The Auxiliary Model Based Hierarchical Estimation Algorithms for Bilinear Stochastic Systems with Colored Noises

Abstract

This paper considers the parameter identification for a class of nonlinear stochastic systems with colored noise. An input-output representation is derived by eliminating the state variables in the bilinear system. Based on the obtained identification model, a recursive generalized extend least squares algorithm is proposed by using the auxiliary model identification idea. Moreover, a two-stage recursive generalized extended least squares algorithm is presented to reduce the computational burden by using the hierarchical identification principle and the auxiliary model identification idea, respectively. A stochastic gradient identification algorithm is proposed for comparison. The simulation results show that the proposed algorithms have a good performance in estimating the parameters of the bilinear systems with colored noises.