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Consider a sensor network consisting of both anchor and non-anchor nodes. Weaddress the following sensor network localization (SNL) problem: given thephysical locations of anchor nodes and relative measurements among all nodes,determine the locations of all non-anchor nodes. The solution to the SNLproblem is challenging due to its inherent non-convexity. In this paper, theproblem takes on the form of a multi-player non-convex potential game in whichcanonical duality theory is used to define a complementary dual potentialfunction. After showing the Nash equilibrium (NE) correspondent to the SNLsolution, we provide a necessary and sufficient condition for a stationarypoint to coincide with the NE. An algorithm is proposed to reach the NE andshown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim ofreducing the information exchange within a network, a distributed algorithm forNE seeking is implemented and its global convergence analysis is provided.Extensive simulations show the validity and effectiveness of the proposedapproach to solve the SNL problem.

Global solution to sensor network localization: A non-convex potential game approach and its distributed implementation