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TSRT14 Sensor fusion

Course Information VT2, 2019


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

Exercises: 8

Laboratory exercises: 2

  • Localization in acoustic sensor networks. A moving target is transmitting short acoustic signals and a network with microphones detects, localizes and tracks the target. Matlab files are provided.

    The lab contains one data collection part in our lab (RT3, Laboteket, which is located in house B, entrance 27, corridor C) and one data processing part where algorithms will be developed and applied to the data.

    The participants will be examined with a lab report which will be peer-reviewed by other students attending the course. Each lab group will review one report each. The report is due on Wednesday May 8, 2019, at 23:59, the review report is due on Tuesday May 14, 2019, at 23:59. The updated report based on the review feedback is due on Sunday May 19, 2019, at 23:59. Feedback on the report will be provided on Friday May 24, at 23:59, and the resubmission of the lab report (if required) is due on Sunday June 02 2019, at 23:59. The report should be written in English.

    Lab reports: The lab and review report should be submitted (as a PDF file) to the peer review system available here. The first version of the lab report should also be sent to Urkund (e-mail: daniel.arnstrom.liu@analys.urkund.se). Each group is also expected to create a reviewer account (one per each group) in the peer review system and review the assigned report. To make things more clear, you will create your reviewer accounts during the lab sesion under the supervision of a lab assistant. Keycode for the reviewer registration is tsrt14reviewer.

  • Orientation estimation using smartphone sensors. In this lab an orientation filter will be implemented using measurements from gyroscope, accelerometer and magnetometer in a smartphone. The lab is compatible with any android phone containing these sensors (which most modern smartphones do). The students can either use their own phones, or use a phone provided by the course. Matlab files are provided as well as the Sensor Fusion Android app which will be needed to stream sensor data from the phone to matlab.

    The lab will consist of a 4 hour lab session in our computer rooms. The participants will be examined during the session and no written report will be required.

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.

Involved The course assistant is responsible for the lab schedule Kamiar Radnosrati (kamiar.radnosrati@liu.se, 013-286740).

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. To use the latest version of the toolbox in the computer labs, please download and run this file to set the proper paths.


  • 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.


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, 12.3, 13.1, 13.2, (12.2) 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: 2019-11-01