Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results.

翻译：传感器网络定位（SNL）问题需要确定网络中所有传感器的物理坐标。该过程依赖于锚点的全局坐标以及非锚节点与锚节点之间的可用测量值。由于固有的非凸性，获取SNL的全局最优解及实现相应算法具有挑战性。本文针对一般SNL问题构建了一个非凸多人势博弈模型，以研究其中全局纳什均衡（NE）的识别条件——全局NE对应SNL的全局解。我们采用对偶理论将非凸博弈转化为互补对偶问题，进而提出一种基于共轭的算法来计算互补对偶问题的驻点。在此基础上，我们给出全局纳什均衡的识别条件：所提算法的驻点满足对偶关系。最后，通过仿真结果验证了理论结果的有效性。