Headings denoted with an asterisk ( * ) is retrieved from the course syllabus version Spring 2019
Content and learning outcomes
Course contents
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
Intended learning outcomes
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.
Learning activities
9 Lectures
7 sets of weekly homeworks.
One project assignment, written report. Groups of 2students.
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.
Literature
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!
Software
Matlab and/or Python, for the homework and project.
Support for students with disabilities
Students at KTH with a permanent disability can get support during studies from Funka:
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.
Other requirements for final grade
● 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
Grading criteria/assessment criteria
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:
point: More than 50% of the difficulties have been solved, at least by providing a valid approach and working out some details.
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.
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):
point: The presentation manages to convey the main ideas of the solved problems, but not fully convincing in all details.
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.
Ethical approach
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.
The section below is not retrieved from the course syllabus:
