Almost-sure convergence of the continuous-time LMS algorithm

Author

Voltz, Peter J. ; Kozin, Frank

Author_Institution

Polytech. Univ., Farmingdale, NY, USA

Volume

40

Issue

2

fYear

1992

fDate

2/1/1992 12:00:00 AM

Firstpage

395

Lastpage

401

Abstract

The authors consider the stability properties of the conventional continuous-time least mean square algorithm. The algorithm for the case of stationary ergodic inputs is investigated and a necessary and sufficient condition for exponential almost-sure convergence is presented. This condition is shown to be less restrictive than the well-known persistency of excitation condition. Also, the authors point out and clarify an apparently common error regarding the connections between persistency of excitation and positive definite autocorrelation in stationary ergodic vector waveforms

Keywords

convergence of numerical methods; least squares approximations; signal processing; stability; LMS algorithm; continuous-time least mean square algorithm; exponential almost-sure convergence; persistency of excitation; positive definite autocorrelation; stability properties; stationary ergodic inputs; vector waveforms; Adaptive arrays; Adaptive control; Autocorrelation; Convergence; Helium; Least squares approximation; Stability; Sufficient conditions; System identification; Vectors;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.124949

Filename

124949