IDENTIFICATION FOR WIENER SYSTEMS WITH INTERNAL NOISE

Qijiang SONG; Hanfu CHEN

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Journal of Systems Science & Complexity ›› 2008, Vol. 21 ›› Issue (3) : 378-393.

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IDENTIFICATION FOR WIENER SYSTEMS WITH INTERNAL NOISE

Qijiang SONG, Hanfu CHEN

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Abstract

This paper considers identification of Wiener systems for which the internal variables and output are corrupted by noises. When the internal noise is a sequence of independent and identically distributed (iid) Gaussian random variables, by the Weierstrass transformation (WT) the system under consideration
turns to be a Wiener system without internal noise. The nonlinear part of the latter is nothing else than the WT of the nonlinear function of the original system, while the linear subsystem is the same for both systems before and after WT. Under reasonable conditions, the recursive identification algorithms are proposed
for the transformed Wiener system, and strong consistency for the
estimates is established. By using the inverse WT the nonparametric estimates for the nonlinearity of the original system are derived, and they are strongly consistent if the nonlinearity in the original system is a polynomial. Similar results also hold in the case where the internal noise is non-Gaussian. Simulation results are fully consistent with the theoretical analysis.