DSP-CIS Chapter-12: Least Mean Squares (LMS) Algorithm

DSP-CIS

Chapter-12: Least Mean Squares (LMS) Algorithm

Marc MoonenDept. E.E./ESAT, KU Leuven

[email protected]

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

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

(Widrow 1965 !!)

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Least Mean Squares (LMS) Algorithm

Bernard Widrow

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

large λ_max implies

a small stepsize

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Least Mean Squares (LMS) Algorithm

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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

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm

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Least Mean Squares (LMS) Algorithm