tailieunhanh - Lecture Adaptive filtering - Theory and applications

Lecture Adaptive filtering - Theory and applications has contents: Adaptive filtering applications, adaptive filtering principles, iterative solutions for the optimum filtering problem, stochastic gradient algorithms, deterministic algorithms, analysis. | Adaptive Filtering - Theory and Applications Jos´ C. M. Bermudez e Department of Electrical Engineering Federal University of Santa Catarina Florian´polis – SC o Brazil IRIT - INP-ENSEEIHT, Toulouse May 2011 Jos´ Bermudez (UFSC) e Adaptive Filtering IRIT - Toulouse, 2011 1 / 107 1 Introduction 2 Adaptive Filtering Applications 3 Adaptive Filtering Principles 4 Iterative Solutions for the Optimum Filtering Problem 5 Stochastic Gradient Algorithms 6 Deterministic Algorithms 7 Analysis Jos´ Bermudez (UFSC) e Adaptive Filtering IRIT - Toulouse, 2011 2 / 107 Introduction Jos´ Bermudez (UFSC) e Adaptive Filtering IRIT - Toulouse, 2011 3 / 107 Estimation Techniques Several techniques to solve estimation problems. Classical Estimation Maximum Likelihood (ML), Least Squares (LS), Moments, etc. Bayesian Estimation Minimum MSE (MMSE), Maximum A Posteriori (MAP), etc. Linear Estimation Frequently used in practice when there is a limitation in computational complexity – Real-time operation Jos´ Bermudez (UFSC) e Adaptive Filtering IRIT - Toulouse, 2011 4 / 107 Linear Estimators Simpler to determine: depend on the first two moments of data Statistical Approach – Optimal Linear Filters ◮ ◮ Minimum Mean Square Error Require second order statistics of signals Deterministic Approach – Least Squares Estimators ◮ ◮ Minimum Least Squares Error Require handling of a data observation matrix Jos´ Bermudez (UFSC) e Adaptive Filtering IRIT - Toulouse, 2011 5 / .