system, or synthesize controllers. However, many of these models are too complex or too large for standard analysis and synthesis methods to be applicable. Hence, there is a need to reduce the complexity of models. In this thesis, techniques for reducing complexity of large linear time-invariant (lti) state-space models and linear parameter-varying (lpv) models are presented. Additionally, a method for synthesizing controllers is also presented.

The methods in this thesis all revolve around a system theoretical measure called the *H*_{2}-norm, and the minimization of this norm using nonlinear optimization. Since the optimization problems rapidly grow large, significant effort is spent on understanding and exploiting the inherent structures available in the problems to reduce the computational complexity when performing the optimization.

The first part of the thesis addresses the classical model-reduction problem of lti state-space models. Various *H _{2}* problems are formulated and solved using the proposed structure-exploiting nonlinear optimization technique. The standard problem formulation is extended to incorporate also frequency-weighted problems and norms defined on finite frequency intervals, both for continuous and discrete-time models. Additionally, a regularization-based method to account for uncertainty in data is explored. Several examples reveal that the method is highly competitive with alternative approaches.

Techniques for finding lpv models from data, and reducing the complexity of lpv models are presented. The basic ideas introduced in the first part of the thesis are extended to the lpv case, once again covering a range of different setups. lpv models are commonly used for analysis and synthesis of controllers, but the efficiency of these methods depends highly on a particular algebraic structure in the lpv models. A method to account for and derive models suitable for controller synthesis is proposed. Many of the methods are thoroughly tested on a realistic modeling problem arising in the design and flight clearance of an Airbus aircraft model.

Finally, output-feedback *H _{2}* controller synthesis for lpv models is addressed by generalizing the ideas and methods used for modeling. One of the ideas here is to skip the lpv modeling phase before creating the controller, and instead synthesize the controller directly from the data, which classically would have been used to generate a model to be used in the controller synthesis problem. The method specializes to standard output-feedback

*H*controller synthesis in the lti case, and favorable comparisons with alternative state-of-the-art implementations are presented.

_{2}```
@phdthesis{diva2:647068,
author = {Petersson, Daniel},
title = {{A Nonlinear Optimization Approach to \emph{H$_{2}$}-Optimal Modeling and Control}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1528}},
year = {2013},
address = {Sweden},
}
```

Mathematical models are commonly used in technical applications to describe the behavior of a system. These models can be estimated from data, which is known as system identification. Usually the models are used to calculate the output for a given input, but in this thesis, the estimation of inverse models is investigated. That is, we want to find a model that can be used to calculate the input for a given output. In this setup, the goal is to minimize the difference between the input and the output from the cascaded systems (system and inverse). A good model would be one that reconstructs the original input when used in series with the original system.

Different methods for estimating a system inverse exist. The inverse model can be based on a forward model, or it can be estimated directly by reversing the use of input and output in the identification procedure. The models obtained using the different approaches capture different aspects of the system, and the choice of method can have a large impact. Here, it is shown in a small linear example that a direct estimation of the inverse can be advantageous, when the inverse is supposed to be used in cascade with the system to reconstruct the input.

Inverse systems turn up in many different applications, such as sensor calibration and power amplifier (PA) predistortion. PAs used in communication devices can be nonlinear, and this causes interference in adjacent transmitting channels, which will be noise to anyone that transmits in these channels. Therefore, linearization of the amplifier is needed, and a prefilter is used, called a predistorter. In this thesis, the predistortion problem has been investigated for a type of PA, called outphasing power amplifier, where the input signal is decomposed into two branches that are amplified separately by highly efficient nonlinear amplifiers, and then recombined. If the decomposition and summation of the two parts are not perfect, nonlinear terms will be introduced in the output, and predistortion is needed.

Here, a predistorter has been constructed based on a model of the PA. In a first method, the structure of the outphasing amplifier has been used to model the distortion, and from this model, a predistorter can be estimated. However, this involves solving two nonconvex optimization problems, and the risk of obtaining a suboptimal solution. Exploring the structure of the PA, the problem can be reformulated such that the PA modeling basically can be done by solving two least-squares (LS) problems, which are convex. In a second step, an analytical description of an ideal predistorter can be used to obtain a predistorter estimate. Another approach is to compute the predistorter without a PA model by estimating the inverse directly. The methods have been evaluated in simulations and in measurements, and it is shown that the predistortion improves the linearity of the overall power amplifier system.

```
@phdthesis{diva2:647126,
author = {Jung, Ylva},
title = {{Estimation of Inverse Models Applied to Power Amplifier Predistortion}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1605}},
year = {2013},
address = {Sweden},
}
```

With the demand for more advanced fighter aircraft, relying on relaxed stability or even unstable flight mechanical characteristics to gain flight performance, more focus has been put on model-based system engineering to help with the design work. The flight control system design is one important part that relies on this modeling. Therefore it has become more important to develop flight mechanical models that are highly accurate in the whole flight envelop. For today’s newly developed fighters, the basic aircraft characteristics change between linear and nonlinear as well as stable and unstable as an effect of the desired capability of advanced maneuvering at subsonic, transonic and supersonic speeds.

This thesis combines the subject of system identification, which is the art of building mathematical models of dynamical systems based on measurements, with aeronautics in order to find methods to identify flight mechanical characteristics from flight tests. Here, a challenging aeronautical identification problem combining instability and nonlinearity is treated.

Two aspects are considered. The first is identification during a flight test with the intent to ensure that enough information is available in the resulting test data. Here, a frequency domain method is used. This idea has been taken from an existing method to which some improvements have been made. One of these improvements is to use an Instrumental Variable approach to take care of disturbances coming from atmospheric turbulence. The method treats linear systems that can be both stable and unstable. The improved method shows promising results, but needs further work to become robust against outliers and missing data.

The other aspect is post-flight identification. Here, five different direct identification methods, which treat unstable and nonlinear systems, have been compared. Three of the methods are variations of the prediction-error method. The fourth is a parameter and state estimation method and the fifth method is a state estimation method based on an augmented system approach. The simplest of the prediction-error methods, based on a parametrized observer approach, is least sensitive to noise and initial offsets of the model parameters for the studied cases. This approach is attractive since it does not have any parameters that the user has to tune in order to get the best performance.

All methods in this thesis have been validated on simulated data where the system is known, and have also been tested on real flight test data.

```
@phdthesis{diva2:622859,
author = {Larsson, Roger},
title = {{System Identification of Flight Mechanical Characteristics}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1599}},
year = {2013},
address = {Sweden},
}
```

Over the last 20 years, navigation has almost become synonymous with satellite positioning, e.g. the Global Positioning System (GPS). On land, sea or in the air, on the road or in a city, knowing ones position is a question of getting a clear line of sight to enough satellites. Unfortunately, since the signals are extremely weak there are environments the GPS signals cannot reach but where positioning is still highly sought after, such as indoors and underwater. Also, because the signals are so weak, GPS is vulnerable to jamming. This thesis is about alternative means of positioning for three scenarios where gps cannot be used.

Indoors, there is a desire to accurately position first responders, police officers and soldiers. This could make their work both safer and more efficient. In this thesis an inertial navigation system using a foot mounted inertial magnetic mea- surement unit is studied. For such systems, zero velocity updates can be used to significantly reduce the drift in distance travelled. Unfortunately, the estimated direction one is moving in is also subject to drift, causing large positioning errors. We have therefore chosen to throughly study the key problem of robustly estimating heading indoors.

To measure heading, magnetic field measurements can be used as a compass. Unfortunately, they are often disturbed indoors making them unreliable. For estimation support, the turn rate of the sensor can be measured by a gyro but such sensors often have bias problems. In this work, we present two different approaches to estimate heading despite these shortcomings. Our first system uses a Kalman filter bank that recursively estimates if the magnetic readings are disturbed or undisturbed. Our second approach estimates the entire history of headings at once, by matching integrated gyro measurements to a vector of magnetic heading measurements. Large scale experiments are used to evaluate both methods. When the heading estimation is incorporated into our positioning system, experiments show that positioning errors are reduced significantly. We also present a probabilistic stand still detection framework based on accelerometer and gyro measurements.

The second and third problems studied are both maritime. Naval navigation systems are today heavily dependent on GPS. Since GPS is easily jammed, the vessels are vulnerable in critical situations. In this work we describe a radar based backup positioning system to be used in case of GPS failure. radar scans are matched using visual features to detect how the surroundings have changed, thereby describing how the vessel has moved. Finally, we study the problem of underwater positioning, an environment gps signals cannot reach. A sensor network can track vessels using acoustics and the magnetic disturbances they induce. But in order to do so, the sensors themselves first have to be accurately positioned. We present a system that positions the sensors using a friendly vessel with a known magnetic signature and trajectory. Simulations show that by studying the magnetic disturbances that the vessel produces, the location of each sensor can be accurately estimated.

```
@phdthesis{diva2:618300,
author = {Callmer, Jonas},
title = {{Autonomous Localization in Unknown Environments}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1520}},
year = {2013},
address = {Sweden},
}
```

Localization is essential in a variety of applications such as navigation systems, aerospace and surface surveillance, robotics and animal migration studies to mention a few. There are many standard techniques available, where the most common are based on information from satellite or terrestrial radio beacons, radar networks or vision systems.

In this thesis, two alternative techniques are investigated.The first localization technique is based on one or more magnetometers measuring the induced magnetic field from a magnetic object. These measurements depend on the position and the magnetic signature of the object and can be described with models derived from the electromagnetic theory. For this technology, two applications have been analyzed. The first application is traffic surveillance, which has a high need for robust localization systems. By deploying one or more magnetometer in the vicinity of the traffic lane, vehicles can be detected and classified. These systems can be used for safety purposes, such as detecting wrong-way drivers on highways, as well as for statistical purposes by monitoring the traffic flow.

The second application is indoor localization, where a mobile magnetometer measures the stationary magnetic field induced by magnetic structures in indoor environments. In this work, models for such magnetic environments are proposed and evaluated.The second localization technique uses light sensors measuring light intensity during day and night. After registering the time of sunrise and sunset from this data, basic formulas from astronomy can be used to locate the sensor. The main application is localization of small migrating animals. In this work, a framework for localizing migrating birds using light sensors is proposed. The framework has been evaluated on data from a common swift, which during a period of ten months was equipped with a light sensor.

