Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter.

The parameter estimation problem for multi‐input multi‐output Hammerstein systems is considered. For the Hammerstein model to be identified, its dynamic time‐invariant subsystem is described by a controlled autoregressive model with a communication delay. The modified Kalman filter (MKF) algorithm is derived to estimate the unknown intermediate variables in the system and the MKF‐based recursive least squares (LS) algorithm is presented to estimate all the unknown parameters. Furthermore, the hierarchical identification is adopted to decompose the system into two fictitious subsystems: one containing the unknown parameters in the non‐linear block and the other containing the unknown parameters in the linear subsystem. Then an MKF‐based hierarchical LS algorithm is derived. The convergence analysis shows the performance of the presented algorithms. The numerical simulation results indicate that the proposed algorithms are effective. [ABSTRACT FROM AUTHOR]