Estimation and Filtering

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

The objective of the subject is to introduce parametr estimation and state filtering methods from a unified bayesian viewpoint. Methods for the estimation of parameters of ARX models and filtering of state of a dynamic system including implementation and numerically robust algorithms, as well as Monte Carlo methods, are studied in details. Also, basic fault detection and isolation methods based on multiple models are introduced.

Requirements:

Dynamic system theory, control theory, basic probability and statistics

Syllabus of lectures:

1.Introduction

2.Estimation and filtering - bayesian problem formulation

3.One-shot and recursive parameter estimation for constant parameters

4.Tracking of time-varying parameters, forgetting

5.Robust numerical implementation of identification algorithms

6.Utilization of prior information, parallel and alternative models

7.Stochastic system, bayesian definition of state

8.Kalman filter, basic properties

9.Kalman filter for coloured noise

10.Simultaneous state estimation and arameter tracking

11.Extended Kalman filter, applications

12.Smoothing, backward Kalman filter

13.Nonlinear estimation and filtering

14.Monte Carlo implementation, sampling/resampling algorithms

Syllabus of tutorials:

1. Probability, risk function, uncertainty, game theory and relationships

with estimation

2. Methods of estimation, the method of moments, functional methods,

likelihood based

3. Maximum likelihood method, recursive likelihood update calculations

4. Bayes paradigm, examples and comarison with the classical solutions

5. Algorithms for recursive parameter estimation and their implementation

6. Seminary work setting, QR and LDU decomposition and their application for

estimation

7. Hybrid and parallel models

8. Presentation of proposed solutions to the seminary works

9. Algorithms for system state estimation

10. Kalman filter

11. Non-linear estimation via linearization, non-linear least squares via

Gauss-Newton method, Extended Kalman filter of the 1st and 2nd order

12. Smoothing

13. Numerical methods, bootstrap, sampling-resamplig

14. Presentation of seminary works

Study Objective:

Study materials:

[1]Lewis, F.L.: Optimal Estimation. J.Wiley and Sons, N.Y. 1986, 1993

[2]Ljung, L.: System identification/Theory for the user. Springer V., N.Y.,1989

[3]Box, Jenkins: Time series analysis, Prentice Hall, 1994

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory elective course)
• Cybernetics and Measurements - Artificial Intelligence- structured studies (compulsory elective course)
• Cybernetics and Measurements - Measurement and Instrumentation Systems- structured studies (compulsory elective course)
• Cybernetics and Measurements - Aeronautical Engineering and Control Systems- structured studies (compulsory elective course)