Multi-Sensor Kalman Filtering with Intermittent Measurements

In this paper, we extend the stability theory on Kalman filtering with intermittent measurements from the scenario of one single sensor to the one of multiple sensors. Consider that a group of sensors take measurement of the states of a process and then send the data to a remote estimator. The estimator receives the measurements intermittently, which may be caused by the fact that the channels have packet dropouts or that the sensors schedule the data transmission stochastically. Based on the received measurements, the estimator computes the estimates of the process states by multi-sensor Kalman filtering. Because of the intermittent measurements, the estimator may be unstable. This stability issue is mainly investigated in this paper. A notion of transmission capacity, which is related to the communication rates of sensors, is proposed. It is shown that the expected estimation error covariance diverges for all feasible communication rates collections of the sensors when the transmission capacity is below a certain value; meanwhile, when the transmission capacity is above another certain value, there exists a feasible communication rates collection such that the expected estimation error covariance is bounded.