# EQ2800 Optimal Filtering 6.0 credits

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.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus EQ2800 (Autumn 2012–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

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.

### 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 disposition

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

## Literature and preparations

### Specific prerequisites

180hp and English B or equivalent

### Recommended prerequisites

EQ2300 Digital Signal Processing – grade above pass

### Equipment

No information inserted

### Literature

Linear Estimation, Kailath, Sayed, Hassibi

Additional material on non-linear filtering will be distributed.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

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

### Examination

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

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.

### Other 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)

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### 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.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web EQ2800

### Main field of study

Electrical Engineering

Second cycle