Linear Distributed Algorithms For Localization In Mobile Networks

This paper studies the problem of distributed self-localization in noisy networks of mobile agents. Agent mobility is captured by means of a stochastic motion model and the goal of each agent is to dynamically track its (location) state using noisy inter-agent relative distance measurements and communication with a subset of neighboring agents. The Bayesian tracking formulation thus obtained is highly non-standard, in that the distance measurements relate to the location in a non-linear way; and in a mobile setting, it is not clear how connectivity can be maintained for the localization process to provide unambiguous location results. To make the collaborative filtering problem tractable, the paper first presents a barycentric-coordinate based reparametrization of the state-space model; the transformed formulation leads to a bilinear state-space. Under mild network connectivity assumptions, specifically, the inter-agent communication network stays connected on an average, and a structural convexity condition, specifically, infinitely often the agents lie in the convex hull of a set of $m+1$ neighboring agents, where m denotes the dimension of the space, a distributed filtering scheme is proposed that enables each agent to track its location with bounded mean-squared error as long as there is at least one anchor in the network (agent with known location). Simulations are presented to illustrate the efficacy of the proposed distributed filtering procedure and the theoretical results.