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 ℓ₁-regularization. The regularization constant regulates the complexity and is used to trade off the fit and the number of submodels.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

We provide a sensor fusion framework for solving the problem of joint egomotionand road geometry estimation. More specifically we employ a sensorfusion framework to make systematic use of the measurements from a forwardlooking radar and camera, steering wheel angle sensor, wheel speedsensors and inertial sensors to compute good estimates of the road geometryand the motion of the ego vehicle on this road. In order to solve this problemwe derive dynamical models for the ego vehicle, the road and the leadingvehicles. The main difference to existing approaches is that we make use ofa new dynamic model for the road. An extended Kalman filter is used to fusedata and to filter measurements from the camera in order to improve the roadgeometry estimate. The proposed solution has been tested and comparedto existing algorithms for this problem, using measurements from authentictraffic environments on public roads in Sweden. The results clearly indicatethat the proposed method provides better estimates.

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.

A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ¹⁸O 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.

A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ¹⁸O 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.

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.

Shooter localization in a wireless network of microphones is studied. Both the acoustic muzzle blast (MB) from the gunfire and the ballistic shock wave (SW) from the bullet can be detected by the microphones and considered as measurements. The MB measurements give rise to a standard sensor network problem, similar to time difference of arrivals in cellular phone networks, and the localization accuracy is good, provided that the sensors are well synchronized compared to the MB detection accuracy. The detection times of the SW depend on both shooter position and aiming angle and may provide additional information beside the shooter location, but again this requires good synchronization. We analyze the approach to base the estimation on the time difference of MB and SW at each sensor, which becomes insensitive to synchronization inaccuracies. Cramer-Rao lower bound analysis indicates how a lower bound of the root mean square error depends on the synchronization error for the MB and the MB-SW difference, respectively. The estimation problem is formulated in a separable nonlinear least squares framework. Results from field trials with different types of ammunition show excellent accuracy using the MB-SW difference for both the position and the aiming angle of the shooter.

In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the local stability, and, respectively, the asymptotic small gain theorem to establish the global convergence property, of the closed-loop system An example is given to show that a redesign of the controller is required to guarantee the global robust asymptotic stability in the presence of the input unmodeled dynamics

System identification is the art and science of building mathematical models of dynamic systems from observed input-output data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous necessity for successful applications System identification is a very large topic, with different techniques that depend on the character of the models to be estimated: linear, nonlinear, hybrid, nonparametric, etc At the same time, the area can be characterized by a small number of leading principles, e.g. to look for sustainable descriptions by proper decisions in the triangle of model complexity, information contents in the data, and effective validation. The area has many facets and there are many approaches and methods A tutorial or a survey in a few pages is not quite possible Instead, this presentation aims at giving an overview of the "science" side, i.e. basic principles and results and at pointing to open problem areas in the practical, "art", side of how to approach and solve a real problem.

The standard continuous time state space model with stochastic disturbances contains the mathematical abstraction of continuous time white noise. To work with well defined, discrete time observations, it is necessary to sample the model with care. The basic issues are well known, and have been discussed in the literature. However, the consequences have not quite penetrated the practice of estimation and identification. One example is that the standard model of an observation, being a snapshot of the current state plus noise independent of the state, cannot be reconciled with this picture. Another is that estimation and identification of time continuous models require a more careful treatment of the sampling formulas. We discuss and illustrate these issues in the current contribution. An application of particular practical importance is the estimation of models based on irregularly sampled observations.

In this article, a primal-dual interior-point algorithm for semidefinite programming that can be used for analysing e.g. polytopic linear differential inclusions is tailored in order to be more computationally efficient. The key to the speedup is to allow for inexact search directions in the interior-point algorithm. These are obtained by aborting an iterative solver for computing the search directions prior to convergence. A convergence proof for the algorithm is given. Two different preconditioners for the iterative solver arc proposed. The speedup is in many cases more than an order of magnitude. Moreover, the proposed algorithm can be used to analyse much larger problems as compared to what is possible with off-the-shelf interior-point solvers.

