Robust Localization Using Range Measurements with Unknown and Bounded Errors

TL;DR

This paper develops a robust localization method that minimizes worst-case errors using range measurements with unknown but bounded errors, avoiding reliance on statistical error models.

Contribution

It formulates a non-convex optimization problem for robust localization, relaxes it to a convex form, and proposes a distributed algorithm with fast convergence.

Findings

More robust to large measurement errors than existing methods

Convex relaxation enables efficient distributed solutions

Geometrical analysis offers additional insights

Abstract

Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in practice. Compared with the statistical knowledge of measurement errors, it can often be easier to obtain the measurement error bound. This work investigates a localization problem assuming unknown measurement error distribution except for a bound on the error. We first formulate this localization problem as an optimization problem to minimize the worst-case estimation error, which is shown to be a non-convex optimization problem. Then, relaxation is applied to transform it into a convex one. Furthermore, we propose a distributed algorithm to solve the problem, which will converge in a few iterations. Simulation results show that the proposed algorithms are more robust to large measurement errors than existing algorithms in the literature. Geometrical analysis providing additional insights is also provided.