Identification of Wiener systems with quantized inputs and binary-valued output observations

Abstract

This paper investigates identification of Wiener systems with quantized inputs and binary-valued output observations. By parameterizing the static nonlinear function and incorporating both linear and nonlinear parts, we begin by investigating system identifiability under the input and output constraints. Then a three-step algorithm is proposed to estimate the unknown parameters by using the empirical measure, input persistent patterns, and information on noise statistics. Convergence properties of the algorithm, including strong convergence and mean-square convergence rate, are established. Furthermore, by selecting a suitable transformation matrix, the asymptotic efficiency of the algorithm is proved in terms of the Cramér–Rao lower bound. Finally, numerical simulations are presented to illustrate the main results of this paper.