EQ2801 Optimal Filtering 7.5 credits
Optimal filtrering
This course gives thorough knowledge of linear estimation theory. The main theme of the course is optimal linear estimation, Kalman and Weiner filtering, which are systematic methods to solve estimation problems with applications in several technical disciplines, for example in telecommunications, automatic control and signal processing but also in other disciplines, such as econometrics and statistics.The course also provides an introduction to optimal filtering for nonlinear systems. The course assumes familiarity with basic concepts from matrix theory, stochastic processes, and linear systems theory. The course is directed towards the students who intend to work with development and research within these fields.
The following topics are covered; Basic estimation theory, time discrete and time continuous Wiener filters, time discrete Kalman filters, properties of Wiener and Kalman filters, smoothing, Extended Kalman filters, sigmapoint filters and particle filters.
Education cycle
Second cycleMain field of study
Electrical Engineering
Grading scale
A, B, C, D, E, FX, F
Course offerings
Autumn 18 for programme students

Periods
Autumn 18 P1 (7.5 credits)

Application code
51060
Start date
27/08/2018
End date
26/10/2018
Language of instruction
English
Campus
KTH Campus
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Schedule
Planned timeslots
P1: D1. more info
Course responsible
Mats Bengtsson <matben@kth.se>
Teacher
Magnus Jansson <janssonm@kth.se>
Mats Bengtsson <matben@kth.se>
Part of programme
 Master's Programme, Information and Network Engineering, 120 credits, year 1, Recommended
 Master's Programme, Information and Network Engineering, 120 credits, year 1, INF, Recommended
 Master's Programme, Information and Network Engineering, 120 credits, year 1, MMB, Recommended
 Master's Programme, Information and Network Engineering, 120 credits, year 2, Recommended
 Master's Programme, Information and Network Engineering, 120 credits, year 2, INF, Recommended
 Master's Programme, Information and Network Engineering, 120 credits, year 2, MMB, Recommended
 Master's Programme, Systems, Control and Robotics, 120 credits, year 2, SCTY, Conditionally Elective
Intended learning outcomes
After successfully completing the course, the student should be able to
• 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 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.
• Know about common methods for optimal filtering in the case of nonGaussian noise or nonlinear models, such as Extended Kalman filter, sigma point filtering and particle filtering.
• Formulate logical arguments, orally and in writing, in a way that is considered valid in scientific publications and presentations within the topic area.
Course main content
This course gives thorough knowledge of linear estimation theory. The main theme of the course is optimal linear estimation, Kalman and Weiner filtering, which are systematic methods to solve estimation problems with applications in several technical disciplines, for example in telecommunications, automatic control and signal processing but also in other disciplines, such as econometrics and statistics.The course also provides an introduction to optimal filtering for nonlinear systems. The course assumes familiarity with basic concepts from matrix theory, stochastic processes, and linear systems theory. The course is directed towards the students who intend to work with development and research within these fields.
The following topics are covered; Basic estimation theory, time discrete and time continuous Wiener filters, time discrete Kalman filters, properties of Wiener and Kalman filters, smoothing, Extended Kalman filters, sigmapoint filters and particle filters.
Eligibility
For single course students: 180hp and English B or equivalent
Recommended prerequisites
EQ1220/EQ1270 Signal Theory/Stochastic Signals and Systems, or equivalent
EQ2300 Digital Signal Processing, EQ2401 Adaptive Signal Processing
Literature
D. Simon "Optimal State Estimation", Wiley, 2006, or similarly (to be announced before course start).
Examination
 INL1  Homework assignments, 4.5, grading scale: A, B, C, D, E, FX, F
 PRO1  Project assignment, 1.5, grading scale: A, B, C, D, E, FX, F
 PRO2  Project assignment, 1.5, grading scale: A, B, C, D, E, FX, F
Requirements for final grade
• PRO1 – Project assignment, 1.5, grade scale: A, B, C, D, E, FX, F
• PRO2 – Project assignment, 1.5, grade scale: A, B, C, D, E, FX, F
• INL1 – Homework assignments, 4.5, grade scale: A, B, C, D, E, FX, F
Final grade based on 70% from INL1 and 15% each from PRO1 and PRO2, respectively.
The course requires significant individual effort. Solving the homework problems requires good familiarity with the theory but also an ability to formulate a practical problem using suitable mathematical models and applying the theory to these. The written presentation of solutions and project also provide training in the ability to formulate logical arguments in a way that is considered valid in scientific publications. One of the project assignments is presented in a technical report, the other one in an oral presentation.
Offered by
EECS/Intelligent Systems
Examiner
Mats Bengtsson <matben@kth.se>
Version
Course syllabus valid from: Spring 2019.
Examination information valid from: Spring 2019.