This paper treats several aspects relevant to the identification of continuous-time output error (OE) models based on non-uniformly sampled output data. The exact method for doing this is well known in the time domain, where the continuous-time system is discretized, simulated and the result is fitted in a mean square sense to measured data. The material presented here is based on a method proposed in a companion paper (Gillberg andamp; Ljung, 2010) which deals with the same topic but for the case of uniformly sampled data. In this text it will be shown how that method suggests that the output should be reconstructed using a B-spline with uniformly distributed knots. This representation can then be used to directly identify the continuous-time system without proceeding via discretization. Only the relative degree of the model is used to choose the order of the spline.

This paper considers the problem of fingerprinting localization in wireless networks based on received-signal-strength (RSS) observations. First, the performance of static localization using power maps (PMs) is improved with a new approach called the base-station-strict (BS-strict) methodology, which emphasizes the effect of BS identities in the classical fingerprinting. Second, dynamic motion models with and without road network information are used to further improve the accuracy via particle filters. The likelihood-calculation mechanism proposed for the particle filters is interpreted as a soft version (called BS-soft) of the BS-strict approach applied in the static case. The results of the proposed approaches are illustrated and compared with an example whose data were collected from a WiMAX network in a challenging urban area in the capitol city of Brussels, Belgium.

Sensor localization is a central problem for sensor networks. If the sensor positions are uncertain, the target tracking ability of the sensor network is reduced. Sensor localization in underwater environments is traditionally addressed using acoustic range measurements involving known anchor or surface nodes. We explore the usage of triaxial magnetometers and a friendly vessel with known magnetic dipole to silently localize the sensors. The ferromagnetic field created by the dipole is measured by the magnetometers and is used to localize the sensors. The trajectory of the vessel and the sensor positions are estimated simultaneously using an Extended Kalman Filter (EKF). Simulations show that the sensors can be accurately positioned using magnetometers.

System identification based on quantized observations requires either approximations of the quantization noise, leading to suboptimal algorithms, or dedicated algorithms tailored to the quantization noise properties. This contribution studies fundamental issues in estimation that relate directly to the core methods in system identification. As a first contribution, results from statistical quantization theory are surveyed and applied to both moment calculations (mean, variance etc) and the likelihood function of the measured signal. In particular, the role of adding dithering noise at the sensor is studied. The overall message is that tailored dithering noise can considerably simplify the derivation of optimal estimators. The price for this is a decreased signal to noise ratio, and a second contribution is a detailed study of these effects in terms of the Cramer-Rao lower bound. The common additive uniform noise approximation of quantization is discussed, compared, and interpreted in light of the suggested approaches.

A benchmark problem for robust feedback control of a flexible manipulator is presented. The system to be controlled is a four-mass system subject to input saturation, nonlinear gear elasticity, model uncertainties, and load disturbances affecting both the motor and the arm. The system should be controlled by a discrete-time controller that optimizes performance for given robustness requirements. Four suggested solutions are presented, and even though the solutions are based on different design methods, they give comparable results.

A new approach for computing upper error bounds for reduced-order models of linear time-varying systems is presented. It is based on a transformation technique of the Hankel singular values using positive-real, odd incremented functions. By applying such time-varying functions, the singular values to be removed can be forced to become equal and constant, so that they can be reduced. Two variations of this method are proposed: one for finite-time horizons and the other for infinite-time problems including periodic systems.

The subject of this paper is the direct identification of continuous-time autoregressive moving average (CARMA) models. The topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous-time power spectral density (CT-PSD) into a key issue. The first part of the paper therefore concerns the approximate estimation of the CT-PSD from uniformly sampled data under the assumption that the model has a certain relative degree. The approach has its point of origin in the frequency domain Whittle likelihood estimator. The discrete- or continuous-time spectral densities are estimated from equidistant samples of the output. For low sampling rates the discrete-time spectral density is modeled directly by its continuous-time spectral density using the Poisson summation formula. In the case of rapid sampling the continuous-time spectral density is estimated directly by modifying its discrete-time counterpart.

Checking non-negativity of polynomials using sum-of-squares has recently been popularized and found many applications in control. Although the method is based on convex programming, the optimization problems rapidly grow and result in huge semidefinite programs. Additionally, they often become increasingly ill-conditioned. To alleviate these problems, it is important to exploit properties of the analyzed polynomial, and post-process the obtained solution. This technical note describes how the sum-of-squares module in the MATLAB toolbox YALMIP handles these issues.

