Kalman filtering for continuous-time systems with time-varying delay

The optimal filtering problem for continuous-time linear systems with time-varying delay is considered. The purpose is to find a Riccati equation-based solution to the linear minimum mean square error filter. The time-varying delayed observation is firstly rewritten as an equivalent observation with multiple constant delays by defining a binary variable to model the arrival process of the observation. Then, by constructing certain multiple channel observations sequence that contains the same amount of information as the original one and applying the re-organised innovation analysis approach, the proposed problem is transformed to performing standard time-varying Kalman filtering.