Bearing-only distributed localization: A unified barycentric approach

This paper studies the distributed localization problem of d-dimensional (d=2,3) sensor networks using local bearing measurements. Firstly, a distributed algorithm for computing barycentric coordinates in both 2-D and 3-D sensor networks is proposed where only local bearing measurements are required. Secondly, some necessary and/or sufficient conditions for the localizability of sensor networks, which are related to the rank of a matrix constructed from the barycentric coordinates, are provided. Thirdly, given position knowledge of at least d+1 anchors, a distributed iterative algorithm is presented such that all the sensor nodes can localize themselves cooperatively in the global coordinate system via local bidirectional communications. Some illustrative simulations are provided to demonstrate the effectiveness of our theoretic analysis.