Many optimization problems gain from being interpreted and solved in either primal or dual forms. For a user with a particular application, one of these forms is usually much more natural to use, but this is not always the most efficient. This paper presents an implementation in the optimization modelling tool YALMIP that allows the user to define conic optimization problems in a preferred format, and then automatically derive a symbolic YALMIP model of the dual of this problem, solve the dual, and recover original variables. Applications in flexible generation of sum-of-squares programs, and efficient formulations of large-scale experiment design problems are used as illustrative examples.

Systems biology and its usage of mathematical modeling to analyse biological data is rapidly becoming an established approach to biology. A crucial advantage of this approach is that more information can be extracted from observations of intricate dynamics, which allows nontrivial complex explanations to be evaluated and compared. In this minireview we explain this process, and review some of the most central available analysis tools. The focus is on the evaluation and comparison of given explanations for a given set of experimental data and prior knowledge. Three types of methods are discussed: (a) for evaluation of whether a given model is sufficiently able to describe the given data to be nonrejectable; (b) for evaluation of whether a slightly superior model is significantly better; and (c) for a general evaluation and comparison of the biologically interesting features in a model. The most central methods are reviewed, both in terms of underlying assumptions, including references to more advanced literature for the theoretically oriented reader, and in terms of practical guidelines and examples, for the practically oriented reader. Many of the methods are based upon analysis tools from statistics and engineering, and we emphasize that the systems biology focus on acceptable explanations puts these methods in a nonstandard setting. We highlight some associated future improvements that will be essential for future developments of model based data analysis in biology.

This paper details an approach to the integration of INS (Inertial Navigation System) and TAP (Terrain-Aided Positioning). The solution is characterized by a joint design of INS and TAP, meaning that the highly nonlinear TAP is not designed separately but jointly with the INS using one and the same filter. The applied filter extends the theory of the MPF (Marginalized Particle Filter) given by [1]. The key idea with MPF is to estimate the nonlinear part using the particle filter and the part which is linear, conditionally upon the nonlinear part, is estimated using the Kalman filter. The extension lies in the possibility to deal with a third multi-modal part, where the discrete mode variable is also estimated jointly with the linear and nonlinear parts. Conditionally upon the mode and the nonlinear part, the resulting subsystem is linear and estimated using the Kalman filter. Given the nonlinear motion equations which the INS uses to compute navigation data, the INS equations must be linearized for the MPF to work. A set of linearized equations is derived and the linearization errors are shown to be insignificant with respect to the final result. Simulations are performed and the result indicates near-optimal accuracy when compared to the Cramer-Rao lower bound.

This paper describes an online maximum likelihood estimator for the transition probabilities associated with a jump Markov linear system (JMLS). The maximum likelihood estimator is derived using the reference probability method, which exploits an hypothetical probability measure to find recursions for complex expectations. Expectation maximization (EM) procedure is utilized for maximizing the likelihood function. In order to avoid the exponential increase in the number of statistics of the optimal EM algorithm, we make interacting multiple model (IMM)-type approximations. The resulting method needs the mode weights of an IMM filter with N3 components, where N is the number of models in the JMLS. The algorithm can also supply base-state estimates and covariances as a by-product. The performance of the estimator is illustrated on two simulated examples and compared to a recently proposed alternative. © 2008 IEEE.

Regressor selection can be viewed as the first step in the system identification process. The benefits of finding good regressors before estimating complex models are especially clear for nonlinear systems, where the class of possible models is huge. In this article, a structured way of using the tool analysis of variance (ANOVA) is presented and used for NARX model (nonlinear autoregressive model with exogenous input) identification with many candidate regressors. © 2007 Elsevier Ltd. All rights reserved.

