Course Information HT, 2023

The course aims at giving the participant thorough knowledge in linear estimation and filter theory for discrete time systems. The main theme of the course is optimal linear filtering, i.e., Kalman and Wiener filtering. The Kalman and Wiener filtering theory provide a systematic methodology to solve estimation problems with applications in technical disciplines, such as telecommunications, automatic control, and signal processing, as well as in other disciplines such as econometrics and statistics.

The following topics are covered: basic estimation theory, least squares problems, the innovations process, state-space models, time discrete Wiener filters, time discrete Kalman filters, properties of optimal filters, smoothing, and extended Kalman filtering.


After successfully completing the course, the participant should be able to:

  • Explain to which type of estimation problems linear estimation can be applied.
  • Explain the relationship between computational complexity, filter structure, and performance.
  • Explain the relationship between optimal filtering, linear estimation, and Wiener/Kalman filtering.
  • Approach estimation problems in a systematic way.
  • Derive and manipulate the time discrete Wiener filter equations and compute the Wiener filter for a given estimation problem.
  • Derive and manipulate the time discrete Kalman filter equations and compute the Kalman filter for a given estimation problem.
  • Analyze properties of optimal filters.
  • Implement Wiener and Kalman filters (time discrete) and state-space models using Matlab.
  • Simulate state-space models and optimal filters, analyze the results, optimize the filter performance, and provide a written report on the findings.
  • Formulate logical arguments, orally and in writing, in a way that is considered valid in scientific publications and presentations within the topic area.

Course Responsible


The course assumes familiarity with basic concepts from matrix theory, stochastic processes, and linear systems.


The course comprises 6 lectures. See the preliminary lecture plan for content.


  • Weekly homework assignment, to be solved and reported individually
  • Project assignments, to be solved using Matlab. A written report describing the solution to the assignment should be handed in.
  • Peer grading of homework assignments

See the Assignments page for details.

The course is based on the similar courses given at KTH by Mats Bengtson and Isaac Skog, and later at LiU by Isaac Skog.