Nonparametric Recovering of Nonlinearity in Wiener-hammerstein Systems

In the paper we recover the static characteristic of Wiener-Hammerstein (sandwich) system from inputoutput data. The system is excited and disturbed by random processes with arbitrary distribution. Two kernel-based estimates are proposed and compared. It is shown that they can successfully recover the system characteristic under small amount of a priori information about the static characteristic and the surrounding dynamic blocks. The identified nonlinear function is not parametrized and is not assumed to be invertible, which is common restriction in the literature. The orders of linear dynamic blocks are also unknown. The convergence of the estimates take place for the points in which the input probability density function in positive. The effectiveness of the algorithms is illustrated in simulation example.