Analysis of stochastic gradient tracking of time-varying polynomial Wiener systems

This paper presents analytical and Monte Carlo results for a stochastic gradient adaptive scheme that tracks a time-varying polynomial Wiener (1958) system [i.e., a linear time-invariant (LTI) filter with memory followed by a time-varying memoryless polynomial nonlinearity]. The adaptive scheme cons...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2000-06, Vol.48 (6), p.1676-1686
Main Authors: Bershad, N.J., Celka, P., Vesin, J.-M.
Format: Article
Language:English
Subjects:
Adaptive filters
Algorithms
Computer simulation
Economic models
Least squares approximation
Monte Carlo methods
Nonlinear filters
Nonlinearity
Optimization
Phase estimation
Polynomials
Recursion
Stochastic processes
Stochastic systems
Stochasticity
Studies
Time varying systems
Tracking
Wiener filter
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Summary:This paper presents analytical and Monte Carlo results for a stochastic gradient adaptive scheme that tracks a time-varying polynomial Wiener (1958) system [i.e., a linear time-invariant (LTI) filter with memory followed by a time-varying memoryless polynomial nonlinearity]. The adaptive scheme consists of two phases: (1) estimation of the LTI memory using the LMS algorithm and (2) tracking the time-varying polynomial-type nonlinearity using a second coupled gradient search for the polynomial coefficients. The time-varying polynomial nonlinearity causes a time-varying scaling for the optimum Wiener filter for Phase 1. These time variations are removed for Phase 2 using a novel coupling scheme to Phase 1. The analysis for Gaussian data includes recursions for the mean behavior of the LMS algorithm for estimating and tracking the optimum Wiener filter for Phase 1 for several different time-varying polynomial nonlinearities and recursions for the mean behavior of the stochastic gradient algorithm for Phase 2. The polynomial coefficients are shown to be accurately tracked. Monte Carlo simulations confirm the theoretical predictions and support the underlying statistical assumptions.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.845925