# EQ2800 Optimal Filtering 6.0 credits

## Optimal filtrering

## Please note

This course has been cancelled.

This course gives thorough knowledge of linear estimation theory. The main theme of the course is optimal linear estimation, Kalman and Wiener 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 non-linear systems.

The course is directed towards the students who intend to work with development and research within these fields.

#### Education cycle

Second cycle#### Main field of study

Electrical Engineering

#### Grading scale

A, B, C, D, E, FX, F

Last planned examination: autumn 20.

At present this course is not scheduled to be offered.

## 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 non-Gaussian noise or non-linear models, such as Extended Kalman filter, sigma point filtering and particle filtering.

## 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 non-linear 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, sigma-point filters and particle filters.

## Disposition

Lectures, weekly homework assignments and a smaller project assignment to be presented in the form of a technical report.

## Eligibility

180hp and English B or equivalent

## Recommended prerequisites

EQ2300 Digital Signal Processing – grade above pass

## Literature

Linear Estimation, Kailath, Sayed, Hassibi

Additional material on non-linear filtering will be distributed.

## Examination

- PRO1 - Project Assignment, 1.0, grading scale: P, F
- TENA - Exam, 5.0, grading scale: A, B, C, D, E, FX, F

The course requires significant individual effort. Solving the homework problems require good familiarity with the theory but also an ability to formulate a practical problem using suitable mathematical modles 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.

## Requirements for final grade

- Individually solved homework assignments every week and a completementary exam if the homework has not been solved satisfactory (TEN1).
- A project assignment presented in the form of a technical report (PRO1)

## Offered by

EES/Information Science and Engineering

## Contact

Mats Bengtsson

## Examiner

Mats Bengtsson <matben@kth.se>

## Supplementary information

Given in period 1 every even year.

## Version

Course syllabus valid from: Autumn 2012.

Examination information valid from: Autumn 2012.