Optimal Filtering for Delay System with Multiplicative Noise

The paper deals with the Kalman filtering problem for linear discrete-time systems with parametric uncertainty of multiplicative noise in both instantaneous and delayed measurements. Although the problem may be addressed by applying an existing Kalman filtering technique to an augmented system, the computation of the Kalman filter could be demanding. To improve the efficiency of computation, we propose a new approach through the re-organization of innovation. The calculation of the optimal filter involves two Riccati equations associated with the Kalman filter of a delay-free system and the instantaneous measurement, respectively. The Riccati equations have the same dimension as the system.