Stochastic Sensor Scheduling via Distributed Convex Optimization

TL;DR

This paper introduces a stochastic sensor scheduling method for multiple linear systems, optimizing resource use to minimize estimation error, and offers distributed algorithms for implementation.

Contribution

It formulates a novel stochastic scheduling approach with a distributed convex optimization solution for resource-constrained sensor systems.

Findings

The stochastic scheduling provides an upper bound on optimal performance.

The problem is relaxed into a tractable quasi-convex form.

Distributed algorithms effectively solve the scheduling problem.

Abstract

In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples.