We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding, and aligning uniquely realizable subsets of neighboring sensors called patches. In the noise-free case, each patch agrees with its global positioning up to an unknown rigid motion of translation, rotation, and possibly reflection. The reflections and rotations are estimated using the recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. The algorithm is scalable as the number of nodes increases and can be implemented in a distributed fashion. Extensive numerical experiments show that it compares favorably to other existing algorithms in terms of robustness to noise, sparse connectivity, and running time. While our approach is applicable to higher dimensions, in the current article, we focus on the two-dimensional case.

中文翻译：

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欧几里得群上基于特征向量同步的传感器网络定位

我们提出了一种从欧几里得距离子集的噪声测量中定位传感器的新方法。我们的算法首先查找、嵌入和对齐相邻传感器的唯一可实现子集，称为补丁。在无噪声情况下，每个补丁都与它的全局定位一致，直到未知的平移、旋转和可能的反射的刚性运动。使用最近开发的特征向量同步算法估计反射和旋转，而通过求解超定线性系统来估计平移。该算法可以随着节点数量的增加而扩展，并且可以以分布式方式实现。大量的数值实验表明，它在对噪声的鲁棒性、稀疏连通性和运行时间方面优于其他现有算法。