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We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the nonconvex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization properties to the full to obtain an approach that is completely distributed, has a simple implementation at each node, and capitalizes on an optimal gradient method to attain fast convergence. We offer a parallel but also an asynchronous flavor, both with theoretical convergence guarantees and iteration complexity analysis. Experimental results establish leading performance. Our algorithms top the accuracy of a comparable state-of-the-art method by one order of magnitude, using one order of magnitude fewer communications.

Simple and Fast Convex Relaxation Method for Cooperative Localization in Sensor Networks Using Range Measurements