Regularized estimation of Hammerstein systems using a decomposition-based iterative instrumental variable method

Abstract

This paper presents a two-step instrumental variable (IV) method to obtain the regularized and consistent parameter estimates of the Hammerstein ARMAX model based on the bilinear parameterized form. The two-step identification method consists of estimating the bilinear parameters in the first step, followed by parameter reduction in the second step. An iterative identification method is proposed, based on the idea of separating the bilinear form in the two separable forms with partial parameters and solving the decomposed model forms iteratively. The IV-based estimation is integrated into the formulated decomposed structure by introducing the instruments constructed from the estimated auxiliary model outputs. It is shown that in a stochastic environment the proposed IV method produces consistent estimates in the presence of correlated noise disturbances. The validity of the proposed algorithm is verified with the help of extensive simulations using a Monte Carlo study.