Anotation:
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.
Content:
MS, LMS and ML estimation. Bayesian approach to uncertainty description, model of dynamic system. Identification of ARX model parameters. Tracking of time varying parameters, forgetting, prior information. Numerically robust algorithms for parameter estimation. Gaussian process regression. Stochastic system, probabilistic state definition, Kalman filter. Kalman filter for colored noise, extended Kalman filter. Stochastic dynamic programming, LQ and LQG controller, certainty equivalence principle. Fault detection and isolation methods. Likelihood ratio - theory and applications. Nonlinear estimation - local vs. global approximation. Monte Carlo methods.
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 outline:
Individual assigments - implementation of selected algorithms in Matlab, solution of individual technical problems. Deliverables: running algorithm, technical report. Homeworks: theoretical assignments. Deliverables: report.
