NDLI: Bayesian step least mean squares algorithm for Gaussian signals

Content Provider	IET Digital Library
Author	Lopes, Paulo A. C.
Abstract	Selecting the step of the least mean squares (LMS) algorithm is an old problem. This study uses a new approach to address this problem resulting in a new algorithm with excellent system identification performance. The LMS algorithm, with time-varying step, size can be shown to be equivalent to the Kalman filter in some conditions. This is as long as the state noise of the Kalman filter and the step size of the LMS algorithm are chosen carefully. The Kalman filter is the optimum linear estimator (Bayesian) given the state and the measurement noise covariance matrices, but these matrices are not always known. This work considers the case where these matrices are not known, in the special cases that the Kalman filter reduces to the LMS. This results in an algorithm to select the step-size of the LMS algorithm with few priors. The optimum step size can be calculated using estimates of the probability density function (PDF) of the coefficient estimation error variance (qw ) and measurement noise variance (qv ). The PDFs can be estimated from the data using Bayes’ rule and assuming Gaussian reference and measurement noise signals. The resulting algorithm to determine qw and qv is a second small Kalman filter, and the outputs of this filter (means and covariances) are used to determine the expected value of the step.
Starting Page	506
Ending Page	512
Page Count	7
ISSN	17519675
Volume Number	14
e-ISSN	17519683
Issue Number	Issue 8, Oct (2020)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/14/8
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2020.0058
Journal	IET Signal Processing
Publisher Date	2020-07-30
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Bayes Method Bayesian Step Least Mean Squares Algorithm Coefficient Estimation Error Variance Covariance Matrices Filtering Method in Signal Processing Filtering Theory Gaussian Processes Gaussian Signal Interpolation And Function Approximation Kalman Filter Least Mean Squares Method Linear Algebra LMS Algorithm Measurement Noise Covariance Matrix Numerical Analysis Optimum Linear Estimator Optimum Step Size Probability Density Function Signal Processing Theory State Noise Statistics System Identification Performance Time-varying Step
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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