Recursive Identification for MIMO Hammerstein Systems

This technical note considers the recursive identification for the multi-input and multi-output (MIMO) Hammerstein system with internal noise and observation noise and with linear part being an ARX system. With the help of the generalized Yule-Walker equation and the correlations of system signals, the recursive algorithms are proposed for estimating unknown coefficients of the linear subsystem, while the system nonlinearity is recursively estimated by using the multivariable kernel functions. Strong consistency of the estimates is proved under reasonable conditions, and a simulation example is provided.