Robust Kalman filtering for discrete-time systems with measurement delay

The paper deals with the robust Kalman filtering problem for linear discrete-time systems with norm-bounded parametric uncertainty under both instantaneous and delayed measurements. Although the problem may be addressed by applying an existing robust Kalman filtering technique to an augmented system, much computation of the robust filter could be demanding. To improve the efficiency of computation, we propose a new approach through the re-organization of measurements. A sufficient condition for the existence of a robust Kalman filter is derived. The calculation of the robust filter involves two Riccati difference equations (RDEs) associated with the robust Kalman filter of a delay-free system and another two Riccati recursions related to the instantaneous measurement. The RDEs have the same dimension as the system. Both finite and infinite horizon filters are investigated.