Edge Localization in Two Dimensional Space via Orientation Estimation

TL;DR

This paper introduces a distributed method for edge localization in 2D multi-agent networks using orientation estimation, ensuring exponential convergence under certain graph conditions.

Contribution

It proposes a novel edge localization graph and a distributed orientation estimation approach that guarantees convergence when the graph has an oriented spanning tree.

Findings

Estimated bearing vectors exponentially converge to true values.

Convergence is guaranteed if the graph has an oriented spanning tree.

The method achieves exponential convergence with a known bearing vector at the root.

Abstract

This paper focuses on the problem of estimating bearing vectors between the agents in a two dimensional multi-agent network based on subtended angle measurements, called edge localization problem. We propose an edge localization graph to investigate the solvability of this problem and a distributed estimation method via orientation estimation of virtual agents to solve the problem. Under the proposed method, the estimated bearing vector exponentially converges to the real one with a common bias if and only if the edge localization graph has an oriented spanning tree. Furthermore, the estimated variables exponentially converge to the true values if the edge localization graph has an oriented spanning tree with a root knowing the bearing vector from it to one of its neighbors.