Optimal filtering for continuous-time linear systems with time-varying delay

The estimation problem for linear systems with time-varying delay in continuous setting is considered in this paper. The purpose is to find an optimal estimator based on MMSE for continuous-time linear systems subject to time-varying delay, where, as well known, the standard Kalman filtering can not be used directly. The key sight to deal with the time-varying delay of this paper is to re-organize the observations as new delay-free observations and introduce the innovations associated with the re-organized observations. Under this framework, to solve the optimal estimate problem for continuous-time linear system states over the linear observations with time-varying delay is transformed to the problem of performing standard time-varying Kalman filtering.