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Identification of Wiener state–space models utilizing Gaussian sum smoothing

Abstract:

In this paper, we address the problem of system identification for Wiener state–space models. Our approach is based on the Maximum Likelihood method and the Expectation–Maximization algorithm. In the problem of interest, we model the output nonlinearity as a piecewise polynomial function and we jointly estimate the parameters of the linear system with the coefficients of each polynomial section. In our proposal, the computation of the cost function in the Expectation–Maximization algorithm requires the computation of the joint distribution of the state and the output of the linear system given the output of the nonlinear block. These quantities are obtained from an approximation that leads to a novel Gaussian sum smoothing algorithm. Additionally, we show that our method also addresses the identification of state–space systems in which the output is produced by a known quantizer. We present numerical examples to illustrate the benefits of the proposed identification technique.