### Estimation, filtering and detection

##### B232 - Summer 23/24
This course is not present in Moodle. You can visit its homepage by clicking the "Course page (outside Moodle)" button on the right (if available).

#### Estimation, filtering and detection - B3M35OFD

 Credits 6 Semesters Winter Completion Assessment + Examination Language of teaching Czech Extent of teaching 2P+2C
Annotation
This course will cover description of the uncertainty of hidden variables (parameters and state of a dynamic system) using the probability language and methods for their estimation. Based on bayesian problem formulation principles of rational behavior under uncertainty will be analyzed and used to develop algorithms for parameter estimations (ARX models, Gaussian process regression), filtering (Kalman filter) and detection (likelihood ratio theory) . We will demonstrate numerically robust implementation of the algorithms applicable in real life problems for the areas of industrial process control, robotics and avionics.
Study targets
Ability to solve engineering problems in the area of estimation and filtering, using rigorous theoretical background.
Course outlines
1. Review of basic concepts of statistics
2. MS, LMS and ML estimation
3. Bayesian approach to uncertainty description, model of dynamic system
4. Identification of ARX model parameters
5. Tracking of time varying parameters, forgetting, prior information
6. Numerically robust algorithms for parameter estimation
7. Gaussian process regression
8. Stochastic system, probabilistic state definition, Kalman filter
9. Kalman filter for colored noise, extended Kalman filter
10. Stochastic dynamic programming, LQ and LQG controller, certainty equivalence principle
11. Fault detection and isolation methods
12. Likelihood ratio - theory and applications
13. Nonlinear estimation - local vs. global approximation
14. Monte Carlo methods
Exercises outlines
Individual assigments - implementation of selected algorithms in Matlab, solution of individual technical problems. Deliverables: running algorithm, technical report.
Homeworks: theoretical assignments. Deliverables: report.
Literature
Lewis, F. L., L. Xie, D. Popa: Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, CRC Press, 2005. ISBN 978-1-4200-0829-6
Simon, D.: Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches. Wiley, 2006, ISBN: 978-0-471-70858-2
Lectures - published on WEB/Moodle
Assignments-homework - published on WEB/Moodle
Requirements
Basics of dynamic system theory, probability and statistics.