Optimal Scheduling of Multiple Sensors with Packet Length Constraint

TL;DR

This paper addresses optimal scheduling of multiple sensors with varying packet lengths to minimize estimation error, formulating the problem as an MDP and revealing a threshold-based optimal policy.

Contribution

It introduces a novel MDP formulation for sensor scheduling with packet length constraints and proves the existence of a threshold-structured optimal policy.

Findings

Optimal policy has a threshold structure.

Existence of a deterministic stationary policy is proven.

Numerical example illustrates the policy's effectiveness.

Abstract

This paper considers the problem of sensory data scheduling of multiple processes. There are $n$ independent linear time-invariant processes and a remote estimator monitoring all the processes. Each process is measured by a sensor, which sends its local state estimate to the remote estimator. The sizes of the packets are different due to different dimensions of each process, and thus it may take different lengths of time steps for the sensors to send their data. Because of bandwidth limitation, only a portion of all the sensors are allowed to transmit. Our goal is to minimize the average of estimation error covariance of the whole system at the remote estimator. The problem is formulated as a Markov decision process (MDP) with average cost over an infinite time horizon. We prove the existence of a deterministic and stationary policy for the problem. We also find that the optimal policy has a consistent behavior and threshold type structure. A numerical example is provided to illustrate our main results.