Parameters estimation for the Hammerstein-Wiener models with colored noise based on hybrid signals

A three-stage estimation approach of the Hammerstein-Wiener model with colored noise using hybrid signals is considered in this article. The Hammerstein-Wiener model where a linear dynamic block is embedded between two static nonlinear elements, in which two nonlinear elements represented by two independent neural fuzzy models and a linear element represented by autoregressive exogenous model. The designed hybrid signals that consist of separable signals and random signals are devoted to estimating independently. First, the characteristics of separable signals in the action of the static nonlinear element are analyzed, then the output nonlinear element parameters are estimated utilizing two groups of separable signals with a multiple. Moreover, least squares based on correlation analysis method is applied to estimate linear element using one set of separable signals, which handles the interference of colored process noise. Finally, the recursive extended least squares algorithm is derived to estimate the input nonlinear element and the autoregressive moving average noise model, which improves parameters estimation accuracy owing to estimating colored noise model parameters in recursive estimate process. The feasibility of the presented estimation technique is demonstrated by an illustrative simulation example and a practical nonlinear process.