Sensor Scheduling for Linear Systems: A Covariance Tracking Approach

TL;DR

This paper introduces a novel covariance tracking approach for sensor scheduling in linear systems, transforming a complex NP-hard problem into a convex design problem and an approximate tracking solution, validated through experiments.

Contribution

It proposes a convex relaxation and covariance tracking framework that efficiently approximates optimal sensor schedules for linear systems.

Findings

The method effectively approximates sensor schedules with sub-optimality bounds.

The framework reduces computational complexity of sensor scheduling.

Experimental results demonstrate the approach's efficacy.

Abstract

We consider the classical sensor scheduling problem for linear systems where only one sensor is activated at each time. We show that the sensor scheduling problem has a close relation to the sensor design problem and the solution of a sensor schedule problem can be extracted from an equivalent sensor design problem. We propose a convex relaxation to the sensor design problem and a reference covariance trajectory is obtained from solving the relaxed sensor design problem. Afterwards, a covariance tracking algorithm is designed to obtain an approximate solution to the sensor scheduling problem using the reference covariance trajectory obtained from the sensor design problem. While the sensor scheduling problem is NP-hard, the proposed framework circumvents this computational complexity by decomposing this problem into a convex sensor design problem and a covariance tracking problem. We provide theoretical justification and a sub-optimality bound for the proposed method using dynamic programming. The proposed method is validated over several experiments portraying the efficacy of the framework.