```
@phdthesis{diva2:606554,
author = {Wahlström, Niklas},
title = {{Localization using Magnetometers and Light Sensors}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1581}},
year = {2013},
address = {Sweden},
}
```

Sensor networks are everywhere around us. Developments in sensor technology and advances in hardware miniaturization open up brand-new application areas. In the future networks of cheap and small sensor nodes will be deployed for a variety of purposes. Military needs have been a major motivation for the development in the past, but today it has changed. Other applications such as traffic monitoring, security threat detection, ecology and environmental protection are the new driving forces behind further development.

The thesis considers the problem of calibration of ground sensor networks. In order to perform its operational tasks – detection, classification and tracking ofobjects of interest, the network has to be correctly calibrated. Improper calibration might result in a degraded performance, problems with data association and appearance of multiple track instances representing one object.

In order to find the unknown calibration parameters (biases), in most cases we need to use reference targets with known positions. If such targets are not available, one has to use opportunistic targets and simultaneously estimate both target positions and bias parameters. In this thesis, the expectation maximization algorithm is applied to that problem, where the unknown states are treated as latent (unknown) variables in the process of bias estimation.

Next, the problem of estimating a large number of calibration parameters is tackled. In the case when the measurement data is not informative enough – due to a limited range of sensors or a small number of samples – standard approaches such as the least squares algorithm might provide unreliable results. One solution to the problem is to apply a regularization (or prior in a Bayesian case). In this thesis, the problem of selecting the parameters (the so called hyper-parameters) for the regularization process, based on the set of measurements, is considered. The solution is provided through the evidence approximation method, where both the bias parameters and the hyper-parameters are estimated simultaneously. As a result, one obtains a robust algorithm that, thanks to the application of Occam’s razor, allows to find the good trade-off between model complexity and its fit to the data.

Finally, both methods are combined together, in order to provide a robust and accurate algorithm for the calibration of sensor networks using targets of opportunity.

The applicability of algorithms was also verified during field trials with good final outcome, confirming the expected performance.

```
@phdthesis{diva2:643476,
author = {Syldatk, Marek},
title = {{On Calibration of Ground Sensor Networks}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1611}},
year = {2012},
address = {Sweden},
}
```

In system identification, the choice of model structure is important and it is sometimes desirable to use a flexible model structure that is able to approximate a wide range of systems. One such model structure is the Wiener class of systems, that is, systems where the input enters a linear time-invariant subsystem followed by a time-invariant nonlinearity. Given a sequence of input and output pairs, the system identification problem is often formulated as the minimization of the mean-square prediction error. Here, the prediction error has a nonlinear dependence on the parameters of the linear subsystem and the nonlinearity. Unfortunately, this formulation of the estimation problem is often nonconvex, with several local minima, and it is therefore difficult to guarantee that a local search algorithm will be able to find the global optimum.

In the first part of this thesis, we consider the application of dimension reduction methods to the problem of estimating the impulse response of the linear part of a system in the Wiener class. For example, by applying the inverse regression approach to dimension reduction, the impulse response estimation problem can be cast as a principal components problem, where the reformulation is based on simple nonparametric estimates of certain conditional moments. The inverse regression approach can be shown to be consistent under restrictions on the distribution of the input signal provided that the true linear subsystem has a finite impulse response. Furthermore, a forward approach to dimension reduction is also considered, where the time-invariant nonlinearity is approximated by a local linear model. In this setting, the impulse response estimation problem can be posed as a rank-reduced linear least-squares problem and a convex relaxation can be derived.

Thereafter, we consider the extension of the subspace identification approach to include linear time-invariant rational models. It turns out that only minor structural modifications are needed and already available implementations can be used. Furthermore, other a priori information regarding the structure of the system can incorporated, including a certain class of linear gray-box structures. The proposed extension is not restricted to the discrete-time case and can be used to estimate continuous-time models.

The final topic in this thesis is the estimation of discrete-time models containing polynomial nonlinearities. In the continuous-time case, a constructive algorithm based on differential algebra has previously been used to prove that such model structures are globally identifiable if and only if they can be written as a linear regression model. Thus, if we are able to transform the nonlinear model structure into a linear regression model, the parameter estimation problem can be solved with standard methods. Motivated by the above and the fact that most system identification problems involve sampled data, a discrete-time version of the algorithm is developed. This algorithm is closely related to the continuous-time version and enables the handling of noise signals without differentiations.

```
@phdthesis{diva2:559895,
author = {Lyzell, Christian},
title = {{Structural Reformulations in System Identification}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1475}},
year = {2012},
address = {Sweden},
}
```

The world in which we live is becoming more and more automated, exemplified by the numerous robots, or autonomous vehicles, that operate in air, on land, or in water. These robots perform a wide array of different tasks, ranging from the dangerous, such as underground mining, to the boring, such as vacuum cleaning. In common for all different robots is that they must possess a certain degree of awareness, both of themselves and of the world in which they operate. This thesis considers aspects of two research problems associated with this, more specifically the Simultaneous Localization and Mapping (SLAM) problem and the Multiple Target Tracking (MTT) problem.

The SLAM problem consists of having the robot create a map of an environment and simultaneously localize itself in the same map. One way to reduce the effect of small errors that inevitably accumulate over time, and could significantly distort the SLAM result, is to detect loop closure. In this thesis loop closure detection is considered for robots equipped with laser range sensors. Machine learning is used to construct a loop closure detection classifier, and experiments show that the classifier compares well to related work.

The resulting SLAM map should only contain stationary objects, however the world also contains moving objects, and to function well a robot should be able to handle both types of objects. The MTT problem consists of having the robot keep track of where the moving objects, called targets, are located, and how these targets are moving. This function has a wide range of applications, including tracking of pedestrians, bicycles and cars in urban environments. Solving the MTT problem can be decomposed into two parts: one part is finding out the number of targets, the other part is finding out what the states of the individual targets are.

In this thesis the emphasis is on tracking of so called extended targets. An extended target is a target that can generate any number of measurements, as opposed to a point target that generates at most one measurement. More than one measurement per target raise interesting possibilities to estimate the size and the shape of the target. One way to model the number of targets and the target states is to use random finite sets, which leads to the Probability Hypothesis Density (PHD) filters. Two implementations of an extended target PHD filter are given, one using Gaussian mixtures and one using Gaussian inverse Wishart (GIW) mixtures. Two models for the size and shape of an extended target measured with laser range sensors are suggested. A framework for estimation of the number of measurements generated by the targets is presented, and reduction of GIW mixtures is addressed. Prediction, spawning and combination of extended targets modeled using GIW distributions is also presented. The extended target tracking functions are evaluated in simulations and in experiments with laser range data.

```
@phdthesis{diva2:558084,
author = {Granström, Karl},
title = {{Extended target tracking using PHD filters}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1476}},
year = {2012},
address = {Sweden},
}
```

Buffer tanks are widely used within the process industry to prevent flow variations from being directly propagated throughout a plant. The capacity of the tank is used to smoothly transfer inlet flow upsets to the outlet. Ideally, the tank thus works as a low pass filter where the available tank capacity limits the achievable flow smoothing.

For infrequently occurring upsets, where the system has time to reach steady state between flow changes, the averaging level control problem has been extensively studied. After an inlet flow change, flow filtering has traditionally been obtained by letting the tank level deviate from its nominal value while slowly adapting the outlet to cancel out the flow imbalance and eventually bringing back the level to its set-point. The system is then again in steady state and ready to surge the next upset. By ensuring that the single largest upset can be handled without violating the level constraints, satisfactory flow smoothing is obtained.

In this thesis, the smoothing of frequently changing inlet flows is addressed. In this case, standard level controllers struggle to obtain acceptable flow smoothing since the system rarely is in steady state and flow upsets can thus not be treated as separate events. To obtain a control law that achieves optimal filtering while directly accounting for future upsets, the averaging level control problem was approached using robust model predictive control (MPC).

The robust MPC differs in the way it obtains flow smoothing by not returning the tank level to a fixed set-point. Instead, it lets the steady state tank level depend on the current value of the inlet flow. This insight was then used to propose a linear control structure, designed to filter frequent upsets optimally. Analyses and simulation results indicate that the proposed linear and robust MPC controller obtain flow smoothing comparable to the standard optimal averaging level controllers for infrequent upsets while handling frequent upsets considerably better.

```
@phdthesis{diva2:524729,
author = {Rosander, Peter},
title = {{Averaging level control in the presence of frequent inlet flow upsets}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1527}},
year = {2012},
address = {Sweden},
}
```

Vision and infrared sensors are very common in surveillance and security applications, and there are numerous examples where a critical infrastructure, e.g. a harbor, an airport, or a military camp, is monitored by video surveillance systems. There is a need for automatic processing of sensor data and intelligent control of the sensor in order to obtain efficient and high performance solutions that can support a human operator. This thesis considers two subparts of the complex sensor fusion system; namely target tracking and sensor control.The multiple target tracking problem using particle filtering is studied. In particular, applications where road constrained targets are tracked with an airborne video or infrared camera are considered. By utilizing the information about the road network map it is possible to enhance the target tracking and prediction performance. A dynamic model suitable for on-road target tracking with a camera is proposed and the computational load of the particle filter is treated by a Rao-Blackwellized particle filter. Moreover, a pedestrian tracking framework is developed and evaluated in a real world experiment. The exploitation of contextual information, such as road network information, is highly desirable not only to enhance the tracking performance, but also for track analysis, anomaly detection and efficient sensor management. Planning for surveillance and reconnaissance is a broad field with numerous problem definitions and applications. Two types of surveillance and reconnaissance problems are considered in this thesis. The first problem is a multi-target search and tracking problem. Here, the task is to control the trajectory of an aerial sensor platform and the pointing direction of its camera to be able to keep track of discovered targets and at the same time search for new ones. The key to successful planning is a measure that makes it possible to compare different tracking and searching tasks in a unified framework and this thesis suggests one such measure. An algorithm based on this measure is developed and simulation results of a multi-target search and tracking scenario in an urban area are given. The second problem is aerial information exploration for single target estimation and area surveillance. In the single target case the problem is to control the trajectory of a sensor platform with a vision or infrared camera such that the estimation performance of the target is maximized. The problem is treated both from an information filtering and from a particle filtering point of view. In area exploration the task is to gather useful image data of the area of interest by controlling the trajectory of the sensor platform and the pointing direction of the camera. Good exploration of a point of interest is characterized by several images from different viewpoints. A method based on multiple information filters is developed and simulation results from area and road exploration scenarios are presented.

