Energy-Efficient Optimal Sensor Scheduling for State Estimation Over Multihop Sensor Networks

In this article, we consider the power scheduling problem of the multihop transmission with limited power resources. For a discrete-time linear time-invariant process, we consider a more practical scenario where the forward-error-correcting (FEC) coding scheme is utilized. An approximate communication model is introduced to formulate the nonanalytical relationship between the consumption of power and the successful-decoding-probability. For the single-hop transmission, we propose an analytical method to figure out the optimal offline scheduling for the finite-time case and the optimal periodic schedule for the infinite-time case. We consider the process and terminal errors simultaneously, and explicitly discuss how different values of parameters affect the optimality. Moreover, we extend our conclusions to the multihop case. In order to deal with the difficulty and complexity brought by the multihop scenario, a novel method based on the equivalent-scheduling matrix (ESM) is proposed to describe the accumulated effects through the multihop transmission. Meanwhile, explicit solutions of the multihop case are provided for finite- and infinite-time cases, respectively. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.