A re-organized innovation approach to Kalman filtering for time-varying systems

The paper deals with the Kalman filtering problem for linear time-delayed continuous-time systems. Both the optimal filter for systems with single delayed measurement and with multiple ones are considered. Such problem has much application in sensor fusion and network systems. Existing solutions to this problem are usually related to solving partial differential equations (PDEs), which, however, are difficult to be performed in practice. This paper aims to propose an explicit solution to the Kalman filtering problem. The proposed approach is the re-organized innovation analysis. The obtained Kalman filter is given in terms of Riccati differential equations (RDEs). More importantly, the proposed approach can be applied to solve the more complicated problems such as H(infinity) fixed-lag smoothing and H(infinity) preview control.