```
@phdthesis{diva2:517336,
author = {Skoglar, Per},
title = {{Tracking and Planning for Surveillance Applications}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1432}},
year = {2012},
address = {Sweden},
}
```

Industrial robots are designed to endure several years of uninterrupted operation and therefore are very reliable. However, no amount of design effort can prevent deterioration over time, and equipments will eventually fail. Its impacts can, nevertheless, be considerably reduced if good maintenance/service practices are performed. The current practice for service of industrial robots is based on preventive and corrective policies, with little consideration about the actual condition of the system. In the current scenario, the serviceability of industrial robots can be greatly improved with the use of condition monitoring/diagnosis methods, allowing for condition-based maintenance (cbm).

This thesis addresses the design of condition monitoring methods for industrial robots. The main focus is on the monitoring and diagnosis of excessive degradations caused by wear of the mechanical parts. The wear processes may take several years to be of significance, but can evolve rapidly once they start to appear. An early detection of excessive wear levels can therefore allow for cbm, increasing maintainability and availability. Since wear is related to friction, the basic idea pursued is to analyze the friction behavior to infer about wear.

To allow this, an extensive study of friction in robot joints is considered in this work. The effects of joint temperature, load and wear changes to static friction in robot a joint are modeled based on empirical observations. It is found that the effects of load and temperature to friction are comparable to those caused by wear. Joint temperature and load are typically not measured, but will always be present in applications. Therefore, diagnosis solutions must be able to cope with them.

Different methods are proposed which allow for robust wear monitoring. First, a wear estimator is suggested. Wear estimates are made possible with the use of a test-cycle and a friction model. Second, a method is defined which considers the repetitive behavior found in many applications of industrial robots. The result of the execution of the same task in different instances of time are compared to provide an estimate of how the system changed over the period. Methods are suggested that consider changes in the distribution of data logged from the robot. It is shown through simulations and experiments that robust wear monitoring is made possible with the proposed methods.

```
@phdthesis{diva2:464280,
author = {Carvalho Bittencourt, Andr\'{e}},
title = {{On Modeling and Diagnosis of Friction and Wear in Industrial Robots}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1516}},
year = {2012},
address = {Sweden},
}
```

The need to determine ones position is common and emerges in many different situations. Tracking soldiers or a robot moving in a building or aiding a tourist exploring a new city, all share the questions ”where is the unit?“ and ”where is the unit going?“. This is known as the localization problem.Particularly, the problem of determining ones position in a map while building the map at the same time, commonly known as the simultaneous localization and mapping problem (slam), has been widely studied. It has been performed in cities using different land bound vehicles, in rural environments using au- tonomous aerial vehicles and underwater for coral reef exploration. In this thesis it is studied how radar signals can be used to both position a naval surface ves- sel but also to simultaneously construct a map of the surrounding archipelago. The experimental data used was collected using a high speed naval patrol boat and covers roughly 32 km. A very accurate map was created using nothing but consecutive radar images.A second contribution covers an entirely different problem but it has a solution that is very similar to the first one. Underwater sensors sensitive to magnetic field disturbances can be used to track ships. In this thesis, the sensor positions them- selves are considered unknown and are estimated by tracking a friendly surface vessel with a known magnetic signature. Since each sensor can track the vessel, the sensor positions can be determined by relating them to the vessel trajectory. Simulations show that if the vessel is equipped with a global navigation satellite system, the sensor positions can be determined accurately.There is a desire to localize firefighters while they are searching through a burn- ing building. Knowing where they are would make their work more efficient and significantly safer. In this thesis a positioning system based on foot mounted in- ertial measurement units has been studied. When such a sensor is foot mounted, the available information increases dramatically since the foot stances can be de- tected and incorporated in the position estimate. The focus in this work has therefore been on the problem of stand still detection and a probabilistic frame- work for this has been developed. This system has been extensively investigated to determine its applicability during different movements and boot types. All in all, the stand still detection system works well but problems emerge when a very rigid boot is used or when the subject is crawling. The stand still detection frame- work was then included in a positioning framework that uses the detected stand stills to introduce zero velocity updates. The system was evaluated using local- ization experiments for which there was very accurate ground truth. It showed that the system provides good position estimates but that the estimated heading can be wrong, especially after quick sharp turns.

```
@phdthesis{diva2:459882,
author = {Callmer, Jonas},
title = {{Topics in Localization and Mapping}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1489}},
year = {2011},
address = {Sweden},
}
```

One of the main tasks for an industrial robot is to move the end-effector in a predefined path with a specified velocity and acceleration. Different applications have different requirements of the performance. For some applications it is essential that the tracking error is extremely low, whereas other applications require a time optimal tracking. Independent of the application, the controller is a crucial part of the robot system. The most common controller configuration uses only measurements of the motor angular positions and velocities, instead of the position and velocity of the end-effector.

The development of new cost optimised robots have introduced unwanted flexibilities in the joints and the links. It is no longer possible to get the desired performance and robustness by only measuring the motor angular positions. This thesis investigates if it is possible to estimate the end-effector position when an accelerometer is mounted at the end-effector. The main focus is to investigate Bayesian estimation methods for state estimation, here represented by the extended Kalman filter (EKF) and the particle filter (PF).

A simulation study is performed on a two degrees of freedom industrial robot model using an EKF. The study emphasises three important problems to take care of in order to get a good performance. The first one is related to model errors which in general requires better identification methods. The second problem is about tuning of the EKF, i.e., the choice of covariance matrices for the measurement and process noise. It is desirable to have an automatic tuning procedure which minimises the estimation error and is robust to initial conditions of the tuned parameters. A variant of the expectation maximisation (EM) algorithm is proposed for estimation of the process noise covariance matrix Q. The EM algorithm iteratively estimates the unobserved state sequence and the matrix Q based on the observations of the process, where the extended Kalman smoother (EKS) is the instrument to find the unobserved state sequence.

The third problem considers the orientation and position of the accelerometer mounted to the end-effector. A novel method to find the orientation and position of the triaxial accelerometer is proposed and evaluated on experimental data. The method consists of two consecutive steps, where the first is to estimate the orientation of the sensor from static experiments. In the second step the sensor position relative to the robot base is identified using sensor readings when the sensor moves in a circular path and where the sensor orientation is kept constant in a path fixed coordinate system.

Finally, experimental evaluations are performed on an ABB IRB4600 robot. Different observers using the EKF, EKS and PF with different estimation models are proposed. The estimated paths are compared to the true path measured by a laser tracking system. There is no significant difference in performance between the six observers. Instead, execution time, model complexities and implementation issues have to be considered when choosing the method.

```
@phdthesis{diva2:458630,
author = {Axelsson, Patrik},
title = {{On Sensor Fusion Applied to Industrial Manipulators}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1511}},
year = {2011},
address = {Sweden},
}
```

In this thesis, we investigate two problems in robustness analysis of uncertain systems with structured uncertainty. The first problem concerns the robust finite frequency range *H _{2}* analysis of such systems. Classical robust H2 analysis methods are based on upper bounds for the robust

*H*norm of a system which are computed over the whole frequency range. These bounds can be overly conservative, and therefore, classical robust

_{2}*H*analysis methods can produce misleading results for finite frequency range analysis. In the first paper in the thesis, we address this issue by providing two methods for computing upper bounds for the robust finite-frequency

_{2}*H*norm of the system. These methods utilize finitefrequency Gramians and frequency partitioning to calculate upper bounds for the robust finite-frequency

_{2}*H*norm of uncertain systems with structured uncertainty. We show the effectiveness of these algorithms using both theoretical and practical experiments.

_{2}```
@phdthesis{diva2:458313,
author = {Khoshfetrat Pakazad, Sina},
title = {{Topics in Robustness Analysis}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1512}},
year = {2011},
address = {Sweden},
}
```

Mapping stationary objects and tracking moving targets are essential for many autonomous functions in vehicles. In order to compute the map and track estimates, sensor measurements from radar, laser and camera are used together with the standard proprioceptive sensors present in a car. By fusing information from different types of sensors, the accuracy and robustness of the estimates can be increased.

Different types of maps are discussed and compared in the thesis. In particular, road maps make use of the fact that roads are highly structured, which allows relatively simple and powerful models to be employed. It is shown how the information of the lane markings, obtained by a front looking camera, can be fused with inertial measurement of the vehicle motion and radar measurements of vehicles ahead to compute a more accurate and robust road geometry estimate. Further, it is shown how radar measurements of stationary targets can be used to estimate the road edges, modeled as polynomials and tracked as extended targets.

Recent advances in the field of multiple target tracking lead to the use of finite set statistics (FISST) in a set theoretic approach, where the targets and the measurements are treated as random finite sets (RFS). The first order moment of a RFS is called probability hypothesis density (PHD), and it is propagated in time with a PHD filter. In this thesis, the PHD filter is applied to radar data for constructing a parsimonious representation of the map of the stationary objects around the vehicle. Two original contributions, which exploit the inherent structure in the map, are proposed. A data clustering algorithm is suggested to structure the description of the prior and considerably improving the update in the PHD filter. Improvements in the merging step further simplify the map representation.

When it comes to tracking moving targets, the focus of this thesis is on extended targets, i.e., targets which potentially may give rise to more than one measurement per time step. An implementation of the PHD filter, which was proposed to handle data obtained from extended targets, is presented. An approximation is proposed in order to limit the number of hypotheses. Further, a framework to track the size and shape of a target is introduced. The method is based on measurement generating points on the surface of the target, which are modeled by an RFS.

