Parameter estimation of Hammerstein-Wiener ARMAX systems using unscented Kalman filter

In this paper unscented Kalman filter parameter estimation algorithm is stated for identification of dynamic systems´ model which may be considered as the Hammerstein-Wiener autoregressive moving average model with exogenous inputs (ARMAX). Kalman filter is used broadly for control and estimation applications due to its merits such as simplicity, optimality, tractability and robustness. In nonlinear scope, some extensions of this method are developed like extended Kalman filter and unscented Kalman filter. The latter is an alternative to EKF in practical applications where improved performance and greater accuracy are demanded. This algorithm is presented for estimation of coefficients in a typical system mathematical model in three stages. Hammerstein-Wiener ARMAX model is selected as the intended system. Its general formulation is introduced and also the parameter estimation algorithm is described in this study. Finally the performance of UKF has been verified by illustrating the simulation results based on two examples of dynamic systems. Also the acquired results by using some other methods such as EKF, extended stochastic gradient (ESG) and extended forgetting factor stochastic gradient (EFG) from referenced studies are appended for comparison. Additionally this technique is implemented for identifying the parameters of a typical gas turbine model using physical data.