A Novel Filtering Method for Hammerstein-Wiener State-Space Systems

In this paper, we develop a novel filtering algorithm for Hammerstein-Wiener State-Space Systems. The likelihood function of the noisy nonlinear output signal given the system state is approximated by a Gaussian-Legendre quadrature rule. This approximation produces an explicit model of this likelihood function with a Gaussian Sum structure. Based on the general Bayesian filtering framework, we develop a Gaussian Sum Filter algorithm to obtain the a posteriori probability density function of the state given the current and past nonlinear output. With the characterization of the a posteriori probability function, we can obtain the associated statistics of the state. Finally, we present numerical examples to illustrate the benefits of our proposal.