This paper presents a threat-assessment algorithm for general road scenes. A road scene consists of a number of objects that are known, and the threat level of the scene is based on their current positions and velocities. The future driver inputs of the surrounding objects are unknown and are modeled as random variables. In order to capture realistic driver behavior, a dynamic driver model is implemented as a probabilistic prior, which computes the likelihood of a potential maneuver. A distribution of possible future scenarios can then be approximated using a Monte Carlo sampling. Based on this distribution, different threat measures can be computed, e.g., probability of collision or time to collision. Since the algorithm is based on the Monte Carlo sampling, it is computationally demanding, and several techniques are presented to increase performance without increasing computational load. The algorithm is intended both for online safety applications in a vehicle and for offline data analysis.

Based on simple Frequency Response Function (FRF) measurements, we give the user some guidance in the selection of an appropriate nonlinear block structure for the system to be modeled. The method consists in measuring the FRF using a Gaussian-like input signal and varying in a first experiment the root-mean-square (rms) value of this signal while maintaining the coloring of the power spectrum. Next, in a second experiment, the coloring of the power spectrum is varied while keeping the rms value constant. Based on the resulting behavior of the FRF, an appropriate nonlinear block structure can be selected to approximate the real system. The identification of the selected block-oriented model itself is not addressed in this paper. A theoretical analysis and two practical applications of this structure identification method are presented for some nonlinear block structures. © 2008 IEEE.

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.

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

This chapter is concerned with the problem of estimating a map of theimmediate surroundings of a vehicle as it moves. In order to compute these mapestimates sensor measurements from radars, lasers and/or cameras are used togetherwith the standard proprioceptive sensors present in a car. Four different types ofmaps are discussed. Feature based maps are represented by a set of salient features.Road maps make use of the fact that roads are highly structured, since they are builtaccording to clearly specified road construction standards, which allows relativelysimple and powerful models of the road to be employed. Location based maps,where occupancy grid maps belong and finally intensity based maps, which can beviewed as a continuous version of the location based maps. The aim is to provide aself-contained presentation of how these maps can be built from measurements. Realdata from Swedish roads are used throughout the chapter to illustrate the methodsintroduced.

In this chapter parallel implementations of hybrid MPC will bediscussed. 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.

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.

Wireless sensor networks (WSN) localization relies on measurements. Availability of, and the information content in, these measurements depend on the network architecture, connectivity, node time synchronization and the signaling bandwidth between the sensor nodes. This chapter addresses wireless sensor networks measurements in a general framework based on a set of nodes, where each node either emits or receives signals. The emitted signal can for example be a radio, acoustic, seismic, infrared or sonic wave that is propagated in a certain media to the receiver. This general observation model does not make any difference between localization of sensor network nodes or unknown objects, or whether the nodes or objects are stationary or mobile. The information available for localization in wireless cellular networks (WCN) is in literature classified as direction of arrival (DOA), time of arrival (TOA), time difference of arrival (TDOA) and received signal strength (RSS). This chapter generalizes these concepts to the more general wireless sensor networks.

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.

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.

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.

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.

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.

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.

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.

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.

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. 

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.

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.

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.

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. 

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.

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.

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.

We consider measurements from possibly zero-meanstochastic processes in a nonlinear filtering framework. This is achallenging problem, since it is only the second order propertiesof the measurements that bear information about the unknownstate vector. The covariance function of the measurements canhave both spatial and temporal correlation that depend on thestate. Recently, a solution to this problem was presented forthe case of Gaussian processes. We here extend the theory toStudent’s t processes. We illustrate the state observability by asimple but still realistic simulation example.

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.

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.

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.

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.

Piecewise affine systems serve as an important approximation of nonlinear systems. The identification of piecewise affine systems is here tackled by overparametrizing and assigning a regressor-parameter to each of the observations. Regressor parameters are then 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 generalizationof the l1-regularization. The regularization constant is used to tradeoff fit and the number of partitions.

The robust H₂ 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 H₂ norm, and we provide an algorithmic method for calculating an upper bound for the mentioned quantity.

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.

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.

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.

The task of generating time optimal trajectories for a six degrees offreedom industrial robot is discussed and an existing convexoptimization formulation of the problem is extended to include newtypes of constraints. The new constraints are speed dependent and canbe motivated from physical modeling of the motors and the drivesystem. It is shown how the speed dependent constraints should beadded in order to keep the convexity of the overall problem. A methodto, conservatively, approximate the linear speed dependent constraintsby a convex constraint is also proposed. A numerical example provesversatility of the extension proposed in this paper.

