A distributed Gauss-Newton approach for range-based localization of multi agent formations

We propose a distributed technique for estimating position of nodes in a networked system from pairwise distance measurements. The localization problem is firstly formulated as an unconstrained optimization problem and the well-known Gauss-Newton centralized approach for obtaining a local solution is reviewed. Then, a distributed Gauss-Newton approach is presented, which is proved to converge to the same solution as its centralized counterpart, under an hypothesis of network connectivity. Localization performance and computational effort of the described approach are evaluated through numerical examples. The distributed solution allows each agent to autonomously compute its position estimate, exchanging information only with its neighbors, without need of communicating with a central station. Furthermore, when the initial guess for optimization is shared among the nodes, each node may retrieve the whole network configuration (i.e., its own position and the positions of all the other nodes in the network), exploiting local measurements into a global representation.