DSP-CIS Chapter-12: Least Mean Squares (LMS) Algorithm
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DSP-CIS
Chapter-12: Least Mean Squares (LMS) Algorithm
Marc MoonenDept. E.E./ESAT, KU Leuven
marc.moonen@esat.kuleuven.be
www.esat.kuleuven.be/scd/
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 2
Part-III : Optimal & Adaptive Filters
: Optimal & Adaptive Filters - Intro• General Set-Up
• Applications
• Optimal (Wiener) Filters
– : Least Squares & Recursive Least Squares Estimation• Least Squares Estimation
• Recursive Least Squares (RLS) Estimation
• Square-Root Algorithms
– : Least Means Squares (LMS) Algorithm• LMS/NLMS : Stochastic Gradient Algorithms
• LMS analysis
• LMS Family
– : Fast Recursive Least Squares Algorithms
: Kalman Filtering
Chapter-11
Chapter-12
Chapter-13
Chapter-14
Chapter-15
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 3
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 4
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 5
Least Mean Squares (LMS) Algorithm
(Widrow 1965 !!)
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 6
Least Mean Squares (LMS) Algorithm
Bernard Widrow
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 7
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 8
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 9
Least Mean Squares (LMS) Algorithm
large λ_max implies
a small stepsize
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 10
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 11
Least Mean Squares (LMS) Algorithm
error vector projected onto eigenvectors initial error vector projected onto eigenvectors
(=projection on i-th eigenvector)
small λ_i implies slow convergence λ_min <<λ_max (hence small μ) implies *very* slow convergence
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 12
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 13
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 14
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 15
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 16
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 17
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 18
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 19
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 20
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 21
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 22
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 23
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 24
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 25
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 26
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 27
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 28
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 29
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 30
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 31
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 32
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 33
Least Mean Squares (LMS) Algorithm
DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2012-2013 p. 34
Least Mean Squares (LMS) Algorithm
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