Recursive prediction error identification using the nonlinear wiener model

Abstract

The nonlinear Wiener model, consisting of a linear dynamic block in cascade with a static nonlinearity, is considered. A recursive prediction error identification algorithm, based on the Wiener model, is derived. The linear dynamic block is modelled as a SISO transfer function operator, and the static nonlinearity is approximated with a piecewise linear function. A theoretical analysis of the method is carried out, and conditions for local convergence to the true parameter vector are given. In particular, the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation. A numerical example illustrates the performance of the algorithm further. Practical guidelines on how to apply the algorithm are also included in the paper.