Semi-Definite Programming Relaxation for Non-Line-of-Sight Localization

TL;DR

This paper introduces a semidefinite programming relaxation method for localizing points in space using noisy, potentially corrupted distance measurements, demonstrating robustness and exact recovery under certain graph conditions.

Contribution

It proposes a novel SDP relaxation approach for NLOS localization that is computationally efficient and guarantees exact solutions for non-contractible graphs.

Findings

The method accurately localizes points in indoor environments.

It is robust to large additive noise and NLOS errors.

The approach outperforms existing techniques in tested scenarios.

Abstract

We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements can be arbitrarily corrupted by large additive noise. Given that the problem is highly non-convex, we propose a simple semidefinite programming relaxation that can be efficiently solved using standard algorithms. We define a notion of non-contractibility and show that the relaxation gives the exact point locations when the underlying graph is non-contractible. The performance of the algorithm is evaluated on an experimental data set obtained from a network of 44 nodes in an indoor environment and is shown to be robust to non-line-of-sight errors.