Distributed Maximum Likelihood Sensor Network Localization

TL;DR

This paper introduces a distributed convex relaxation approach for sensor network localization based on maximum likelihood, utilizing ADMM for efficient, asynchronous, and resilient local computation, especially effective in large-scale networks.

Contribution

It develops a novel edge-based convex relaxation framework and a distributed ADMM algorithm for sensor localization that is scalable, convergent, and robust to computation errors.

Findings

The proposed method converges to the centralized solution.

It performs well in large-scale sensor networks.

The algorithm is asynchronous and error-resilient.

Abstract

We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements. We derive a computational efficient edge-based version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation error-resilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for large-scale networks.