Finally, an efficient and novel Bayesian method is proposed for approximating the tire radii of a vehicle based on particle filters and the marginalization concept. This is done under the assumption that a change in the tire radius is caused by a change in tire pressure, thus obtaining an indirect tire pressure monitoring system.

The approaches presented in this thesis have all been evaluated on real data from both freeways and rural roads in Sweden.

```
@phdthesis{diva2:451021,
author = {Lundquist, Christian},
title = {{Sensor Fusion for Automotive Applications}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1409}},
year = {2011},
address = {Sweden},
}
```

Processing and interpretation of visual content is essential to many systems and applications. This requires knowledge of how the content is sensed and also what is sensed. Such knowledge is captured in models which, depending on the application, can be very advanced or simple. An application example is scene reconstruction using a camera; if a suitable model of the camera is known, then a model of the scene can be estimated from images acquired at different, unknown, locations, yet, the quality of the scene model depends on the quality of the camera model. The opposite is to estimate the camera model and the unknown locations using a known scene model. In this work, two such problems are treated in two rather different applications.

There is an increasing need for navigation solutions less dependent on external navigation systems such as the Global Positioning System (GPS). Simultaneous Localisation and Mapping (slam) provides a solution to this by estimating both navigation states and some properties of the environment without considering any external navigation systems.

The first problem considers visual inertial navigation and mapping using a monocular camera and inertial measurements which is a slam problem. Our aim is to provide improved estimates of the navigation states and a landmark map, given a slam solution. To do this, the measurements are fused in an Extended Kalman Filter (ekf) and then the filtered estimates are used as a starting solution in a nonlinear least-squares problem which is solved using the Gauss-Newton method. This approach is evaluated on experimental data with accurate ground truth for reference.

In Augmented Reality (ar), additional information is superimposed onto the surrounding environment in real time to reinforce our impressions. For this to be a pleasant experience it is necessary to have a good models of the ar system and the environment.

The second problem considers calibration of an Optical See-Through Head Mounted Display system (osthmd), which is a wearable ar system. We show and motivate how the pinhole camera model can be used to represent the osthmd and the user’s eye position. The pinhole camera model is estimated using the Direct Linear Transformation algorithm. Results are evaluated in experiments which also compare different data acquisition methods.

```
@phdthesis{diva2:421464,
author = {Skoglund, Martin A.},
title = {{Visual Inertial Navigation and Calibration}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1500}},
year = {2011},
address = {Sweden},
}
```

The usage of inertial sensors has traditionally been confined primarily to the aviation and marine industry due to their associated cost and bulkiness. During the last decade, however, inertial sensors have undergone a rather dramatic reduction in both size and cost with the introduction of MEMS technology. As a result of this trend, inertial sensors have become commonplace for many applications and can even be found in many consumer products, for instance smart phones, cameras and game consoles. Due to the drift inherent in inertial technology, inertial sensors are typically used in combination with aiding sensors to stabilize andimprove the estimates. The need for aiding sensors becomes even more apparent due to the reduced accuracy of MEMS inertial sensors.

This thesis discusses two problems related to using inertial sensors in combination with aiding sensors. The first is the problem of sensor fusion: how to combine the information obtained from the different sensors and obtain a good estimate of position and orientation. The second problem, a prerequisite for sensor fusion, is that of calibration: the sensors themselves have to be calibrated and provide measurement in known units. Furthermore, whenever multiple sensors are combined additional calibration issues arise, since the measurements are seldom acquired in the same physical location and expressed in a common coordinate frame. Sensor fusion and calibration are discussed for the combination of inertial sensors with cameras, UWB or GPS.

Two setups for estimating position and orientation in real-time are presented in this thesis. The first uses inertial sensors in combination with a camera; the second combines inertial sensors with UWB. Tightly coupled sensor fusion algorithms and experiments with performance evaluation are provided. Furthermore, this thesis contains ideas on using an optimization based sensor fusion method for a multi-segment inertial tracking system used for human motion capture as well as a sensor fusion method for combining inertial sensors with a dual GPS receiver.

The above sensor fusion applications give rise to a number of calibration problems. Novel and easy-to-use calibration algorithms have been developed and tested to determine the following parameters: the magnetic field distortion when an IMU containing magnetometers is mounted close to a ferro-magnetic object, the relative position and orientation of a rigidly connected camera and IMU, as well as the clock parameters and receiver positions of an indoor UWB positioning system.

```
@phdthesis{diva2:417835,
author = {Hol, Jeroen D.},
title = {{Sensor Fusion and Calibration of Inertial Sensors, Vision, Ultra-Wideband and GPS}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1368}},
year = {2011},
address = {Sweden},
}
```

When designing controllers with robust performance and stabilization requirements, H-infinity synthesis is a common tool to use. These controllers are often obtained by solving mathematical optimization problems. The controllers that result from these algorithms are typically of very high order, which complicates implementation. Low order controllers are usually desired, since they are considered more reliable than high order controllers. However, if a constraint on the maximum order of the controller is set that is lower than the order of the so-called augmented system, the optimization problem becomes nonconvex and it is relatively difficult to solve. This is true even when the order of the augmented system is low.

In this thesis, optimization methods for solving these problems are considered. In contrast to other methods in the literature, the approach used in this thesis is based on formulating the constraint on the maximum order of the controller as a rational function in an equality constraint. Three methods are then suggested for solving this smooth nonconvex optimization problem.

The first two methods use the fact that the rational function is nonnegative. The problem is then reformulated as an optimization problem where the rational function is to be minimized over a convex set defined by linear matrix inequalities (LMIs). This problem is then solved using two different interior point methods.

In the third method the problem is solved by using a partially augmented Lagrangian formulation where the equality constraint is relaxed and incorporated into the objective function, but where the LMIs are kept as constraints. Again, the feasible set is convex and the objective function is nonconvex.

The proposed methods are evaluated and compared with two well-known methods from the literature. The results indicate that the first two suggested methods perform well especially when the number of states in the augmented system is less than 10 and 20, respectively. The third method has comparable performance with two methods from literature when the number of states in the augmented system is less than 25.

```
@phdthesis{diva2:413954,
author = {Ankelhed, Daniel},
title = {{On design of low order H-infinity controllers}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1371}},
year = {2011},
address = {Sweden},
}
```

We consider the two related problems of state inference in nonlinear dynamical systems and nonlinear system identification. More precisely, based on noisy observations from some (in general) nonlinear and/or non-Gaussian dynamical system, we seek to estimate the system state as well as possible unknown static parameters of the system. We consider two different aspects of the state inference problem, filtering and smoothing, with the emphasis on the latter. To address the filtering and smoothing problems, we employ sequential Monte Carlo (SMC) methods, commonly referred to as particle filters (PF) and particle smoothers (PS).

Many nonlinear models encountered in practice contain some tractable substructure. If this is the case, a natural idea is to try to exploit this substructure to obtain more accurate estimates than what is provided by a standard particle method. For the filtering problem, this can be done by using the well-known Rao-Blackwellised particle filter (RBPF). In this thesis, we analyse the RBPF and provide explicit expressions for the variance reduction that is obtained from Rao-Blackwellisation. Furthermore, we address the smoothing problem and develop a novel Rao-Blackwellised particle smoother (RBPS), designed to exploit a certain tractable substructure in the model.

Based on the RBPF and the RBPS we propose two different methods for nonlinear system identification. The first is a recursive method referred to as the Rao-Blackwellised marginal particle filter (RBMPF). By augmenting the state variable with the unknown parameters, a nonlinear filter can be applied to address the parameter estimation problem. However, if the model under study has poor mixing properties, which is the case if the state variable contains some static parameter, SMC filters such as the PF and the RBPF are known to degenerate. To circumvent this we introduce a so called “mixing” stage in the RBMPF, which makes it more suitable for models with poor mixing properties.

The second identification method is referred to as RBPS-EM and is designed for maximum likelihood parameter estimation in a type of mixed linear/nonlinear Gaussian statespace models. The method combines the expectation maximisation (EM) algorithm with the RBPS mentioned above, resulting in an identification method designed to exploit the tractable substructure present in the model.

```
@phdthesis{diva2:416071,
author = {Lindsten, Fredrik},
title = {{Rao-Blackwellised particle methods for inference and identification}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1480}},
year = {2011},
address = {Sweden},
}
```

Since its discovery, in the 1940's, radar (Radio Detection and Ranging) has become an important ranging sensor in many areas of technology and science. Most of the military and many civilian applications are unimaginable today without radar. With technology development, radar application areas have become larger and more available. One of these applications is Synthetic Aperture Radar (SAR), where an airborne radar is used to create high resolution images of the imaged scene. Although known since the 1950's, the SAR methods have been continuously developed and improved and new algorithms enabling real-time applications have emerged lately. Together with making the hardware components smaller and lighter, SAR has become an interesting sensor to be mounted on smaller unmanned aerial vehicles (UAV's). One important thing needed in the SAR algorithms is the estimate of the platform's motion, like position and velocity. Since this estimate is always corrupted with errors, particularly if lower grade navigation system, common in UAV applications, is used, the SAR images will be distorted. One of the most frequently appearing distortions caused by the unknown platform's motion is the image defocus. The process of correcting the image focus is called auto-focusing in SAR terminology. Traditionally, this problem was solved by methods that discard the platform's motion information, mostly due to the off-line processing approach, i.e. the images were created after the flight. Since the image (de)focus and the motion of the platform are related to each other, it is possible to utilise the information from the SAR images as a sensor and improve the estimate of the platform's motion. The auto-focusing problem can be cast as a sensor fusion problem. Sensor fusion is the process of fusing information from different sensors, in order to obtain best possible estimate of the states. Here, the information from sensors measuring platform's motion, mainly accelerometers, will be fused together with the information from the SAR images to estimate the motion of the flying platform. Two different methods based on this approach are tested on the simulated SAR data and the results are evaluated. One method is based on an optimisation based formulation of the sensor fusion problem, leading to batch processing, while the other method is based on the sequential processing of the radar data, leading to a filtering approach. The obtained results are promising for both methods and the obtained performance is comparable with the performance of a high precision navigation aid, such as Global Positioning System (GPS).

```
@phdthesis{diva2:385959,
author = {Sjanic, Zoran},
title = {{Navigation and SAR Auto-focusing in a Sensor Fusion Framework}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1464}},
year = {2011},
address = {Sweden},
}
```

In the past two decades, robotics and autonomous vehicles have received ever increasing research attention. For an autonomous robot to function fully autonomously alongside humans, it must be able to solve the same tasks as humans do, and it must be able to sense the surrounding environment. Two such tasks are addressed in this thesis, using data from laser range sensors.

