Some results on simultaneous input and state estimation for linear systems

This paper is concerned with the problem of simultaneous input and state estimation for linear discrete-time systems with missing measurements. First, in order to simultaneously estimate the input and state in the sense of unbiased minimum variance, a recursive estimator is designed in terms of one Lyapunov equation and one Riccati equation. Then some mild conditions for the existence of the infinite horizon estimator are presented. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach