NONPARAMETRIC IDENTIFICATION OF WIENER SYSTEMS BY ORTHOGONAL SERIES

A Wiener system, i.e., a system comprising a linear dynamic and a nonl inear memoryless subsystems connected in a cascade, is identified. Bot h the input signal and disturbance are random, white, and Gaussian. Th e unknown nonlinear characteristic is strictly monotonous and differen tiable and, therefore, the problem of its recovering from input-output observations of the whole system is nonparametric. It is shown that t he inverse of the characteristic is a regression function and, next, a class of orthogonal series nonparametric estimates recovering the reg ression is proposed and analyzed. The estimates apply the trigonometri c, Legendre, and Hermite orthogonal functions. Pointwise consistency o f all the algorithms is shown. Under some additional smoothness restri ctions, the rates of their convergence are examined and compared. An a lgorithm to identify the impulse response of the linear subsystem is p roposed.