Parameter reduction of MISO Wiener-Schetzen models using the best linear approximation

This paper concerns the identification of MISO (multiple inputs single output) Wiener systems. For each input-output path, the linear dynamics are modeled by a set of orthonormal basis functions (OBFs). The static nonlinearity is modeled through a multivariate polynomial. The parameters of the model are the coefficients of this polynomial. In this paper, an identification procedure for SISO (single input single output) Wiener systems is extended towards MISO Wiener systems. The poles of the OBFs are estimated using an extension of the best linear approximation (BLA) towards MIMO (multiple input multiple output) systems. As the number of parameters can increase significantly compared to the SISO case, a parameter reduction step, first developed for the SISO case, is extended in this paper to the MISO case. In each set of OBFs, one OBF is replaced by the BLA of the input-output path corresponding to that set. It is shown that in this way the number of relevantly contributing terms in the multivariate polynomial is significantly reduced. Simulation results show a major reduction of the number of parameters, with only a minor increase in the rms error on the simulated output.