A Delta Operator State Estimation Algorithm for Discrete-Time Systems With State Time-Delay

This letter presents a state estimation algorithm for linear discrete-time systems with state-delay. In order to overcome the difficulty that the traditional Kalman filter cannot estimate the states of the systems with state-delay, a state estimation strategy is developed by combining the auxiliary model with the delta operator. Then, by constructing and minimizing the covariance matrix of the state reconstruction errors, a delta operator state estimation algorithm is derived and it can fulfill effective state estimation for the linear discrete-time system with state-delay. Moreover, the convergence proof is provided by means of stochastic stability theory. Finally, the experimental results demonstrate that the developed state estimation method is effective.