Optimal sensor scheduling for state estimation over lossy channel

This study studies a sensor scheduling problem for the state estimation of a stochastic discrete-time system where the measurements are to be sent from multiple sensors to a centralised estimator through a lossy channel. By adopting a carrier sense multiple access/collision avoidance (CSMA/CA) protocol, the packet loss rate of the channel increases with the number of competing sensors for data communication. To increase the channel utilisation, it requires to smartly select informative sensors to transmit their measurements. Depending on the availability of the acknowledgment (ACK) messages from the estimator, both online and offline algorithms for scheduling sensor communication are proposed to optimise the expected performance of minimum mean-square error state estimator. Particularly, the online scheduling uses the ACK to trigger the sensor communication while the offline version adopts a random transmission framework and only decides the probability of sending measurements for each sensor in an offline manner. The optimal online scheduler is given by the solution of an integer programming, which is approximated by a practically solvable optimisation. Simulations are included to demonstrate the effectiveness of the proposed algorithms.