A multi-innovation state and parameter estimation algorithm for a state space system with d-step state-delay

This paper considers the state and parameter estimation problem of a state-delay system. On the basis of the stochastic gradient algorithm (i.e., the gradient based search estimation algorithm), this work extends the scalar innovation into an innovation vector and presents a multi-innovation gradient parameter estimation algorithm for a state-space system with d-step state-delay by means of the multi-innovation identification theory. For thesystems whose states are unknown, we use the states of the state observer for the parameter estimation and use the estimated parameters for the state estimation. This forms a joint multi-innovation state and parameter estimation algorithm for the state-delay systems with immeasurable states. The simulation results indicate that the proposed algorithms can work well.