The first task is recognising that the robot has returned to a previously visited location, a problem called loop closure detection. Loop closure detection is a fundamental part of the simultaneous localisation and mapping problem, which consists of mapping an unknown area and simultaneously localise in the same map. In this thesis, a classification approach is taken to the loop closure detection problem. The laser range data is described in terms of geometrical and statistical properties, called features. Pairs of laser range data from two different locations are compared by using adaptive boosting to construct a classifier that takes as input the computed features. Experiments using real world laser data are used to evaluate the properties of the classifier, and the classifier is shown to compare well to existing solutions.

The second task is keeping track of objects that surround the robot, a problem called target tracking. Target tracking is an estimation problem in which data association between the estimates and measurements is of high importance. The data association is complicated by things such as noise and false measurements. In this thesis, extended targets, i.e. targets that potentially generate more than one measurement per time step, are considered. The multiple measurements per time step further complicate the data association. Tracking of extended targets is performed using an implementation of a probability hypothesis density filter, which is evaluated in simulations using the optimal sub-pattern assignment metric. The filter is also used to track humans with real world laser range data, and the experiments show that the filter can handle the so called occlusion problem.

```
@phdthesis{diva2:389565,
author = {Granström, Karl},
title = {{Loop detection and extended target tracking using laser data}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1465}},
year = {2011},
address = {Sweden},
}
```

In many applications industrial robots perform the same motion repeatedly. One way of compensating the repetitive part of the error is by using iterative learning control (ILC). The ILC algorithm makes use of the measured errors and iteratively calculates a correction signal that is applied to the system.

The main topic of the thesis is to apply an ILC algorithm to a dynamic system where the controlled variable is not measured. A remedy for handling this difficulty is to use additional sensors in combination with signal processing algorithms to obtain estimates of the controlled variable. A framework for analysis of ILC algorithms is proposed for the situation when an ILC algorithm uses an estimate of the controlled variable. This is a relevant research problem in for example industrial robot applications, where normally only the motor angular positions are measured while the control objective is to follow a desired tool path. Additionally, the dynamic model of the flexible robot structure suffers from uncertainties. The behaviour when a system having these difficulties is controlled by an ILC algorithm using measured variables directly is illustrated experimentally, on both a serial and a parallel robot, and in simulations of a flexible two-mass model. It is shown that the correction of the tool-position error is limited by the accuracy of the robot model.

The benefits of estimation-based ILC is illustrated for cases when fusing measurements of the robot motor angular positions with measurements from an additional accelerometer mounted on the robot tool to form a tool-position estimate. Estimation-based ILC is studied in simulations on a flexible two-mass model and on a flexible nonlinear two-link robot model, as well as in experiments on a parallel robot. The results show that it is possible to improve the tool performance when a tool-position estimate is used in the ILC algorithm, compared to when the original measurements available are used directly in the algorithm. Furthermore, the resulting performance relies on the quality of the estimate, as expected.

In the last part of the thesis, some implementation aspects of ILC are discussed. Since the ILC algorithm involves filtering of signals over finite-time intervals, often using non-causal filters, it is important that the boundary effects of the filtering operations are appropriately handled when implementing the algorithm. It is illustrated by theoretical analysis and in simulations that the method of implementation can have large influence over stability and convergence properties of the algorithm.

```
@phdthesis{diva2:386643,
author = {Wall\'{e}n, Johanna},
title = {{Estimation-based iterative learning control}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1358}},
year = {2011},
address = {Sweden},
}
```

Many control problems can be cast as semideﬁnite programs. However, since the size of these problems grow quite quickly, the computational time to solve them can be quite substantial. In order to reduce the computational time, many proposals of how to tailormake algorithms to various types of control problems can be found in the literature. In this thesis, two papers with similar ambitions are presented.

The ﬁrst paper deals with the case where the constraints of the optimization problem are of the type that stems from the Kalman-Yakubovic-Popov lemma, and where some of these constraints are so called complicating constraints. This means the optimization problem will be greatly simpliﬁed if these constraints were not present. By the use of Lagrangian relaxation, the optimization problem is decomposed into smaller ones, which can be solved independently of each other. Computational results show that for some classes of problems, this algorithm can reduce the computational time compared to using a solver which does not take into account the nature of the complicating constraints.

In the second paper, the fact that many control-related semideﬁnite programs have matrix-valued variables is utilized to speed up computations. This implies that the corresponding basis matrices have a certain low-rank structure which can be exploited when formulating the equations for the search directions, something that was discovered in the 90s and is implemented in LMI Lab. However, much has happened in the area of semidefinite programming since the release of LMI Lab, and new, faster algorithms have been developed. However, the idea of using the lowrank structure in the basis matrices can still be used. We implement this, using the publicly available solver SDPT3 in combination with our code for formulating the system of equations for the search directions. In order to facilitate for potential users, we also describe how the modeling language YALMIP is changed so that this lowrank structure can be tracked, and how the code can be easily interfaced. Computational results show that the computational time is decreased.

```
@phdthesis{diva2:652429,
author = {Falkeborn, Rikard},
title = {{Structure Exploitation in Semidefinite Programming for Control}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1430}},
year = {2010},
address = {Sweden},
}
```

_{2}-norm based LPV modelling and control", Linköping Studies in Science and Technology. Thesis, No. 1453, 2010.

To be able to analyze certain classes of non-linear systems, it is necessary to try to represent them as linear parameter varying systems or even as linear fractional representations. For linear parameter varying systems and linear fractional representations of systems there exists many advanced analysis methods such as IQC-analysis and μ-analysis. This means that an important intermediate step in all this is to generate a linear parameter varying model that describes these non-linear system sufficiently well.

The first contribution in this thesis is a novel method that tries, through nonlinear programming and a quasi-Newton framework, to generate a linear parameter varying model given linearized state space models. The idea behind the method is to preserve the input-output relations of the given linearized systems and, in an H_{2}-measure, find the best one. To handle uncertainties in data an extension of the proposed method is presented. It is shown how the computationally hard robust optimization approach to the uncertain case can be approximated using a problem specific regularization.

The second contribution in this thesis is a method for synthesizing output-feedback H_{2} controllers of arbitrary order. This method also uses non-linear programming and a quasi-Newton framework to achieve this. One great benefit with this method is that it also possible to impose structure in the controller.

Both of the methods described above tries to solve non-linear and non-convex problems, which means that the problem of finding a good initial estimate is an important problem. For both methods an initialization procedure is proposed to try to find an initial estimate.

The methods are evaluated on several examples and show promising results. A contributing factor is that significant effort has been spent on utilizing the structure of the optimization problems to make the methods efficient.

```
@phdthesis{diva2:359906,
author = {Petersson, Daniel},
title = {{Nonlinear optimization approaches to H$_{2}$-norm based LPV modelling and control}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Thesis No. 1453}},
year = {2010},
address = {Sweden},
}
```

Industrial robot manipulators are general-purpose machines used for industrial automation in order to increase productivity, flexibility, and product quality. Other reasons for using industrial robots are cost saving, and elimination of hazardous and unpleasant work. Robot motion control is a key competence for robot manufacturers, and the current development is focused on increasing the robot performance, reducing the robot cost, improving safety, and introducing new functionalities. Therefore, there is a need to continuously improve the mathematical models and control methods in order to fulfil conflicting requirements, such as increased performance of a weight-reduced robot, with lower mechanical stiffness and more complicated vibration modes. One reason for this development of the robot mechanical structure is of course cost-reduction, but other benefits are also obtained, such as lower environmental impact, lower power consumption, improved dexterity, and higher safety.

This thesis deals with different aspects of modeling and control of flexible, i.e., elastic, manipulators. For an accurate description of a modern industrial manipulator, this thesis shows that the traditional flexible joint model, described in literature, is not sufficient. An improved model where the elasticity is described by a number of localized multidimensional spring-damper pairs is therefore proposed. This model is called the extended flexible joint model. The main contributions of this work are the design and analysis of identification methods, and of inverse dynamics control methods, for the extended flexible joint model.

The proposed identification method is a frequency-domain non-linear gray-box method, which is evaluated by the identification of a modern six-axes robot manipulator. The identified model gives a good description of the global behavior of this robot.

The inverse dynamics problem is discussed, and a solution methodology is proposed. This methodology is based on the solution of a differential algebraic equation (DAE). The inverse dynamics solution is then used for feedforward control of both a simulated manipulator and of a real robot manipulator.

The last part of this work concerns feedback control. First, a model-based nonlinear feedback control (feedback linearization) is evaluated and compared to a model-based feedforward control algorithm. Finally, two benchmark problems for robust feedback control of a flexible manipulator are presented and some proposed solutions are analyzed.

```
@phdthesis{diva2:370497,
author = {Moberg, Stig},
title = {{Modeling and Control of Flexible Manipulators}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1349}},
year = {2010},
address = {Sweden},
}
```

In system identification, the Akaike Information Criterion (AIC) is a well known method to balance the model fit against model complexity. Regularization here acts as a price on model complexity. In statistics and machine learning, regularization has gained popularity due to modeling methods such as Support Vector Machines (SVM), ridge regression and lasso. But also when using a Bayesian approach to modeling, regularization often implicitly shows up and can be associated with the prior knowledge. Regularization has also had a great impact on many applications, and very much so in clinical imaging. In e.g., breast cancer imaging, the number of sensors is physically restricted which leads to long scantimes. Regularization and sparsity can be used to reduce that. In Magnetic Resonance Imaging (MRI), the number of scans is physically limited and to obtain high resolution images, regularization plays an important role.

Regularization shows-up in a variety of different situations and is a well known technique to handle ill-posed problems and to control for overfit. We focus on the use of regularization to obtain sparseness and smoothness and discuss novel developments relevant to system identification and signal processing.

