Parameter Estimation for the Hammerstein State Space System with Measurement Noise

Abstract

This paper considered the parameters estimation algorithm for the Hammerstein state space system with measurement noise using special test signals. The Hammerstein nonlinear system has a static nonlinear subsystem represented by neural fuzzy system and a dynamical linear subsystem represented by state space system, and the parameters estimation separation of the two subsystems is realized by using special test signals composed of binary signal and random signal. In the first place, characteristics of static nonlinear subsystem without activation using binary signals, the parameters of state space subsystem and colored noise model can be obtained by recursive extended least squares algorithm, which deals with noise interference issue. In addition, unmeasured state variable of estimated system is replaced with instrumental variable, the parameters of the nonlinear subsystem are identified by using cluster algorithm and the instrumental variable-based recursive least squares method based on measurement random signals. The results of simulation indicate that the proposed parameter estimation algorithm can realize good estimation accuracy for the Hammerstein state space system with measurement noise.