A distributed range-based algorithm for localization in mobile networks

In this paper, we provide a distributed algorithm to locate an arbitrary number of agents moving in a bounded region. Assuming that each agent can estimate a noisy version of its motion and the distances to the nodes in its communication radius, we provide a simple linear update to find the locations of an arbitrary number of mobile agents when they follow some convexity in their deployment and motion, given at least one anchor, agent with known location, is present in R^m. At each iteration, agents update their location estimates as a convex combination of the states of the neighbors, if they lie inside their convex hull, and do not update otherwise. We abstract the corresponding localization algorithm as a Linear Time-Varying (LTV) system, and using slice notation we show that it asymptotically converges to the true locations of the agents. We study the effects of noise on our localization algorithm, and provide simulations to verify our analytical results.