Stochastic gradient identification of polynomial Wiener systems: analysis and application

Author

Celka, Patrick ; Bershad, Neil J. ; Vesin, Jean-Marc

Author_Institution

Signal Processing Res. Centre, Queensland Univ. of Technol., Brisbane, Qld., Australia

Volume

49

Issue

2

fYear

2001

fDate

2/1/2001 12:00:00 AM

Firstpage

301

Lastpage

313

Abstract

This paper presents analytical, numerical, and experimental results for a stochastic gradient adaptive scheme that identifies a polynomial-type nonlinear system with memory for noisy output observations. The analysis includes the computation of the stationary points, the mean square error surface, and the stability regions of the algorithm for Gaussian data. Convergence of the mean is studied using L ₂ and Euclidian norms. Monte Carlo simulations confirm the theoretical predictions that show a small sensitivity to the observation noise. An application is presented for the identification of a nonlinear time-delayed feedback system

Keywords

Gaussian processes; Monte Carlo methods; Wiener filters; adaptive filters; adaptive signal processing; delays; digital simulation; feedback; filtering theory; gradient methods; identification; learning systems; nonlinear systems; numerical stability; polynomials; Euclidian norm; Gaussian data; L₂ norm; Monte Carlo simulations; adaptive filter; experimental results; linear FIR time-invariant system; linear filter learning; mean convergence; mean square error surface; memory; noisy output observations; nonlinear stochastic gradient learning algorithm; nonlinear time-delayed feedback system; observation noise sensitivity; polynomial Wiener systems; polynomial-type nonlinear system; stability regions; stationary points; stochastic gradient adaptive identification; Algorithm design and analysis; Convergence; Finite impulse response filter; Mean square error methods; Nonlinear systems; Optical feedback; Polynomials; Signal processing algorithms; Stochastic resonance; Stochastic systems;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.902112

Filename

902112