  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.
