Identification of the Hammerstein system with time delay and Colored Noise

This paper presents a method for identifying Hammerstein system in the presence of time delay and colored noise. The Hammerstein system is composed of a static nonlinear block cascaded with a dynamic linear block. The static nonlinear block is represented by a neural fuzzy model (NFM), while dynamic linear block is approximated using a time delay autoregressive moving average model with additional input (TD-ARMAX). The parameter identification for each block is accomplished using combined signals, which consist of both separable and random signals. Firstly, utilizing the input and output of separable signals, the parameters of linear block and time-delay value are identified using correlation analysis theory and principle of parameter redundancy. Additionally, the recursive extended theory is employed to enhance the identification accuracy, and a recursive extended least squares (RELS) method is created to identify the parameters of NFM model by using input-output of random signals, thus the effect of colored noise on parameter identification is addressed. The simulation results demonstrate that the proposed method is feasible for identifying the unknown parameters of Hammerstein system.