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.

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.

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.

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.

This paper presents a framework for tracking extendedtargets which give rise to a structured set of measurementsper each scan. The concept of a measurement generating point(MGP) which is defined on the boundary of each target isintroduced. The tracking framework contains an hybrid statespace where MGP:s and the measurements are modeled byrandom finite sets and target states by random vectors. The targetstates are assumed to be partitioned into linear and nonlinearcomponents and a Rao-Blackwellized particle filter is used fortheir estimation. For each state particle, a probability hypothesisdensity (PHD) filter is utilized for estimating the conditionalset of MGP:s given the target states. The PHD kept for eachparticle serves as a useful means to represent information inthe set of measurements about the target states. The earlyresults obtained show promising performance with stable targetfollowing capability and reasonable shape estimates.

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.

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.

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.

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.

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.

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.

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.

Starting from Maxwell’s equations, wederive a sensor model for three-axis magnetometerssuitable for localization and tracking applications. Themodel depends on the relative position between the sensorand the target, and a physical magnetic multipolemodel of the target. Both point targets (far-field) andextended target (near-field) models are provided. Themodels are validated on data taken from various roadvehicles. The suitability of magnetometers for trackingis analyzed in terms of local observability and Cram´erRao lower bound as a function of the sensor positionsin a two sensor scenario. Results from field test dataindicate excellent tracking of position and velocity of thetarget, as well as identification of the magnetic targetmodel suitable for target classification.

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.

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.

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.

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.

In this paper we present a regularization of an H₂-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.

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 atool 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.

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.

A framework for Iterative Learning Control (ILC) is proposed for the situation when the ILC algorithm is based on an estimate of the controlled variable obtained from an observer-based estimation procedure. 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 exemplified by an ILC algorithm applied to a flexible two-mass model of a robot joint.

We present the first step towards a brain computer interface (BCI) for communication using real-time functional magnetic resonance imaging (fMRI). The subject in the MR scanner sees a virtual keyboard and steers a cursor to select different letters that can be combined to create words. The cursor is moved to the left by activating the left hand, to the right by activating the right hand, down by activating the left toes and up by activating the right toes. To select a letter, the subject simply rests for a number of seconds. We can thus communicate with the subject in the scanner by for example showing questions that the subject can answer. Similar BCI for communication have been made with electroencephalography (EEG). The subject then focuses on a letter while different rows and columns of the virtual keyboard are flashing and the system tries to detect if the correct letter is flashing or not. In our setup we instead classify the brain activity. Our system is neither limited to a communication interface, but can be used for any interface where five degrees of freedom is necessary.

To estimate the past climate, for example the ocean temperature 1000 years ago, one has to turn to naturally occurring climate recorders. There exist a number of climate recorders in nature from which the past temperature can be extracted. However, only a few natural archives are able to record climate fluctuations with high enough resolution so that the seasonal variations can be reconstructed. One such archive is a bivalve shell. The chemical composition of a shell of a bivalve depends on a number of chemical and physical parameters of the water in which the shell was composed. Of these parameters, the water temperature is probably the most important one. It should therefore be possible to estimate the water temperature for the years the shell was built, from measurements of the shell's chemical composition. In this paper, we explore this possibility. We do this by first observing that the chemical compositions lie on a one-dimensional manifold parameterized by the water temperature. This manifold is then utilized in the regression to obtain accurate estimates of past water temperatures.

High-dimensional gray-box identification is a fairly unexplored part of system identification. Nevertheless, system identification problems tend to be more high-dimensional nowadays. In this paper we deal with high-dimensional regression with regressors constrained to some manifold. A recent technique in this class is weight determination by manifold regularization (WDMR). WDMR, however, is a black-box identification method. We show how WDMR can be extended to a gray-box method and illustrate the scheme with some examples.

The chemical composition of a bivalve shell is strongly coupled to the seasonal variations in the environment. The nonlinear nature of this relation however makes it hard to predict, e.g. the temperature, from the chemical composition of a shell. In this paper we compare the ability of three nonlinear system identification methods to reconstruct the temperature from the chemical composition of a shell. The comparison shows that nonlinear multi-proxy approaches are potential tools for climate reconstructions with a preference for manifold based methods that results in smoother and a more precise temperature reconstruction.

