Error bound method and its application to the LMS algorithm

Author

Leung, Henry ; Haykin, Simon

Author_Institution

Commun. Res. Lab., McMaster Univ., Hamilton, Ont., Canada

Volume

39

Issue

2

fYear

1991

fDate

2/1/1991 12:00:00 AM

Firstpage

354

Lastpage

358

Abstract

A method to determine a bound on the error performance of an adaptive filter due to roundoff effects is described. The method converts the analysis of a recursive algorithm into two much simpler sub-problems: convergence and momentary error. To apply the method, the input data has to be bounded. By classifying convergence into different categories according to their rates, it is observed that adaptive filtering algorithms that belong to a particular class share similar behavior due to roundoff error or other perturbation effects. The merit of the method is its simplicity and general applicability. Based on this method, a sufficient condition for the numerical stability of an adaptive filter is derived. Application of the method to the least mean square (LMS) algorithm is described. The analysis may also be generalized to include other perturbation effects

Keywords

adaptive filters; convergence of numerical methods; filtering and prediction theory; least squares approximations; roundoff errors; signal processing; LMS algorithm; adaptive filter; adaptive filtering algorithms; convergence; error bound method; error performance; input data; least mean square; momentary error; numerical stability; perturbation effects; recursive algorithm; roundoff effects; signal processing; Adaptive filters; Algorithm design and analysis; Approximation algorithms; Convergence; Costs; Filtering algorithms; Least squares approximation; Numerical stability; Roundoff errors; Stability analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.80818

Filename

80818