Infinite-horizon sensor scheduling for estimation over lossy networks

In this paper, we consider the problem of infinite-horizon sensor scheduling for estimation of a discrete-time linear Gaussian system, where the sensor information may be dropped during communication over a memoryless erasure channel, modeled as an independent Bernoulli process. We assume that due to energy or bandwidth constraints, the sensor can only maintain an average communication rate of r. The optimal communication schedule is thus chosen by the sensor to minimize the average estimation error of the receiver. We prove necessary and sufficient conditions for the feasibility of the optimization problem for two classes of protocols, one where deterministic acknowledgments are transmitted from the central location back to the sensor (ACK) and the other where the acknowledgement structure is absent (No-ACK). We prove that for the No-ACK case, the optimal schedule can be approximated by a periodic schedule with arbitrarily close performance. For the ACK case, we provide the explicit optimal sensor schedule. A numerical example is provided to illustrate the effectiveness of the proposed strategy.