Multi-hop sensor network scheduling for optimal remote estimation

Abstract

This paper studies a design problem of how a group of wireless sensors are selected and scheduled to transmit data efficiently over a multi-hop network subject to energy considerations, when the sensors are observing multiple independent discrete-time linear systems. Each time instant, a subset of sensors is selected to transmit their measurements to a remote estimator. We formulate an optimization problem, in which a network schedule is searched to minimize a linear combination of the averaged estimation error and the averaged transmission energy consumption. It is shown that the optimal network schedule forms a tree with root at the gateway node. From this observation, we manage to separate the optimization problem into two subproblems: tree planning and sensor selection. We solve the sensor selection subproblem by a Markov decision process, showing that the optimal solution admits a periodic structure when the transmission cost is sufficiently low. Efficient algorithms are proposed and they are shown to reduce the computational complexity of the original optimization problem. Numerical studies illustrate the effectiveness of the proposed algorithms, and show that they are scalable to large networks.