Simultaneous estimation of unknown input and state for measurement delay systems based on Kalman filter

In this paper, for the linear discrete-time system with measurement delay, a research scheme is proposed to take the unknown input and state estimation algorithm as the limit of Kalman filter. Firstly, the existing recursive filters of state and input are refined and summarized. Secondly, under the assumption that the unknown input is Gaussian white noise, the Kalman filter theory is used to design recursive filter for unknown input and state. Then, under the specific condition that the variance of unknown input tends to infinity, it is proved that the simultaneous estimation of unknown input and state is a standard Kalman filtering algorithm with specific unknown input model. Finally, a numerical example is given to prove the effectiveness of the research scheme.