Adaptive filtering algorithms designed using control Liapunov functions

Author

Diene, Oumar ; Bhaya, Amit

Author_Institution

Dept. of Electr. Eng., NACAD-COPPE/Fed. Univ. of Rio de Janeiro., Rio De Janeiro, Brazil

Volume

13

Issue

4

fYear

2006

fDate

4/1/2006 12:00:00 AM

Firstpage

224

Lastpage

227

Abstract

The standard conjugate gradient (CG) method uses orthogonality of the residues to simplify the formulas for the parameters necessary for convergence. In adaptive filtering, the sample-by-sample update of the correlation matrix and the cross-correlation vector causes a loss of the residue orthogonality in a modified online algorithm, which, in turn, results in loss of convergence and an increase of the filter quadratic mean error. This letter extends a recently proposed control Liapunov function analysis of the CG method viewed as a dynamic system in the standard feedback configuration to the case of adaptive filtering.

Keywords

adaptive filters; conjugate gradient methods; convergence of numerical methods; correlation methods; signal sampling; CLF; adaptive filtering; control Liapunov function analysis; convergence; correlation matrix; cross-correlation vector; dynamic system; quadratic mean error; sample-by-sample update; standard conjugate gradient method; standard feedback configuration; Adaptive filters; Algorithm design and analysis; Character generation; Control systems; Convergence; Feedback; Filtering algorithms; Iterative algorithms; Iterative methods; Linear systems; Adaptive equalizer; adaptive filtering algorithms; control Liapunov function (CLF); iterative methods; linear prediction; system identification;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2005.863659

Filename

1605244