A Robust and Recursive Identification Method for the Hammerstein Model

Abstract

In this note, a robust identification method of non linear systems using the Hammerstein model is presented. The main property of the proposed approach is that parameters of the linear and nonlinear parts are estimated in a recursive way while the global convergence is guaranted. The proposed method consists first to transform the non linear representation into an input-output model linear in parameters, after, a regular transformation based on the pseudo-inverse technique allows us to estimate in the least squares sense parameters vector of the original realization. For the case of correlated noise, to model measurement disturbances, we propose a simple technique based on the pseudo-linear regression method and we investigate all parameters dependencies to obtain a consistent solution. Sufficient conditions for global convergence are derived. Two numerical examples with different correlation structures and different Signal to Noise Ratio values are provided.