Combined state and parameter estimation for Hammerstein systems with time delay using the Kalman filtering

This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time delay. Both the process and the measurement noises are considered in the system. On the basis of the observable canonical state space form and the key term separation, a pseudolinear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman filterbased least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms, which are missed for the time delay, the Kalman filterbased recursive extended least squares algorithm is derived to obtain the estimates of the unknown time delay, parameters, and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms.