Scheduling and Estimation Strategies in a Sequential Networked Estimation Problem

Consider a remote estimation problem with multiple stochastic subsystems and non-collocated estimators. Each estimator is interested in forming real-time estimates of the state of its corresponding stochastic subsystem over a finite time horizon. Each subsystem can communicate its state to the corresponding estimator via a shared wireless network. In order to avoid packet collisions, a network manager decides at each time which subsystem's state (if any) will be transmitted over the network based on the realization of the states. In this paper, we study the joint design of scheduling strategy for the manager and the estimation strategies for the estimators. Under a symmetry condition on the class of admissible scheduling strategies, we completely characterize the optimal estimation strategy and provide a dynamic program for the optimal scheduling strategy. We further investigate the obtained dynamic program to give some structural insights about the optimal scheduling strategy.