A nonlinear recursive instrumental variables identification method of Hammerstein ARMAX system

Identification of nonlinear Hammerstein models has received much attention due to its ability to describe a wide variety of nonlinear systems. This paper considers the problem of the parameter estimation of the ARMAX models for the Hammerstein systems. A novel nonlinear recursive instrumental variables method, which is simple and easy for practical applications, is proposed to deal with the problem. In order to make the instrumental variables uncorrelated with the colored noise and to obtain better identification effect, three approaches for choosing the instrumental variables usually used in the linear RIV method are introduced. Furthermore, the procedure of the nonlinear RIV method and its property of the mean square convergence of the nonlinear RIV method are rigorously derived. Finally, an example is carried out as illustration, where the ARMAX-RLS method is compared as the basis, and the results show that the nonlinear RIV method is superior to ARMAX-RLS method in terms of identification accuracy and convergence speed under colored noise, which reveals the effectiveness of the proposed method.

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