W. Greblicki, NONPARAMETRIC APPROACH TO WIENER SYSTEM-IDENTIFICATION, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 44(6), 1997, pp. 538-545
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.