In regularization for sparsity a quantity is forced to contain elements equal to zero, or to be sparse. The quantity could e.g., be the regression parameter vectorof a linear regression model and regularization would then result in a tool for variable selection. Sparsity has had a huge impact on neighboring disciplines, such as machine learning and signal processing, but rather limited effect on system identification. One of the major contributions of this thesis is therefore the new developments in system identification using sparsity. In particular, a novel method for the estimation of segmented ARX models using regularization for sparsity is presented. A technique for piecewise-affine system identification is also elaborated on as well as several novel applications in signal processing. Another property that regularization can be used to impose is smoothness. To require the relation between regressors and predictions to be a smooth function is a way to control for overfit. We are here particularly interested in regression problems with regressors constrained to limited regions in the regressor-space e.g., a manifold. For this type of systems we develop a new regression technique, Weight Determination by Manifold Regularization (WDMR). WDMR is inspired byapplications in biology and developments in manifold learning and uses regularization for smoothness to obtain smooth estimates. The use of regularization for smoothness in linear system identification is also discussed.

The thesis also presents a real-time functional Magnetic Resonance Imaging (fMRI) bio-feedback setup. The setup has served as proof of concept and been the foundation for several real-time fMRI studies.

```
@phdthesis{diva2:360033,
author = {Ohlsson, Henrik},
title = {{Regularization for Sparseness and Smoothness:
Applications in System Identification and Signal Processing}},
school = {Linköping University},
type = {{Linköping Studies in Science and Technology. Dissertations No. 1351}},
year = {2010},
address = {Sweden},
}
```

## Other

This paper presents an overview of the extended target tracking research undertaken at the division of Automatic Control at Linköping University. The PHD and CPHD filters for multiple extended target tracking under clutter and unknown association are summarized, with focus on the Gaussian mixture and Gaussian inverse Wishart implementations. The paper elaborates on measurement set partitioning, the measurement generating Poisson rates, the probability of detection, and practical examples of measurement models.

```
@misc{diva2:643658,
author = {Granström, Karl and Lundquist, Christian and Gustafsson, Fredrik and Orguner, Umut},
title = {{On Extended Target Tracking Using PHD Filters}},
howpublished = {},
year = {2012},
}
```

## Reports

We propose a novel method for MAP parameter inference in nonlinear state space models with intractable likelihoods. The method is based on a combination of Gaussian process optimisation (GPO), sequential Monte Carlo (SMC) and approximate Bayesian computations (ABC). SMC and ABC are used to approximate the intractable likelihood by using the similarity between simulated realisations from the model and the data obtained from the system. The GPO algorithm is used for the MAP parameter estimation given noisy estimates of the log-likelihood. The proposed parameter inference method is evaluated in three problems using both synthetic and real-world data. The results are promising, indicating that the proposed algorithm converges fast and with reasonable accuracy compared with existing methods.

```
@techreport{diva2:714542,
author = {Dahlin, Johan and Schön, Thomas Bo and Villani, Mattias},
title = {{Approximate inference in state space models with intractable likelihoods using Gaussian process optimisation}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2014},
type = {Other academic},
number = {LiTH-ISY-R, 3075},
address = {Sweden},
}
```

In this paper, a method for estimating physical parameters using limited sensors is investigated. As a case study, measurements from an IMU are used for estimating the change in mass and the change in center of mass of a ship. The roll motion is studied and an instrumental variable method estimating the parameters of a transfer function from the tangential acceleration to the angular velocity is presented. It is shown that only a subset of the unknown parameters are identifiable simultaneously. A multi-stage identification approach is presented as a remedy for this. A limited simulation study is also presented to show the properties of the estimator. This shows that the method is indeed promising but that more work is needed to reduce the variance of the estimator.

```
@techreport{diva2:709403,
author = {Linder, Jonas and Enqvist, Martin and Gustafsson, Fredrik and Sjöberg, Johan},
title = {{Identifiability of physical parameters in systems with limited sensors}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2014},
type = {Other academic},
number = {LiTH-ISY-R, 3072},
address = {Sweden},
}
```

*O*(log

*N*) Parallel Algorithm for Newton Step Computation in Model Predictive Control", LiTH-ISY-R, No. 3073, 2014.

The use of Model Predictive Control in industry is steadily increasing as more complicated problems can be addressed. Due to that online optimization is usually performed, the main bottleneck with Model Predictive Control is the relatively high computational complexity. Hence, a lot of research has been performed to find efficient algorithms that solve the optimization problem. As parallelism is becoming more commonly used in hardware, the demand for efficient parallel solvers for Model Predictive Control has increased. In this paper, a tailored parallel algorithm that can adopt different levels of parallelism for solving the Newton step is presented. With sufficiently many processing units, it is capable of reducing the computational growth to logarithmic growth in the prediction horizon. Since the Newton step computation is where most computational effort is spent in both interior-point and active-set solvers, this new algorithm can significantly reduce the computational complexity of highly relevant solvers for Model Predictive Control.

```
@techreport{diva2:707876,
author = {Nielsen, Isak and Axehill, Daniel},
title = {{An \emph{O}(log \emph{N}) Parallel Algorithm for Newton Step Computation in Model Predictive Control}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2014},
type = {Refereed},
number = {LiTH-ISY-R, 3073},
address = {Sweden},
}
```

The iterative learning control (ILC) method improvesperformance of systems that repeat the same task several times. In this paper the standard norm-optimal ILC control law for linear systems is extended to an estimation-based ILC algorithm where the controlled variables are not directly available as measurements. The proposed ILC algorithm is proven to be stable and gives monotonic convergence of the error. The estimation-based part of the algorithm uses Bayesian estimation techniques such as the Kalman filter. The objective function in the optimisation problem is modified to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. It is further shown that for linear time-invariant systems the ILC design is independent of the estimation method. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ILC algorithm. It is also discussed how the Kullback-Leibler divergence can be used if linearisation cannot be performed. Finally, the proposed solution for non-linear systems is applied and verified in a simulation study with a simplified model of an industrial manipulator system.

```
@techreport{diva2:664219,
author = {Axelsson, Patrik and Karlsson, Rickard and Norrlöf, Mikael},
title = {{Estimation-based Norm-optimal Iterative Learning Control}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3066},
address = {Sweden},
}
```

_{∞}-Controller Design Methods Applied to One Joint of a Flexible Industrial Manipulator", LiTH-ISY-R, No. 3067, 2013.

Control of a flexible joint of an industrial manipulator using H_{∞} design methods is presented. The considered design methods are i) mixed-H_{∞} design, and ii) H_{∞} loop shaping design. Two different controller configurations are examined: one uses only the actuator position, while the other uses the actuator position and the acceleration of end-effector. The four resulting controllers are compared to a standard PID controller where only the actuator position is measured. The choices of the weighting functions are discussed in details. For the loop shaping design method, the acceleration measurement is required to improve the performance compared to the PID controller. For the mixed-H_{∞} method it is enough to have only the actuator position to get an improved performance. Model order reduction of the controllers is briefly discussed, which is important for implementation of the controllers in the robot control system.

```
@techreport{diva2:664215,
author = {Axelsson, Patrik and Helmersson, Anders and Norrlöf, Mikael},
title = {{H$_{∞}$-Controller Design Methods Applied to One Joint of a Flexible Industrial Manipulator}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3067},
address = {Sweden},
}
```

_{∞}Synthesis Method for Control of Non-linear Flexible Joint Models", LiTH-ISY-R, No. 3068, 2013.

An H_{∞} synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a convex, yet conservative, LMI problem. The method is motivated by the assumption that the joint operates in a specific stiffness region of the non-linear spring most of the time, hence the performance requirements are only valid in that region. However, the controller must stabilise the system in all stiffness regions. The method is validated in simulations on a non-linear flexible joint model originating from an industrial robot.

```
@techreport{diva2:664195,
author = {Axelsson, Patrik and Pipeleers, Goele and Helmersson, Anders and Norrlöf, Mikael},
title = {{H$_{∞}$ Synthesis Method for Control of Non-linear Flexible Joint Models}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3068},
address = {Sweden},
}
```

Many estimation problems require a mixture reduction algorithm with which an increasing number of mixture components are reduced to a tractable level. In this technical report a discussion on dierent aspects of mixture reduction is given followed by a presentation of numerical simulation on reduction of mixture densities where the component density belongs to the exponential family of distributions.

```
@techreport{diva2:661064,
author = {Ardeshiri, Tohid and Özkan, Emre and Orguner, Umut},
title = {{On Reduction of Mixtures of the Exponential Family Distributions}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3076},
address = {Sweden},
}
```

Simultaneous Localisation and Mapping (SLAM) denotes the problem of jointly localizing a moving platform and mapping the environment. This work studies the SLAM problem using a combination of inertial sensors, measuring the platform's accelerations and angular velocities, and a monocular camera observing the environment. We formulate the SLAM problem on a nonlinear least squares (NLS) batch form, whose solution provides a smoothed estimate of the motion and map. The NLS problem is highly nonconvex in practice, so a good initial estimate is required. We propose a multi-stage iterative procedure, that utilises the fact that the SLAM problem is linear if the platform's rotations are known. The map is initialised with camera feature detections only, by utilising feature tracking and clustering of feature tracks. In this way, loop closures are automatically detected. The initialization method and subsequent NLS refinement is demonstrated on both simulated and real data.

```
@techreport{diva2:646572,
author = {Skoglund, Martin and Sjanic, Zoran and Gustafsson, Fredrik},
title = {{Initialisation and Estimation Methods for Batch Optimisation of Inertial/Visual SLAM}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3065},
address = {Sweden},
}
```

Synthetic Aperture Radar (SAR) equipment is a radar imaging system that can be used to create high resolution images of a scene by utilising the movement of a flying platform. Knowledge of the platform's trajectory is essential to get good and focused images. An emerging application field is real-time SAR imaging using small and cheap platforms with poorer navigation systems implying unfocused images. This contribution investigatesa joint estimation of the trajectory and SAR image.

```
@techreport{diva2:627741,
author = {Sjanic, Zoran and Gustafsson, Fredrik},
title = {{Simultaneous Navigation and Synthetic Aperture Radar Focusing}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3063},
address = {Sweden},
}
```

