Stochastic gradient identification of polynomial Wiener systems: analysis and application

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, a...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2001-02, Vol.49 (2), p.301-313
Main Authors: Celka, P., Bershad, N.J., Vesin, J.-M.
Format: Article
Language:English
Subjects:
Adaptive systems
Algorithm design and analysis
Algorithms
Applied sciences
Computer simulation
Convergence
Detection, estimation, filtering, equalization, prediction
Dynamical systems
Exact sciences and technology
Feedback
Finite impulse response filter
Information, signal and communications theory
Mean square error methods
Monte Carlo methods
Nonlinear dynamics
Nonlinear systems
Optical feedback
Polynomials
Signal and communications theory
Signal processing algorithms
Signal, noise
Stochastic resonance
Stochastic systems
Stochasticity
Telecommunications and information theory
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Summary: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/sub 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.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.902112