A Correlation Least-Squares Method for Hammerstein Model Identification with ARX and -Markov Structures

This paper presents a two-step method for identification of the SISO Hammerstein model, which employs input autocorrelation and input-output cross-correlation functions as data for least-squares estimation. Using separable processes as input signals, the proposed method allows the linear block of a Hammerstein model to be identified up to a multiplicative constant, without a priori knowledge of the nonlinear model structure. Both ARX and μ-Markov structures of the linear block are considered, where the main concern is the accuracy of pole and zero estimates. The correlation least-squares method is compared numerically with a wellknown nonlinear least-squares method, which shows that the correlation method is consistently accurate across different nonlinear model structures.