Randomized Greedy Sensor Selection: Leveraging Weak Submodularity

TL;DR

This paper introduces a randomized greedy algorithm for sensor selection in resource-constrained environments, leveraging weak submodularity to optimize estimation accuracy in sensor networks.

Contribution

It formulates sensor selection as a weak submodular optimization problem and provides an efficient randomized algorithm with performance guarantees.

Findings

The objective function exhibits weak submodularity with bounded curvature.

The proposed algorithm outperforms existing greedy and relaxation methods.

Simulation results confirm the effectiveness of the randomized approach.

Abstract

We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space model and the resource are unlimited, the conventional Kalman filter provides the minimum mean-square error (MMSE) estimates. However, at any given time, restrictions on the available communications bandwidth and computational capabilities and/or power impose a limitation on the number of network nodes whose observations can be used to compute the estimates. We formulate the problem of selecting the most informative subset of the sensors as a combinatorial problem of maximizing a monotone set function under a uniform matroid constraint. For the MMSE estimation criterion we show that the maximum element-wise curvature of the objective function satisfies a certain upper-bound constraint and is, therefore, weak submodular. We develop an efficient randomized greedy algorithm for sensor selection and establish guarantees on the estimator's performance in this setting. Extensive simulation results demonstrate the efficacy of the randomized greedy algorithm compared to state-of-the-art greedy and semidefinite programming relaxation methods.