Gradient based estimation methods for a class of nonlinear systems with colored noises

This paper develops an extended stochastic estimation method to identify the parameters of Hammerstein-Wiener nonlinear models with colored noises. By replacing the unmeasurable noise terms in the information vectors of the pseudo-linear regression model with their estimates, the noise estimates can be computed by the obtained parameter estimates. The obtained parameter estimates of the identification model include the products of the original system parameters, two methods of separating the parameter estimates into original parameters are discussed: the average method and the singular value decomposition method. To improve the identification accuracy, an extended stochastic gradient algorithm with a forgetting factor is given. The simulation examples indicate that the introduction of the forgetting factor can improve the estimation accuracy.