Remote state estimation with usage-dependent Markovian packet losses

In this paper, we consider a problem of packet scheduling in the setting of remote estimation with usage-dependent Markovian packet losses. A sensor measures the state of a discrete-time linear process, computes the estimate via a local Kalman filter, and sends the packets to a remote estimator via a network. The link state evolves as a two-state Markov chain, and its state transition depends on the network usage. The aim is to design the scheduling policy which balances the estimation quality and the energy consumption. We identify the problem as a Markov decision process (MDP) and prove the structural properties of the optimal policy. Furthermore, based on the structural properties, we derive the sufficient and necessary condition of the mean square stability of the remote estimator. Simulation examples are provided to illustrate the results.