Limited memory optimal filter for discrete-time systems with measurement delay

This paper considers the limited memory optimal filter for discrete-time systems with measurement delay. Firstly, we deal with the measurement delay using the reorganized innovation analysis approach. According to the projection theory, an optimal linear filter is provided in the linear minimum mean square error (LMMSE) sense. With the increase of time, the size of LMMSE filter problem will grow. Then, in order to avoid this problem, we explore a limited memory optimal filter calculated by applying the recent N measurements. Finally, we give a numerical example to show that the limited memory optimal filter is effective.