The stability of LMS

Author

Solo, Victor

Author_Institution

Dept. of Stat., Macquarie Univ., North Ryde, NSW, Australia

Volume

45

Issue

12

fYear

1997

fDate

12/1/1997 12:00:00 AM

Firstpage

3017

Lastpage

3026

Abstract

New and weak conditions are given under which the LMS algorithm is exponentially convergent with probability one in a stochastic setting. These results show that LMS works under very broad conditions: a small gain, input signal with finite fourth moments; time varying persistence of excitation; and weak assumptions on the correlation structure of the input signal. Previous results at this level of generality linked convergence to peak signal amplitude rather than average amplitude. Under the same conditions stochastic boundedness of a forced LMS system is also established

Keywords

convergence of numerical methods; least mean squares methods; probability; signal processing; stability; stochastic processes; LMS algorithm; LMS stability; average amplitude; convergence; finite fourth moments; input signal; peak signal amplitude; probability; small gain; stochastic boundedness; stochastic setting; time varying excitation persistence; Algorithm design and analysis; Convergence; Eigenvalues and eigenfunctions; Helium; Least squares approximation; Stability; Stochastic processes; Stochastic resonance; Stochastic systems; White noise;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.650261

Filename

650261