The Swedish nuclear waste will be stored in copper canisters and kept isolated deep under ground for at least 100,000 years. To ensure reliable sealing of the canisters, friction stir welding is utilized. To repetitively produce high quality welds, it is vital to use automatic control of the process. A decentralized solution is designed based on an already existing temperature controller and a proposed linear plunge depth controller. The plunge depth control is challenging mainly because of deection in the machine, thermal expansion and cross couplings in the process. The decentralized controller has been implemented and evaluated on the real system with good results, keeping the plunge depth within the necessary 0:1 mm of its setpoint at the same time as the temperature specications are met.

```
@techreport{diva2:618349,
author = {Nielsen, Isak and Garpinger, Olof and Cederqvist, Lars},
title = {{Decentralized Friction Stir Welding Control on Canisters for Spent Nuclear Fuel}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3062},
address = {Sweden},
}
```

Indoor positioning in unknown environments is crucial for rescue personnel and future infotainment systems. Dead-reckoning inertial sensor data gives accurate estimate of distance, for instance using zero velocity updates, while the heading estimation problem is inherently more difficult due to the large degree of magnetic disturbances indoors. We propose a Kalman filter bank approach based on supporting a magnetic compass with gyroscope turn rate information, where a hidden Markov model is used to model the presence of magnetic disturbances. In parallel, we suggest to run a robust heading estimation system based on data from a sliding window. The robust estimate is used to detect filter divergence, and to restart the filter when needed. The underlying assumptions and the heading estimation performance are supported in field trials using more than 500 data sets from more than 50 venues in 5 continents.

```
@techreport{diva2:617588,
author = {Callmer, Jonas and Törnqvist, David and Gustafsson, Fredrik},
title = {{Robust Heading Estimation Indoors}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3061},
address = {Sweden},
}
```

The problem of estimating heading is central in the indoor positioning problem based on mea- surements from inertial measurement and magnetic units. Integrating rate of turn angular rate gives the heading with unknown initial condition and a linear drift over time, while the magnetometer gives absolute heading, but where long segments of data are useless in prac- tice because of magnetic disturbances. A basic Kalman filter approach with outlier rejection has turned out to be difficult to use with high integrity. Here, we propose an approach based on convex optimization, where segments of good magnetometer data are separated from disturbed data and jointly fused with the yaw rate measurements. The optimization framework is flexible with many degrees of freedom in the modeling phase, and we outline one design. A recursive solution to the optimization is derived, which has a computational complexity comparable to the simplest possible Kalman filter. The performance is evaluated using data from a handheld smartphone for a large amount of indoor trajectories, and the result demonstrates that the method effectively resolves the magnetic disturbances.

```
@techreport{diva2:617585,
author = {Callmer, Jonas and Törnqvist, David and Gustafsson, Fredrik},
title = {{Robust Heading Estimation Indoors using Convex Optimization}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3060},
address = {Sweden},
}
```

The effects of wear to friction are studied based on constant-speed friction data collected from dedicated experiments during accelerated wear tests. It is shown how the effects of temperature and load uncertainties produce larger changes to friction than those caused by wear, motivating the consideration of these effects. Based on empirical observations, an extended friction model is proposed to describe the effects of speed, load, temperature and wear. Assuming availability of such model and constant-speed friction data, a maximum likelihood wear estimator is proposed. A criterion for experiment design is proposed which selects speed points to collect constant-speed friction data which improves the achievable performance bound for any unbiased wear estimator. Practical issues related to experiment length are also considered. The performance of the wear estimator under load and temperature uncertainties is found by means of simulations and verified under three case studies based on real data.

```
@techreport{diva2:611255,
author = {Carvalho Bittencourt, Andr\'{e} and Axelsson, Patrik},
title = {{Modeling and Experiment Design for Identification of Wear in a Robot Joint under Load and Temperature Uncertainties based on Constant-speed Friction Data}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3058},
address = {Sweden},
}
```

This paper presents a method for monitoring of systems that operate in a repetitive manner. Considering that data batches collected from a repetitive operation will be similar unless in the presence of an abnormality, a condition change is inferred by comparing the monitored data against a nominal batch. The method proposed considers the comparison of data in the distribution domain, which reveals information of the data amplitude. This is achieved with the use of kernel density estimates and the Kullback-Leibler distance. To decrease sensitivity to unknown disturbances while increasing sensitivity to faults, the use of a weighting vector is suggested which is chosen based on a labeled dataset. The framework is simple to implement and can be used without process interruption, in a batch manner. The method was developed with interests in industrial robotics where a repetitive behavior is commonly found. The problem of wear monitoring in a robot joint is studied based on data collected from a test-cycle. Real data from accelerated wear tests and simulations are considered. Promising results are achieved where the method output shows a clear response to the wear increases.

```
@techreport{diva2:602140,
author = {Carvalho Bittencourt, Andr\'{e} and Saarinen, Kari and Sander Tavallaey, Shiva and Gunnarsson, Svante},
title = {{A Data-Driven Method for Monitoring of Repetitive Systems: Applications to Robust Wear Monitoring of a Robot Joint}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2013},
type = {Other academic},
number = {LiTH-ISY-R, 3056},
address = {Sweden},
}
```

A common assumption when proving stability of linear MPC algorithms fort racking applications is to assume that the desired setpoint is located farinto the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severly limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modiﬁcations that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allowsa setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints are used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile ﬁghter aircraftis given.

```
@techreport{diva2:650887,
author = {Simon, Daniel and Löfberg, Johan and Glad, Torkel},
title = {{Reference Tracking MPC using Terminal Set Scaling}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3044},
address = {Sweden},
}
```

In many real-world optimization applications there are often a number of conﬂicting objective functions that are all important to optimize. The purpose of multiobjective optimization (MOO) is to give the decision maker(DM) an understanding of how these functions are conﬂicting and the possibility to choose an appropriate trade-oﬀ between them. There are multiple methods for solving MOO problems but the focus in this paper is on interactive methods. When the size and complexity of the MOO problem grows the time needed to ﬁnd a solution is too long to yield a pleasant experience for the DM. In this paper, a method to replace the original MOO problem with an approximation is suggested to speed up the process. The approximation is created and used in a two-step framework which makes it possible to investigate the Pareto frontier in real-time and that can handle nonlinear and non-convex MOO problems with m objective functions. The ﬁrst step generates a number of samples of the complete Pareto frontier which is sparse but dense enough for the approximation. The second stepis an interactive tool for the DM to use to continuously and in real-time navigate on the approximated Pareto set in both objective- and decision space. The tool is used to investigate the Pareto frontier and to ﬁnd a preferred solution. A method of decomposing the approximated set into simplices has been developed using Delaunay triangulation. This methodis able to make a good approximation for sets that are non-convex. The method is also able to handle disconnected sets and holes. This makes it possible to change the feasible region in both decision- and objective space. The framework is demonstrated on three example problems that show the functionality and performance of the implemented framework.

```
@techreport{diva2:650882,
author = {Linder, Jonas and Lindkvist, Simon and Sjöberg, Johan},
title = {{Two-Step Framework for Interactive Multi-Objective Optimization}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3043},
address = {Sweden},
}
```

This report contains pseudo-code for, and a computational complexity analysis of, the Gaussian inverse Wishart Probability Hypothesis Density filter.

```
@techreport{diva2:633474,
author = {Granström, Karl and Orguner, Umut},
title = {{Implementation of the GIW-PHD filter}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3046},
address = {Sweden},
}
```

This technical report summarizes a number of results for the multivariate t distribution which can exhibit heavier tails than the Gaussian distribution. It is shown how t random variables can be generated, the probability density function (pdf) is derived, and marginal and conditional densities of partitioned t random vectors are presented. Moreover, a brief comparison with the multivariate Gaussian distribution is provided. The derivations of several results are given in an extensive appendix.

```
@techreport{diva2:618567,
author = {Roth, Michael},
title = {{On the Multivariate t Distribution}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3059},
address = {Sweden},
}
```

We propose a method for model reduction on a given frequency range, without having to specify input and output filter weights. The method uses a nonlinear optimization approach where we formulate a H2 like cost function which only takes the given frequency range into account. We derive a gradient of the proposed cost function which enables us to use off-the-shelf optimization software.

```
@techreport{diva2:606348,
author = {Petersson, Daniel and Löfberg, Johan},
title = {{Model Reduction using a Frequency-Limited H2-Cost}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3045},
address = {Sweden},
}
```

Prediction and filtering of continuous-time stochastic processes require a solver of a continuous-time differential Lyapunov equation (CDLE). Even though this can be recast into an ordinary differential equation (ODE), where standard solvers can be applied, the dominating approach in Kalman filter applications is to discretize the system and then apply the discrete-time difference Lyapunov equation (DDLE). To avoid problems with stability and poor accuracy, oversampling is often used. This contribution analyzes over-sampling strategies, and proposes a low-complexity analytical solution that does not involve oversampling. The results are illustrated on Kalman filtering problems in both linear and nonlinear systems.

```
@techreport{diva2:577958,
author = {Axelsson, Patrik and Gustafsson, Fredrik},
title = {{Discrete-time Solutions to the Continuous-time Differential Lyapunov Equation With Applications to Kalman Filtering}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3055},
address = {Sweden},
}
```

_{∞}Loop Shaping", LiTH-ISY-R, No. 3053, 2012.

