A bias-correction modeling method of Hammerstein–Wiener systems with polynomial nonlinearities using noisy measurements

Abstract

Modeling of Hammerstein–Wiener nonlinear systems has received a lot of attention in the signal processing community. However, all existing model identification methods may fail to provide a consistent parameter estimate for Errors-In-Variables (EIV) Hammerstein–Wiener systems, where both input–output data are contaminated by measurement white noises. In this paper, a bias-correction Least-Squares (LS) algorithm for consistent identification of EIV Hammerstein–Wiener systems with polynomial nonlinearities using noisy measurements is proposed. Firstly, the analytic expression for the estimated bias of the LS algorithm using noisy measurements for EIV Hammerstein–Wiener systems with polynomial nonlinearities is derived, which is caused by the correlation between the input–output signals and measurement noises. Secondly, a consistent estimation method for the bias-correcting term, including a recursive step and a cross-validation step based on the available noisy measurements only, is then proposed to estimate the unknown terms of noises variances and noise-free measurements in the estimated bias. The effectiveness of the proposed algorithm is demonstrated through a simulated example and a robot arm system.