Maximum likelihood identification of stochastic Weiner-Hammerstein-type non-linear systems

Abstract

The identification problem for non-linear Wiener-Hammerstein-type systems is considered. Unlike alternative techniques that are based on deterministic system representations, a stochastic model structure that explicitly accounts for both the input-output and noise dynamics is postulated. The uniqueness properties of this structure are analysed, and appropriate necessary and sufficient conditions derived. A new time-domain identification method based on the Maximum Likelihood principle is then introduced. Unlike alternative approaches that are mainly in the frequency and correlation domains, the proposed method offers statistically optimal estimates from a single record of normal operating data, and is capable of operating directly on the time-domain data and overcoming errors associated with the evaluation of correlation functions/Fourier transforms or multi-stage procedures. The effectiveness and accuracy of the proposed method are verified via numerical simulations with a number of different systems and noise to signal ratios.