Identification of discrete Wiener systems by using adaptive generalized rational orthogonal basis functions

This paper studies the problem of identifying discrete-time Wiener systems consisting of polynomial nonlinearities and linear subsystems with unknown orders. The best linear approximation for a Wiener system is found by using finite generalized rational orthogonal basis functions. The novelty of this work is that the poles of the basis functions are adaptively selected by applying the proposed method. This selection leads to a greedy type of best linear approximation with a fast convergence rate. Further, the nonlinearity is determined by solving the conventional least-squares problem as usual. Moreover, the case in which there are errors in the frequencies is analyzed. The analytical results show that small perturbations have limited effects on the upper bounds of the estimation error. Two numerical examples are given to verify the validity of the proposed method.