Distributed localization with mixed measurements under switching topologies

This paper investigates the distributed localization problem of sensor networks with mixed measurements. Each node holds a local coordinate system without a common orientation and is capable of measuring only one type of information (either distance, bearing, or relative position) to near-by nodes. Thus, three types of measurements are mixed in the sensor networks. Moreover, the communication topologies in the sensor networks may be time-varying due to unreliable communications. This paper develops a fully distributed algorithm called BCDL (Barycentric Coordinate based Distributed Localization) where each node starts from a random initial guess about its true coordinate and converges to the true coordinate via only local node interactions. The key idea in BCDL is to establish a unified linear equation constraints for the sensor coordinates by using the barycentric coordinates of each node with respect to its neighbors though the sensor nodes may have different types of measurements. Then a distributed iterative algorithm is proposed to solve the linear equations under time-varying communication networks. A necessary and sufficient graphical condition is obtained to ensure global convergence of the distributed algorithm.