Distributed Localization from Relative Noisy Measurements: a Gradient Based Approach

In this work we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard least-squares problem, the main challenge is to devise scalable algorithms that allow each agent to estimate its own position by means of only local communication and bounded complexity, independently of the network size and topology. We propose a gradient based algorithm that is guaranteed to have exponentially convergence rate to the optimal centralized least-square solution. Moreover we show the effectiveness also in presence of delays. We finally provide numerical results to support our work.