This paper describes a benchmark for nonlinear system identification. A Wiener-Hammerstein system is selected as test object. In such a structure there is no direct access to the static nonlinearity starting from the measured input/output, because it is sandwiched between two unknown dynamic systems. The signal-to-noise ratio of the measurements is quite high, which puts the focus of the benchmark on the ability to identify the nonlinear behaviour, and not so much on the noise rejection properties. The benchmark is not intended as a competition, but as a tool to compare the possibilities of different methods to deal with this specific nonlinear structure.

Identification of time-continuous models from sampled data is a long standing topic of discussion, and many approaches have been suggested. The Maximum Likelihood method is asymptotically and theoretically superior to other methods. However, it may suffer from numerical inaccuracies at fast sampling and it also requires reliable initial parameter values. A number of efficient and useful alternatives to the maximum-likelihood method have been developed over the years. The most important of these are State-Variable filters, combined with Instrumental Variable methods, including the simplified refined IV method. In this contribution we perform unpretentious numerical experiments to comment on these methods, and their mutual benefits.

For linear and hybrid systems, constrained time-optimal control was shown to be a low complexity alternative to the explicit solution of the constrained finite-time optimal control problem. In this paper we show how Polya's relaxation can be employed to compute minimum-time controllers for discrete-time LPV systems. Contrary to previous publications, our approach allows the use of parameter-varying input matrices. In a comparison over 20 random system, it is shown that compared to explicit LPV-MPC the proposed approach achieves similar or even better control performance, while reducing the complexity of the controller up to an order of magnitude.

In order to accurately identify Linear Parameter-Varying (LPV) systems, order selection of LPV linear regression models has prime importance. Existing identification approaches in this context suffer from the drawback that a set of functional dependencies needs to be chosen a priori for the parametrization of the model coefficients. However in a black-box setting, it has not been possible so far to decide which functions from a given set are required for the parametrization and which are not. To provide a practical solution, a nonnegative garrote approach is applied. It is shown that using only a measured data record of the plant, both the order selection and the selection of structural coefficient dependence can be solved by the proposed method.

There are more and more systems emerging making use of measurements from a forward looking radar and a forward looking camera. It is by now well known how to exploit this data in order to compute estimates of the road geometry, tracking leading vehicles, etc. However, there is valuable information present in the radar concerning stationary objects, that is typically not used. The present work shows how radar measurements of stationary objects can be used to obtain a reliable estimate of the free space in front of a moving vehicle. The approach has been evaluated on real data from highways and rural roads in Sweden.

High performance robot manipulators, in terms of cycle time and accuracy,require well designed control methods, based on accurate dynamicmodels. Robot manipulators are traditionally described by theflexible joint model or the flexible link model. These models only considerelasticity in the rotational direction. When these models are usedfor control or simulation, the accuracy can be limited due to the modelsimplifications, since a real manipulator has a distributed flexibility inall directions. This work investigates different methods for the inversedynamics of a more general manipulator model, called the extendedflexible joint model. The inverse dynamics solution is needed for feedforwardcontrol, which is often used for high-precision robot manipulatorcontrol.The inverse dynamics of the extended flexible joint model can be computedas the solution of a high-index differential algebraic equation(DAE). One method is to solve the discretized DAE using a constantstepsizeconstant-order backwards differentiation formula (BDF). Thiswork shows that there is only a small difference between solving theoriginal high-index DAE and the index-reduced DAE. It is also concludedthat scaling of the algebraic equations and their derivatives isimportant.The inverse dynamics can be solved as an initial-value problem if thezero dynamics of the system is stable, i.e., minimum phase. For unstablezero dynamics, an optimization approach based on the discretizedDAE is suggested. An optimization method, using a continuous DAEformulation, is also suggested and evaluated. The solvers are illustratedby simulation, using a manipulator with two actuators and fivedegrees-of-freedom.

