Localizability and distributed localization of sensor networks using relative position measurements

The paper introduces the localization problem of sensor networks using relative position measurements. It is assumed that relative positions are measured in local coordinate frames of individual sensors, for which different sensors may have different orientations of their local frames and the orientation errors with respect to the global coordinate frame are not known. A new necessary and sufficient condition is developed for localizability of such sensor networks that are modeled as directed graphs. That is, every sensor node should be 2-reachable from the anchor nodes. Moreover, for a localizable sensor network, a distributed, linear, and iterative scheme based on the graph Laplacian of the sensor network is developed to solve the coordinates of the sensor network in the global coordinate frame