Simple and fast convex relaxation method for cooperative localization in sensor networks using range measurements

TL;DR

This paper introduces a simple, fast, and distributed convex relaxation method for sensor network localization using noisy range measurements, achieving high accuracy with fewer communications and guaranteed convergence.

Contribution

It presents a novel convex relaxation approach that is fully distributed, easy to implement, and converges quickly, outperforming existing methods in accuracy and communication efficiency.

Findings

Achieves one order of magnitude higher accuracy than comparable methods.

Uses one order of magnitude fewer communications.

Provides theoretical convergence guarantees for both parallel and asynchronous algorithms.

Abstract

We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the non-convex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization properties to the full to obtain an approach that: is completely distributed, has a simple implementation at each node, and capitalizes on an optimal gradient method to attain fast convergence. We offer a parallel but also an asynchronous flavor, both with theoretical convergence guarantees and iteration complexity analysis. Experimental results establish leading performance. Our algorithms top the accuracy of a comparable state of the art method by one order of magnitude, using one order of magnitude fewer communications.