We present e method for controlling a dynamical system using real-time fMRI. The objective for the subject in the MR scanner is to balance an inverse pendulum by activating the left or right hand or resting. The brain activity is clasified each second by a neural network and the classification is sent to a pendulum simulator to change the state of the pendulum. The state of the inverse pendulum is shown to the subject in a pair of VR goggles. The subject was able to balance the inverse pendulum during a 7 minute test run.

A framework for Iterative Learning Control (ILC) is proposed for the situation when the ILC algorithm is based on an estimate of the controlled variable obtained from an observer-based estimation procedure. 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 exemplified by an ILC algorithm applied to a flexible two-mass model of a robot joint.

ILC is traditionally applied to systems where the controlled variable is the measured variable. However, in standard industrial robots only the motor angles are measured, while the control objective is to follow a tool path. A modern industrial robot is flexible, and assuming that the mechanical flexibilities are concentrated to the robot joints (elastic gearboxes), a flexible two-mass model can be used to describe a single joint. A P-ILC algorithm is applied to the two-mass model, based on only measured angle of the first mass (motor angle) or estimated angle for the second mass (tool angle). Robustness of the algorithm, and performance when model errors are introduced in the model, are discussed considering the error of the tool angle. First, it can be concluded for a flexible system that the characteristics of the motor-angle reference is essential for the resulting tool angle when the tool angle cannot be measured. Second, using an estimate of the tool angle instead of the explicit motor angle in the ILC update reduces the tool-angle error significantly.

This paper presents a framework for making distributed target tracking under significant signal propagation delays between the target and the sensors. Each sensor considered makes estimation using its own measurements compensating for the involved signal propagation delay using a deterministic sampling based algorithm proposed previously. Since the individual sensor readings might not be enough to localize the target, the sensors have to share their estimates with each other at specific time instants and correct their individual estimates. This work is mainly related to how this estimate correction and fusion should be carried out. An internal covariance approximation which keeps consistency but at the same time bypasses the track correlation problem is proposed. The results are illustrated on a challenging two-sensor bearings-only tracking scenario.

Tracking in WiMax networks is gaining a lot of interest; especially after the mobile WiMax became one of the emerging technologies that promote low-cost deployment and evolving to provide IP-based services of high mobility including providing location-based services (LBS). Therefore, locating users in a cheap way thatdepend on the available network resources is becoming more and more interesting and an active topic for researchers. In this paper we consider the problem of tracking in WiMAX networks depending on SCOREobservations. The provided examples show that with efficient measurement data processing and with the help of already available data (street maps), plausible results can be achieved.

In this paper we consider the problem of tracking targets, which can move both on-road and off-road, with particle filters utilizing the road-network information. It is argued that the constraints like speed-limits and/or one-way roads generally incorporated into on-road motion models make it necessary to consider additional high-bandwidth off-road motion models. This is true even if the targets under consideration are only allowed to move on-road due to the possibility of imperfect road-map information and drivers violating the traffic rules. The particle filters currently used struggles during sharp mode transitions, with poor estimation quality as a result. This is due to the fact the number of particles allocated to each motion mode is varying according to the mode probabilities. A recently proposed interacting multiple model (IMM) particle filtering algorithm, which keeps the number of particles in each mode constant irrespective of the mode probabilities, is applied to this problem and its performance is compared to a previously existing algorithm. The results of the simulations on a challenging bearing-only tracking scenario show that the proposed algorithm, unlike the previously existing algorithm, can achieve good performance even under the sharpest mode transitions.

In this paper, two applications of a particular weighting method are described. The first application concerns a nonlinearity test for system identification problems. Starting with a validated linear model, it turns out to be possible to detect nonlinearities from the variations in the linear approximations that are obtained for different input signal distributions. The method is computationally efficient and can be used on a single dataset. The second topic of the paper is an improved weighting method for identification of the linear subsystems in Wiener or Hammerstein systems.

In this paper we are concerned with nonlinear systems subject to a conditionally linear, Gaussian sub-structure. This structure is often exploited in high-dimensional state estimation problems using the marginalized (aka Rao- Blackwellized) particle filter. The main contribution in the present work is to show how an efficient filter can be derived by exploiting this structure within the auxiliary particle filter. Based on a multisensor aircraft tracking example, the superior performance of the proposed filter over conventional particle filtering approaches is demonstrated.

