Distributed Self Localization for Relative Position Sensing Networks in 2D Space

This paper studies the 2D localization problem of a sensor network given anchor node positions in a common global coordinate frame and relative position measurements in local coordinate frames between node pairs. It is assumed that the local coordinate frames of different sensors have different orientations and the orientation difference with respect to the global coordinate frame are not known. In terms of graph connectivity, a necessary and sufficient condition is obtained for self-localizability that leads to a fully distributed localization algorithm. Moreover, a distributed verification algorithm is developed to check the graph connectivity condition, which can terminate successfully when the sensor network is self-localizable. Finally, a fully distributed, linear, and iterative algorithm based on the complex-valued Laplacian associated with the sensor network is proposed, which converges globally and gives the correct localization result.