This article investigates the localization problem of a network in 2-D and 3-D spaces given the positions of anchor nodes in a global frame and internode relative measurements in local coordinate frames. It is assumed that the local frames of different nodes have different unknown orientations. First, an angle-displacement rigidity theory is developed, which can be used to localize all the free nodes by the known positions of the anchor nodes and local relative measurements (local relative position, distance, local relative bearing, angle, or ratio-of-distance measurements). Then, necessary and sufficient conditions for network localizability are given. Finally, a distributed network localization protocol is proposed, which can globally estimate the locations of all the free nodes of a network if the network is infinitesimally angle-displacement rigid. The proposed method unifies local-relative-position-based, distance-based, local-relative-bearing-based, angle-based, and ratio-of-distance-based distributed network localization approaches. The novelty of this article is that the proposed method can be applied in both generic and nongeneric configurations with an unknown global coordinate frame in both 2-D and 3-D spaces.

中文翻译：

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角位移刚度理论及其在分布式网络定位中的应用


本文研究了给定全局坐标系中锚节点的位置和局部坐标系中节点间相对测量的 2D 和 3D 空间中网络的定位问题。假设不同节点的局部框架具有不同的未知方向。首先，提出了角位移刚度理论，该理论可用于通过锚节点的已知位置和局部相对测量（局部相对位置、距离、局部相对方位角、角度或比值）来定位所有自由节点。 - 距离测量）。然后，给出了网络可定位性的充要条件。最后，提出了一种分布式网络定位协议，如果网络是无限小的角位移刚性网络，则该协议可以全局估计网络中所有自由节点的位置。所提出的方法统一了基于局部相对位置、基于距离、基于局部相对方位、基于角度和基于距离比的分布式网络定位方法。本文的新颖之处在于所提出的方法可以应用于 2D 和 3D 空间中未知全局坐标系的通用和非通用配置。