Bias-Correction Errors-in-Variables Hammerstein Model Identification

In this paper, a bias-correction least-squares (LS) algorithm is proposed for identifying block-oriented errors-in-variables nonlinear Hammerstein (EIV-Hammerstein) systems. Because both the input and output of the EIV-Hammerstein system are observed with additive white noises, the estimation bias of traditional LS algorithm is introduced. The estimation bias is derived from a consistency point of view, which is a function about noise variances and monomial of noiseless system input-output measurements. A bias-estimation scheme based only on the available noisy measurements is then proposed for consistent identification of the monomial of noiseless system input-output measurements in a recursive form. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the unknown noise variances for practical applications, such that the noise effect can be eliminated and the consistent estimated parameters are obtained. The effectiveness of the proposed method is demonstrated by a simulation example and an experimental prototype of wireless power transfer system.