Almost-sure sample stability of the continuous-time LMS algorithm

Author

Voltz, Peter J. ; Kozin, Frank

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Polytech Univ., Farmindale, NY, USA

fYear

1990

fDate

3-6 Apr 1990

Firstpage

1253

Abstract

Consideration is given to the stability properties of the conventional continuous-time LMS algorithm. The algorithm is investigated for the case of stationary ergodic inputs, 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 connection between persistency of excitation and positive-definite autocorrelation in stationary ergodic vector waveforms

Keywords

least squares approximations; stability; continuous-time LMS algorithm; excitation condition; exponential almost-sure convergence; necessary condition; positive-definite autocorrelation; stability properties; stationary ergodic inputs; stationary ergodic vector waveforms; sufficient condition; Adaptive control; Array signal processing; Autocorrelation; Convergence; Equations; Least squares approximation; Stability; Sufficient conditions; System identification; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1990. ICASSP-90., 1990 International Conference on

Conference_Location

Albuquerque, NM

ISSN

1520-6149

Type

conf

DOI

10.1109/ICASSP.1990.115600

Filename

115600