In this paper we propose a 6DOF tracking system combining Ultra-Wideband measurements with low-cost MEMS inertial measurements. A tightly coupled system is developed which estimates position as well as orientation of the sensorunit while being reliable in case of multipath effects and NLOS conditions. The experimental results show robust and continuous tracking in a realistic indoor positioning scenario.

This article reviews authors' recently developed algorithm for identification of nonlinear state-space models under missing observations and extends it to the case of unknown model structure. In order to estimate the parameters in a state-space model, one needs to know the model structure and have an estimate of states. If the model structure is unknown, an approximation of it is obtained using radial basis functions centered around a maximum a posteriori estimate of the state trajectory. A particle filter approximation of smoothed states is then used in conjunction with expectation maximization algorithm for estimating the parameters. The proposed approach is illustrated through a real application.

In system identification, the challenge of parameter estimation often lies in solving a non-convex optimization problem. In many cases, this implies that it is difficult to guarantee that the global optimum will be found. The tools of differential algebra, for example, Gr\"{o}bner bases and Ritt's algorithm, have turned out to be quite useful when dealing with certain nonlinear model structures. Some examples of successful applications are the determination of controllability, observability and global identifiability of these model structures. In this paper, difference algebraic techniques, which mimics the differential algebraic methods, will be presented. Besides making it possible to handle discrete-time systems, this opens up the possibility of dealing with noise. It turns out that the classical instrumental variables method plays a role.

In this work we consider a target tracking scenario where a moving observer with a bearings-only sensor is tracking a target. The tracking performance is highly dependent on the trajectory of the sensor platform, and the problem is to determine how it should maneuver for optimal tracking performance. The problem is considered as a stochastic optimal control problem and two sub-optimal control strategies are presented based on the Information filter and the determinant of the information matrix as the optimization objective. Using the determinant of the information matrix as an objective function in the planning problem is equivalent to using differential entropy of the posterior target density when it is Gaussian. For the non-Gaussian case, an approximation of the differential entropy of a density represented by a particle mixture is proposed. Furthermore, a gradient approximation of the differential entropy is derived and used in a stochastic gradient search algorithm applied to the planning problem.

This paper presents the formulation of a flight clearance criterion as a convex optimization problem. The criterion is the stability margins criterion which is specified as an allowable phase and gain margin of a certain loop transfer function. The satisfaction of the criterion amounts to the Nichols plot of the loop transfer function being outside a specified trapezoidal region. It was shown previously that the exclusion condition from an ellipsoidal region is implied by using the generalized stability margin b_PC and its calculation was performed frequency-wise by solving a sequence of convex optimization problems. In this paper we formulate the calculation of a lower bound on b_PC as a convex optimization problem using Integral Quadratic Constraints (IQCs) and avoid the gridding procedure in the frequency domain. Furthermore, we formulate the problem of obtaining a lower bound on the perturbed stability margin, which is defined as the worst-case b_PC over variations in real uncertain parameters.

In this paper we have formulated the problem offinding an LPV-approximation to a system as an optimizationproblem. For this optimization problem we have presentedtwo possible ways to solve this. The problem is posed as amodel reduction problem and formulated such that it shouldtry to preserve the input-output behavior of the system. In thetwo examples in the paper the potential of the new methodsare shown. We have also shown the benefits of using modelreduction techniques to capture the input-output behavior toobtain accurate low order LPV-approximations.One method uses SDP-optimization to solve the problem. SDPoptimizationhas been a hot topic during the last years, but theproblem with the SDP method is that it scales badly with thedimension of the problem. Also here it has bilinear constraintswhich makes the problem really difficult.With the other methodwe try to use a more general nonlinear approach which seemto be more suitable for this problem. For this method we havealso calculated a gradient that can be used to apply a descentor Newton-like method to solve the problem.

Order selection of linear regression models has been thoroughly researched in the statistical community for some time. Different shrinkage methods have been proposed, such as the Ridge and Lasso regression methods. Especially the Lasso regression has won fame because of its ability to set less important parameters exactly to zero. However, these methods do not take dynamical systems into account, where the regressors are ordered via the time lag. To this end, a modified variant of the nonnegative garrote method will be analyzed.