Convergence of fixed‐point iteration for the identification of Hammerstein and Wiener systems

Abstract

SUMMARYConvergence property of the iterative algorithm for Hammerstein or Wiener systems is generally hard to establish because of the existence the unmeasurable internal variables in such systems. In this paper, a fixed‐point iteration is introduced to identifying both Hammerstein and Wiener systems with a unified algorithm. This newly proposed estimation algorithm gives consistent estimates under arbitrary nonzero initial conditions. In addition, the errors of the estimates are established as functions of the noise variance, and thus how the noise affects the quality of parameter estimates for a finite number of data points is made clear. Copyright © 2012 John Wiley & Sons, Ltd.