This paper 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 inter-node 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 work is that the proposed method can be applied in both generic and non-generic configurations with an unknown global coordinate frame in both 2-D and 3-D spaces.

翻译：本文研究了在全局坐标系下已知锚节点位置、局部坐标系下已知节点间相对测量值时的二维和三维网络定位问题。假设不同节点的局部坐标系具有未知的不同朝向。首先，发展了一种角度-位移刚性理论，该理论可利用锚节点已知位置和局部相对测量值（局部相对位置、距离、局部相对方位、角度或距离比测量值）定位所有自由节点。随后，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，当网络满足无穷小角度-位移刚性条件时，该协议可全局估计所有自由节点的位置。所提方法统一了基于局部相对位置、距离、局部相对方位、角度及距离比测量的分布式网络定位方法。本文的创新之处在于，该方法可应用于二维和三维空间中全局坐标系未知的通用及非通用配置。