Limited benefit of cooperation in distributed relative localization

TL;DR

This paper investigates the limitations of cooperation in distributed relative localization, proposing a modified algorithm that improves convergence behavior and demonstrates that cooperation benefits are limited under noisy conditions.

Contribution

It introduces a new algorithm incorporating prior information that ensures monotonic convergence and shows cooperation benefits are bounded in noisy environments.

Findings

The modified algorithm converges monotonically to the optimal performance.

Optimal performance is achieved within a graph- and node-independent time.

Cooperation benefits are limited in the presence of noise.

Abstract

Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: a node-indexed vector has to be reconstructed from measurements of differences between neighbor nodes. In a recent note, we have studied the estimation error of a popular gradient descent algorithm showing that the mean square error has a minimum at a finite time, after which the performance worsens. This paper proposes a suitable modification of this algorithm incorporating more realistic "a priori" information on the position. The new algorithm presents a performance monotonically decreasing to the optimal one. Furthermore, we show that the optimal performance is approximated, up to a 1 + \eps factor, within a time which is independent of the graph and of the number of nodes. This convergence time is very much related to the minimum exhibited by the previous algorithm and both lead to the following conclusion: in the presence of noisy data, cooperation is only useful till a certain limit.