Sensor network localization (SNL) is a challenging problem due to its inherent non-convexity and the effects of noise in inter-node ranging measurements and anchor node position. We formulate a non-convex SNL problem as a multi-player non-convex potential game and investigate the existence and uniqueness of a Nash equilibrium (NE) in both the ideal setting without measurement noise and the practical setting with measurement noise. We first show that the NE exists and is unique in the noiseless case, and corresponds to the precise network localization. Then, we study the SNL for the case with errors affecting the anchor node position and the inter-node distance measurements. Specifically, we establish that in case these errors are sufficiently small, the NE exists and is unique. It is shown that the NE is an approximate solution to the SNL problem, and that the position errors can be quantified accordingly. Based on these findings, we apply the results to case studies involving only inter-node distance measurement errors and only anchor position information inaccuracies.

翻译：传感器网络定位（SNL）因其固有的非凸性以及节点间测距测量和锚节点位置中的噪声影响而成为一个具有挑战性的问题。我们将一个非凸SNL问题表述为多人非凸势博弈，并研究了在无测量噪声的理想场景和有测量噪声的实际场景中纳什均衡（NE）的存在性与唯一性。我们首先证明在无噪声情况下NE存在且唯一，并对应于精确的网络定位。随后，我们研究了存在锚节点位置误差和节点间距离测量误差情况下的SNL问题。具体而言，我们证明当这些误差足够小时，NE存在且唯一。研究表明，该NE是SNL问题的一个近似解，且定位误差可据此进行量化。基于这些结论，我们将结果应用于仅含节点间距离测量误差以及仅含锚节点位置信息不准确性的案例研究。