Decentralized filtering with random sampling and delay

The decentralized minimum-mean-squared-error filtering problem in the presence of random sampling and delay is considered. We consider the situation where sensors are physically separated from the central processor that filters the measurements. We assume that the measurements from the sensor(s) arrive at the central processor with nonnegligible delay due to buffering at the sensor buffer, and transmission and propagation delays. Furthermore, we assume that there may be an uncertainty in the sampling time due to jittering, lack of synchronization between the processor and the sensor(s) clock, or uncertainty in the sensor's position. The problem formulation suggested in this paper constitutes a realistic framework for estimation problems with geographically dispersed sensors such as the multiple sensor tracking problem. Due to random sampling and delay, measurements from the sensor(s) may be received by the central processor at random times, may arrive out of sequence, and may have uncertain time origin. Optimal filters are derived for the cases of random sampling and fixed delay, fixed sampling and random delay, and random sampling and random delay.