Control of a flexible joint of an industrial manipulator using H_{∞} loop shaping design is presented. Two controllers are proposed; 1) H_{∞} loop shaping using the actuator position, and 2) H_{∞} loop shaping using the actuator position and the acceleration of end-effector. The two controllers are compared to a standard PID controller where only the actuator position is measured. Using the acceleration of the end-effector improves the nominal performance. The performance of the proposed controllers is not significantly decreased in the case of model error consisting of an increased time delay or a gain error.

```
@techreport{diva2:562932,
author = {Axelsson, Patrik and Helmersson, Anders and Norrlöf, Mikael},
title = {{Single Joint Control of a Flexible Industrial Manipulator using H$_{∞}$ Loop Shaping}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3053},
address = {Sweden},
}
```

A Wiener model is a fairly simple, well known, and often used nonlinearblock-oriented black-box model. A possible generalization of the class ofWiener models lies in the parallel Wiener model class. This paper presents amethod to estimate the linear time-invariant blocks of such parallel Wienermodels from input/output data only. The proposed estimation methodcombines the knowledge obtained by estimating the best linear approxima-tion of a nonlinear system with a dimension reduction method to estimatethe linear time-invariant blocks present in the model. The estimation of thestatic nonlinearity is fairly easy once the linear blocks are known.

```
@techreport{diva2:559973,
author = {Schoukens, Maarten and Lyzell, Christian and Enqvist, Martin},
title = {{Combining the best linear approximation and dimension reduction to identify thelinear blocks of parallel Wiener systems}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3050},
address = {Sweden},
}
```

Exploration is in this work defined as the task of efficient information gathering of areas, building, roads, etc., by controlling a pan/tilt camera on a sensor platform. Good exploration is characterized by several images from different directions of the areas of interests and that the images can be used to create maps, video mosaics and multi-view imagery for anomaly and change detection. In this paper an aerial exploration framework based on the information filter is presented. The work is inspired by research on optimal trajectory for bearings-only tracking. A number of static grid points represent the area to be explored and the problem is to plan the trajectory of the sensor platform and the pointing direction of the camera to maximize the exploration performance of the grid points.

```
@techreport{diva2:517410,
author = {Skoglar, Per},
title = {{Information Based Planning for Aerial Exploration}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3047},
address = {Sweden},
}
```

This work considers a sensor management problem where a number of road bounded vehicles are monitored by a UAV with a gimballed vision sensor. The problem is to keep track of all discovered targets and simultaneously search for new targets by controlling the pointing direction of the vision sensor and the motion of the UAV. A planner based on a state-machine is proposed with three different modes; target tracking, known target search, and new target search. A high-level decision maker chooses among these sub-tasks to obtain an overall situational awareness. A utility measure for evaluating the combined search and target tracking performance is also proposed. By using this measure it is possible to evaluate and compare the rewards of updating known targets versus searching for new targets in the same framework. The targets are assumed to be road bounded and the road network information is used both to improve the tracking and sensor management performance. The tracking and search are based on flexible target density representations provided by particle mixtures and deterministic grids.

```
@techreport{diva2:517398,
author = {Skoglar, Per and Orguner, Umut and Törnqvist, David and Gustafsson, Fredrik},
title = {{Road Target Search and Tracking with Gimballed Vision Sensor on a UAV}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3049},
address = {Sweden},
}
```

Airborne surveillance systems equipped with a vision/infrared camera require good knowledge about the position and orientation of the camera for successful tracking of ground targets. In particular, this is essential when incorporating prior information, like road maps, that is expressed relative a global reference system. Usually, it is possible to obtain good positioning with inertial/satellite navigation systems, but estimating the orientation is generally more difficult. It might be possible to use SLAM (Simultaneous Localization and Mapping) or image registration approaches to support the navigation system, but not always since such approaches require stable features in the images. In this paper the problem of simultaneous orientation error estimation and road target tracking is considered by assuming that the target is constrained to a known road network. A particle filter approach is proposed and it is shown that the result of this filter is close to the performance of the ideal case where the orientation error is perfectly known. However, the performance depends on how informative the road path is and in rare cases the orientation error is unobservable.

```
@techreport{diva2:517396,
author = {Skoglar, Per and Törnqvist, David},
title = {{Simultaneous Camera Orientation Estimation and Road Target Tracking}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2012},
type = {Other academic},
number = {LiTH-ISY-R, 3048},
address = {Sweden},
}
```

ARX models is a common class of models of dynamical systems. Here, we consider the case when the innovation process is not well described by Gaussian noise and instead propose to model the driving noise as Student's t distributed. The t distribution is more heavy tailed than the Gaussian distribution, which provides an increased robustness to data anomalies, such as outliers and missing observations. We use a Bayesian setting and design the models to also include an automatic order determination. Basically, this means that we infer knowledge about the posterior distribution of the model order from data. We consider two related models, one with a parametric model order and one with a sparseness prior on the ARX coefficients. We derive Markov chain Monte Carlo samplers to perform inference in these models. Finally, we provide three numerical illustrations with both simulated data and real EEG data to evaluate the proposed methods.

```
@techreport{diva2:650880,
author = {Dahlin, Johan and Lindsten, Fredrik and Schön, Thomas and Wills, Adrian},
title = {{Robust ARX Models with Automatic Order Determination and Student's t Innovations}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2011},
type = {Other academic},
number = {LiTH-ISY-R, 3041},
address = {Sweden},
}
```

This paper presents a method for condition monitoring of systems that operate in a repetitive manner. A data driven method is proposed that considers changes in the distribution of data samples obtained from multiple executions of one or several tasks. This is made possible with the use of kernel density estimators and the Kullback-Leibler distance measure between distributions. To increase robustness to unknown disturbances and sensitivity to faults, the use of a weighting function is suggested which can considerably improve detection performance. The method is very simple to implement, it does not require knowledge about the monitored system and can be used without process interruption, in a batch manner. The method is illustrated with applications to robust wear monitoring in a robot joint. Interesting properties of the application are presented through a real case study and simulations. The achieved results show that robust wear monitoring in industrial robot joints is made possible with the proposed method.

```
@techreport{diva2:650879,
author = {Carvalho Bittencourt, Andr\'{e} and Saarinen, Kari and Sander-Tavallaey, Shiva},
title = {{A Data-Driven Method for Monitoring Systems that Operate Repetitively:
Applications to Robust Wear Monitoring inan Industrial Robot Joint}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2011},
type = {Other academic},
number = {LiTH-ISY-R, 3040},
address = {Sweden},
}
```

Performing experiments for system identication is often a time-consuming task which may also interfere with the process operation. With memory prices going down, it is more and more common that years of process data are stored (without compression) in a history database. The rationale for this work is that in such stored data there must already be intervals informative enough for system identication. Therefore, the goal of this project was to find an algorithm that searches and marks intervals suitable for process identication (rather than performing completely automatic system identication). For each loop, 4 stored variables are required; setpoint, manipulated variable, process output and mode of the controller.

The proposed method requires a minimum of knowledge of the process and is implemented in a simple and ecient recursive algorithm. The essential features of the method are the search for excitation of the input and output, followed by the estimation of a Laguerre model combined with a chi-square test to check that at least one estimated parameter is statistically signicant. The use of Laguerre models is crucial to handle processes with deadtime without explicit delay estimation. The method was tested on three years of data from more than 200 control loops. It was able to find all intervals in which known identication experiments were performed as well as many other useful intervals in closed/open loop operation.

```
@techreport{diva2:650878,
author = {Peretzki, Daniel and Isaksson, Alf and Carvalho Bittencourt, Andr\'{e} and Forsman, Krister},
title = {{Data Mining of Historic Data for Process Identification}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2011},
type = {Other academic},
number = {LiTH-ISY-R, 3039},
address = {Sweden},
}
```

Friction is the result of complex interactions between contacting surfaces in a nanoscale perspective. Depending on the application, the different models available are more or less suitable. Available static friction models are typically considered to be dependent only on relative speed of interacting surfaces. However, it is known that friction can be affected by other factors than speed. In this paper, the typical friction phenomena and models used in robotics are reviewed. It is shown how such models can be represented as a sum of linear and nonlinear functions of relevant states, and how the identiﬁcation method described in [1] can be used to identify them when all state sare measured. The discussion follows with a detailed experimental study of friction in a robot joint under changes of joint angle, load torque and temperature. Justiﬁed by their signiﬁcance, load torque and temperature are included in an extended static friction model. The proposed model is validated in a wide operating range, considerably improving the prediction performance compared to a standard model.

```
@techreport{diva2:650876,
author = {Carvalho Bittencourt, Andr\'{e} and Gunnarsson, Svante},
title = {{Static Friction in a Robot Joint:
Modeling and Identificaiton of Load and Temperature Effects}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2011},
type = {Other academic},
number = {LiTH-ISY-R, 3038},
address = {Sweden},
}
```

In the presence of frequent inlet flow upsets, tuning of averaging level controllers is typically quite complicated since not only the size of the individual steps but also the time in between the subsequent steps need to considered. One structured way to achieve optimal filtering for such a case is to use Robust Model Predictive Control. The robust MPC controller is, however, quite computationally demanding and not easy to implement. In this paper two linear controllers, which mimic the behavior of the robust MPC, are proposed. Tuning guidelines to avoid violation of the tank level constraints as well as to achieve optimal filtering are presented.

```
@techreport{diva2:650875,
author = {Rosander, Peter and Isaksson, Alf and Löfberg, Johan and Forsman, Krister},
title = {{Practical Control of Surge Tanks Suffering from Frequent Inlet Flow Upsets}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2011},
type = {Other academic},
number = {LiTH-ISY-R, 3036},
address = {Sweden},
}
```

We consider a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process (GP) model for the static nonlinearity. The GP model is a flexible model that can describe different types of nonlinearities while avoiding making strong assumptions such as monotonicity. We derive an inferential method based on recent advances in Monte Carlo statistical methods, known as Particle Markov Chain Monte Carlo (PMCMC). The idea underlying PMCMC is to use a particle filter (PF) to generate a sample state trajectory in a Markov chain Monte Carlo sampler. We use a recently proposed PMCMC sampler, denoted particle Gibbs with backward simulation, which has been shown to be efficient even when we use very few particles in the PF. The resulting method is used in a simulation study to identify two different Wiener systems with non-invertible nonlinearities.

```
@techreport{diva2:650874,
author = {Lindsten, Fredrik and Schön, Thomas and Jordan, Michael I.},
title = {{A Semiparametric Bayesian Approach to Wiener System Identification}},
institution = {Linköping University, Department of Electrical Engineering},
year = {2011},
type = {Other academic},
number = {LiTH-ISY-R, 3037},
address = {Sweden},
}
```