Information Fusion Filter, Delay Systems With Random Observations

Stochastic systems with random time-delay observations widely exist in many applications. For instance, in network control systems and communication systems, one-step or multi-step random measurement time delays can be induced due to variable transmission channel and the unreliable communication, which will lead to system performance degradation. Reflects in observation equation are the random time delay entries, where.random measurement delays can be described by Bernoulli distributed variables. In this paper, the distributed optimal weighted fusion estimation algorithms are developed for multi-sensor linear discrete time stochastic systems with random measurement delays. The studied main contents are as follows:Based on the projection theory, a system with one-step random time delay is transferred into that without delay by using state augmentation method. Against the new augmented system, the linear minimum variance optimal Kalman estimators are designed for single sensor system. Furthermore, the cross-covariance matrix between any two sensor subsystems is derived for multi-sensor systems. At last, the distributed weighted fusion state estimators are obtained by applying distributed optimal weighted fusion estimation algorithms in the linear minimum variance sense.Based on the projection theory, the full-order filter and predictor in linear unbiased minimum variance sense are presented for the linear discrete-time stochastic single sensor system with one-step random time delay by using non-augmentation method. Further, the cross-covariance matrix between any two sensor subsystems is derived for the multi-sensor systems. At last, the distributed weighted fusion state filter and predictor are obtained by applying the weighted fusion estimation algorithms in the linear minimum variance sense.For the linear discrete stochastic systems with multi-step random time delays, firstly, the optimal Kalman estimators in linear minimum variance sense are designed for single sensor system by using state augmentation method. Further, the cross-covariance matrix between any two sensor subsystems is derived for multi-sensor systems. At last, the distributed weighted fusion Kalman estimators are obtained by applying the weighted fusion estimation algorithms in the linear minimum variance sense.