Wiener-Hammerstein system identification with non-Gaussian input

The paper addresses the problem of non-parametric estimation of the static characteristic in Wiener-Hammerstein (sandwich) system excited and disturbed by random processes. A new, kernel-like method is presented. The proposed estimate is consistent under small amount of a priori information. An IIR dynamics, non-invertible static non-linearity, and non-Gaussian excitations are admitted. The convergence of the estimate is proved for each continuity point of the static characteristic and the asymptotic rate of convergence is analysed. The results of computer simulation example are included to illustrate the behaviour of the estimate for moderate number of observations.