A manifold flattening approach for anchorless localization

We present a new method for anchorless localization of mobile nodes in wireless networks using only measured distances between pairs of nodes. Our method relies on the completion of the Euclidean distance matrix, followed by multidimensional scaling in order to compute the relative locations of the nodes. The key element of novelty of our algorithm is the method of completing the Euclidean distance matrix, which consists of gradually inferring the unknown distances, such as to align all nodes on a k-hyperplane, where typically k is 2 or 3. Our method leads to perfect anchorless localization for noise-free range measurements, if the network is sufficiently connected. We introduce refinements to the algorithm to make it robust to noisy and outlier range measurements. We present results from several localization tests, using both simulated data and experimental results measured using a large indoor network deployment of our WASP platform. Our results show improvements in localization using our algorithm over previously published techniques.