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Hierarchical Least Squares Estimation Algorithm for Hammerstein–Wiener Systems

This letter focuses on identification problems of a Hammerstein-Wiener system with an output error linear element embedded between two static nonlinear elements. A hierarchical least squares algorithm is presented for the Hammerstein-Wiener system by using the auxiliary model identification idea and the hierarchical identification principle. The major contributions of the present study are that the identification model is formulated by using the auxiliary model identification idea (the estimate of the unknown internal variable is replaced with the output of an auxiliary model) and that the bilinear parameter vectors in the identification model are estimated by using the hierarchical identification principle. The proposed hierarchical identification approach is computationally more efficient than the existing over-parametrization method.