Recursive identification for Wiener model with discontinuous piece-wise linear function

This paper deals with identification of Wiener systems with nonlinearity being a discontinuous piece-wise linear function. Recursive estimation algorithms are proposed to estimate six unknown parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem by using the iid Gaussian inputs. The estimates are proved to converge to the corresponding true values with probability one. A numerical example is given to justify the obtained theoretical results.