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

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 crossvalidation 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.