# Popis předmětu - BE3M35OFD

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BE3M35OFD Estimation, Filtering and Detection
Role:PV Rozsah výuky:2P+2C
Katedra:13135 Jazyk výuky:EN
Garanti:Havlena V. Zakončení:Z,ZK
Přednášející:Havlena V. Kreditů:6
Cvičící:Havlena V., Tabaček J. Semestr:Z

Webová stránka:

http://dce.fel.cvut.cz/studium/estimation-filtering-and-detection

Anotace:

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.

Cíle studia:

Ability to solve engineering problems in the area of estimation and filtering, using rigorous theoretical background.

Obsah:

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.

Osnovy přednášek:

 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

Osnovy cvičení:

Individual assigments - implementation of selected algorithms in Matlab, solution of individual technical problems. Deliverables: running algorithm, technical report. Homeworks: theoretical assignments. Deliverables: report.

Literatura:

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

Basics of dynamic system theory, probability and statistics.

Poznámka:

 Rozsah 3+1

Klíčová slova:

Odhadování, filtrace, stochastický system, stav, nelineární systém, věrohodnostní poměr, metoda Monte Carlo.

Předmět je zahrnut do těchto studijních plánů:

 Plán Obor Role Dop. semestr MEKYR_2021 Před zařazením do oboru PV 3

 Stránka vytvořena 23.7.2024 17:51:03, semestry: Z,L/2024-5, Z,L/2023-4, připomínky k informační náplni zasílejte správci studijních plánů Návrh a realizace: I. Halaška (K336), J. Novák (K336)