1.Basic estimation theory and geometric interpretations

2.Wiener filters; continuous time and discrete time

3.Kalman filters; continuous time and discrete time

4.The innovations Process

5.Stationary Kalman Filter, spectral properties

6.Smoothing (fixed-point, fixed-lag, fixed-time)

7.Numerical and computational issues in Kalman filtering

8.Non-linear filtering

Additional topics selected for the student presentations

After the course, each student is expected to:

• Show a good working knowledge of some fundamental tools (specified by the course content) in optimal filtering.
• Understand to which type of estimation problems linear estimation can be applied.
• Understand the relationship between computational complexity, filter structure, and performance.
• Understand the relationship between optimal filtering, linear estimation, and Wiener/Kalman filtering.
• Approach estimation problems in a systematic way.
• Compute, analyze, and modify state space models.
• Derive and manipulate the time discrete and time continuous Wiener filter equations and compute the Wiener filter for a given estimation problem.
• Derive and manipulate the time discrete and time continuous 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.
• Be familiar to the basic theory and know about common methods for optimal filtering in the case of non-Gaussian noise or non-linear models, such as Extended Kalman filter, sigma point filtering and particle filtering.
• Use the acquired knowledge to more easily apprehend research papers in engineering.
• Identify research problems in which linear and non-linear estimation tools may be powerful.
• Apply the knowledge to solve the identified filtering problems.
• Combine several sub problems and solutions to solve more complex problems.
•  Show improved skills in problem solving and proof writing as well as in critical assessment of proofs and solutions.
•  Show improved skills in oral presentation of technical contents.

• 9 Lectures
• 7 sets of weekly homeworks.
• One project assignment, written report. Groups of 2students.
• Group-wise peer grading of the homeworks
• Individual presentation on selected topic
• Take home examination (48 hours).

See the modules in Canvas for detailed dates.

It assumes some familiarity with basic concepts from linear algebra, stochastic processes and linear systems theory, as can be expected by good knowledge from undergraduate studies.

Material from several sources:

• D. Simon, Optimal State Estimation, John Wiley & Sons, 2006
• B. D. O. Anderson, J. B. Moore, Optimal Filtering, Dover Publications, 2012.
• S. Theodoridis, Machine Learning; A Bayesian and Optimization Perspective, 2nd ed., Academic press, 2022.
• Selected journal articles

All available electronically through KTH library!

Matlab and/or Python, for the homework and project.

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

P, F

• EXA1 - Examination, 10 credits, Grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

●      Individual solutions to weekly written homework assignments, 70% of max score

●      Written take-home exam

●      Peer-review grading of assigned problem sets

●      Presentation of assigned topic and actively participating during other students presentations

Homeworks and Project

Each submission (full homework set/project), is graded as a whole according to the following two criteria.

Technical/mathematical content, 1-3 points:

1. point: More than 50% of the difficulties have been solved, at least by providing a valid approach and working
   out some details.
2. points: More than 75% of the difficulties have been solved, at least by providing a valid approach and working
   out some details. In addition, at least two of the problems have been solved fully.
3. points: Full solutions are provided for all problems and only minor details are flawed/missing

Presentation, 1-2 points (only judged if at least 1 point was obtained for the technical content, and only judged for
the problems or parts of the project that have been “solved” according to above):

1. point: The presentation manages to convey the main ideas of the solved problems, but not fully
   convincing in all details.
2. points: Clear and convincing presentation of the solved problems.

To summarize, each approved submission gets between 1+1=2 points and 3+2=5 points.

Home exam

Traditional grading, ≥ 50% are required for passing grade.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Code of Honour

In this course, the EECS code of honor applies.