Characterizing the Worst-Case Position Error in Bearing-Only Target Localization

The worst-case position error provides valuable information for efficiently designing location based services in wireless networks. In this study, a technique based on a geometric approach is investigated for deriving a reasonable upper bound on the position error in bearingonly target localization. Assuming bounded measurement errors, it is first observed that the target node location belongs to a polytope. When a single estimate of the target location is available, the maximum distance from the estimate to extreme points of the polytope gives an upper bound on the position error. In addition, a technique based on outer approximation is proposed to confine the location of the target node to an ellipsoid. Simulation results show that the proposed upper bound is tight in many situations. It is also observed that the proposed techniques can be effectively used to derive sets containing the location of target nodes.