Remote State Estimation Across an Action-Dependent Packet-Drop Link

Consider that a remote estimator seeks to estimate the state of a non-collocated discrete-time finite-dimensional linear time-invariant plant that is persistently excited by process noise. A communication link attempts to relay the state of the plant to the estimator whenever it receives a transmission request. The link experiences packet-drops and has an (action-dependent) state that is influenced by the history of current and past requests. A controlled Markov chain models this dependence and a given function of the link's state governs the packet-drop probability. Every randomized stationary transmission policy is specified by a function that determines the probability of a transmission request in terms of the link's state. The article focuses on the design of these policies. Two theorems provide necessary and sufficient conditions for the existence of a randomized stationary policy that stabilizes the estimation error, in the second-moment sense. They also show that it suffices to search for deterministic stabilizing policies and identify an important case in which the search can be further narrowed to threshold policies.