Distributed Relative Localization Using the Multidimensional Weighted Centroid

A key problem in multiagent systems is the distributed estimation of the localization of agents in a common reference from relative measurements. Estimations can be referred to an anchor node or, as we do here, referred to the weighted centroid of the multiagent system. We propose a Jacobi over-relaxation method for distributed estimation of the weighted centroid of the multiagent system from noisy relative measurements. Contrary to previous approaches, we consider relative multidimensional measurements with general covariance matrices not necessarily diagonal. We prove our weighted centroid method converges faster than anchor-based solutions. We also analyze the method convergence and provide mathematical constraints that ensure avoiding ringing phenomena.