Parameter estimation of Hammerstein-Wiener nonlinear system with noise using special test signals

In this paper, an identification procedure of Hammerstein-Wiener nonlinear system with process noise using special test signals is presented. Special test signals that contain separable signal and uniformly random multi-step signal are employed to separate the identification problems of the linear dynamic part and the output static nonlinear part from that of the input static nonlinear part, and then correlation analysis method is applied to estimate the parameters of the output static nonlinear part and linear dynamic part. Moreover, a filter is embedded to form extended Hammerstein-Wiener system to calculate the noise correlation functions by the information of zeros and poles of the extended system, further an error compensation term which consists of the noise correlation functions is added to least square estimation to compensate the error caused by process noise. Therefore, the unbiased estimation of model parameters can be derived by error compensation based recursive least square method. Simulation results demonstrate that proposed approach can effectively identify parameters of Hammerstein-Wiener nonlinear system in the presence of process noise. (C) 2019 Elsevier B.V. All rights reserve.