This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient is the employment of so-called "particle smoothing" methods to compute required conditional expectations via a sequential Monte Carlo approach. Simulation examples demonstrate the efficacy of these techniques.

This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein-Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and coloured stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method developed here addresses the blind Wiener estimation problem as a special case.

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The Wiener model is a block oriented model, having a linear dynamic system followed by a static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. We show that this will, in general, lead to biased estimates if there are other disturbances present than measurement noise. The implications of Bussgang's theorem in this context are also discussed. For the case with general disturbances, we derive the Maximum Likelihood method and show how it can be efficiently implemented. Comparisons between this new algorithm and the traditional approach, confirm that the new method is unbiased and also has superior accuracy