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TSRT14 Sensor fusion

Course Information VT2, 2021


The student should after the course have the ability to describe the most important methods and algorithms for sensor fusion, and be able to apply these to sensor network, navigation and target tracking applications. More specifically, after the course the student should have the ability to:
  • Understand the fundamental principles in estimation and detection theory.
  • Implement algorithms for parameter estimation in linear and nonlinear models.
  • Implement algorithms for detection and estimation of the position of a target in a sensor network.
  • Apply the Kalman filter to linear state space models with a multitude of sensors.
  • Apply nonlinear filters (extended Kalman filter, unscented Kalman filter, particle filter) to nonlinear or non-Gaussian state space models.
  • Implement basic algorithms for simultaneous localization and mapping (SLAM).
  • Describe and model the most common sensors used in sensor fusion applications.
  • Implement the most common motion models in target tracking and navigation applications.
  • Understand the interplay of the above in a few concrete real applications.

The course comprise:

Lectures: 10

Exercise sessions: 8

Laboratory exercises: 2

Suitable group size is two students and you have to register for both labs, which you can do online, in due time, by following this link.

The course assistant is responsible for the lab schedule Anton Kullberg (anton.kullberg@liu.se).

Email list

Information during the course will be sent to the course mailing list. The list name, together with further information and sign-up, can be found on "Studentsidan".


The toolbox that will be used during the course can be downloaded here. Toolbox Manual can be downloaded here. A video providing an introduction of the toolbox by the author himself is provided here.

To activate the toolbox, run the included command

in matlab. To use the latest version of the toolbox in the Linux computer labs, run:
    module add courses/TSRT14
in a terminal prior to opening matlab, or install a current version of the toolbox in your home directory as you would at home.


  • Statistical Sensor Fusion. Fredrik Gustafsson. Studentlitteratur, 2018, Third Edition.
  • Statistical Sensor Fusion - Exercises. Christian Lundquist, Zoran Sjanic, and Fredrik Gustafsson. Studentlitteratur, 2015.
  • Statistical Sensor Fusion - Laborations. Available from the homepage.
  • Statistical Sensor Fusion - Matlab Toolbox Manual. Available here. (Introductory video.)


Written examination with Matlab.


Lecturer and examiner: Teaching assistant:

Preliminary lecture plan


Slides will be linked from the lecture number in advance.
Nr.ContentSuggested reading
1 (slides, slides-4up) Course overview. Estimation theory for linear models. Chapters 1, 2
2 (slides, slides-4up) Estimation theory for nonlinear models. Chapter 3
3 (slides, slides-4up) Cramér-Rao lower bound (CRLB). Models for sensor network applications. Chapter 4
4 (slides, slides-4up) Detection theory. Filter theory. Chapters 5, 6
5 (slides, slides-4up) Modeling and motion models. Chapters 12-14
6 (slides, slides-4up) Kalman filter. Kalman filter approximations for nonlinear models (EKF, UKF). Chapters 7, 8
7 (slides, slides-4up) The point-mass filter and the particle filter. Chapter 9
8 (slides, slides-4up) The particle filter theory. The marginalized particle filter. Chapter 9
9 (slides, slides-4up) Simultaneous localization and mapping (SLAM). Chapter 11
10 (slides, slides-4up) Sensors and sensor-near signal processing. Filter and model validation. Case study from industry. Chapter 14, 15

Preliminary exercise plan


1 2.1, 2.4, 3.1, 3.2, 3.6b, 2.3, 2.5 Estimation.
2 4.10, 4.2, 4.3, 16.1 Sensor networks.
3 2.10, 3.10, 3.7, 4.7, 4.8, 4.9, 5.4 Computer-based estimation and detection.
4 6.1, 6.2, 12.1, 12.2, 13.2, (12.3), (13.1) Filter theory and models.
5 7.1, 7.2, 7.3, 8.1, 8.2, 8.4 Kalman filters and Kalman filter approximations.
6 7.10, 8.6, 9.5, (16.3) Computer-based filtering.
7 11.1, 11.3 Computer-based SLAM.
8 9.1, 9.2, 9.3, 14.2 Particle filtering and sensors.

Informationsansvarig: Gustaf Hendeby
Senast uppdaterad: 2022-06-02