Distributed localization via barycentric coordinates: Finite-time convergence

We consider distributed localization in a sensor network in ℝ² from inter-agent distances. Sensors and anchors exchange data with their neighbors. No centralized data processing is required. We establish a differential equation for the unknown sensor positions, and show that the estimated positions of sensors converge to their actual values in finite time (assuming noise-free measurements). The key assumption is that all sensors are in the convex hull of three or more anchors. The proposed localization method uses the barycentric coordinates of each sensor with respect to some of its neighbors (which may not include those anchors), assuming the sensor falls in the convex hull of these neighbors.