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

翻译：考虑由锚节点和非锚节点组成的传感器网络。本文研究以下传感器网络定位问题：给定锚节点的物理位置以及所有节点间的相对测量值，确定所有非锚节点的位置。由于该问题固有的非凸性，其求解具有挑战性。本文将问题建模为多人非凸势博弈，利用对偶性理论定义互补对偶势函数。在证明纳什均衡与传感器网络定位解对应后，我们给出了驻点与纳什均衡重合的充要条件。本文提出一种达到纳什均衡的算法，并证明其收敛速度为$\mathcal{O}(1/\sqrt{k})$。为减少网络内信息交换，进一步实现了面向纳什均衡寻优的分布式算法，并给出全局收敛性分析。大量仿真结果验证了所提方法求解传感器网络定位问题的有效性和可行性。