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The authors consider the problem of node localization in sensor networks, and they focus on networks in which the ranging measurements are subject to errors and anchor positions are subject to uncertainty. They consider a statistical model for the uncertainty in the anchor positions and formulate the robust localization problem that finds a maximum likelihood estimation of the node positions. To overcome the non-convexity of the resulting optimization problem, they obtain a convex relaxation that is based on the Second Order Cone Programming (SOCP). They also propose a possible distributed implementation using the SOCP convex relaxation. They present numerical studies that compare the presented approach to other existing convex relaxations for the robust localization problem in terms of positioning error and computational complexity.
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