A Randomized Greedy Algorithm for Near-Optimal Sensor Scheduling in Large-Scale Sensor Networks

TL;DR

This paper introduces a fast randomized greedy algorithm for sensor scheduling in large-scale sensor networks, optimizing state estimation with theoretical performance bounds and demonstrated effectiveness through simulations.

Contribution

It presents a novel randomized greedy approach with performance analysis based on curvature, improving efficiency over existing methods for sensor selection under matroid constraints.

Findings

The algorithm achieves near-optimal sensor selection with lower computational cost.

Performance bounds relate expected MSE to the optimal MSE using curvature analysis.

Simulation results show superior efficiency compared to greedy and SDP relaxation methods.

Abstract

We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as the maximization of a monotone set function under a matroid constraint. We propose a randomized greedy algorithm that is significantly faster than state-of-the-art methods. By introducing the notion of curvature which quantifies how close a function is to being submodular, we analyze the performance of the proposed algorithm and find a bound on the expected mean square error (MSE) of the estimator that uses the selected sensors in terms of the optimal MSE. Moreover, we derive a probabilistic bound on the curvature for the scenario where{\color{black}{ the measurements are i.i.d. random vectors with bounded $\ell_2$ norm.}} Simulation results demonstrate efficacy of the randomized greedy algorithm in a comparison with greedy and semidefinite programming relaxation methods.