NONPARAMETRIC APPROACH TO WIENER SYSTEM-IDENTIFICATION

A Wiener system, i.e., a system consisting of a linear dynamic subsyst em followed by a memoryless nonlinear one is identified. The system is driven by a stationary white Gaussian stochastic process and is distu rbed by Gaussian noise. The characteristic of the nonlinear part can b e of any form. The dynamic subsystem is asymptotically stable. The a p riori information about both the impulse response of the dynamic part of the system and the nonlinear characteristics is nonparametric. Both subsystems are identified from observations taken at the input and ou tput of the whole system. The kernel regression estimate is applied to estimate the invertible part of the non-linearity, An estimate to rec over the impulse response of the dynamic part is also given. Pointwise consistency of the first and consistency of the other estimate is sho wn. The results hold for any nonlinear characteristic, and any asympto tically dynamic subsystem. Convergence rates are also given.