This paper studies the exploratory distributed localization of networked mobile agents using only distance measurements in a GPS-Denied 3D environment. To deal with this challenging problem, an analytic solution is firstly provided to calculate the 3D barycentric coordinates for agents outside the convex hull formed by anchors. Then, a distributed Jacobi Under-Relaxation Iteration (JURI) algorithm is developed to address the static 3D localization problem in a noisy environment. The proposed algorithm is extended for the localization of mobile targets, especially when the mobile agents cannot get enough neighbors' support. Since the proposed algorithms do not suffer from the constraint of the convex hull (exploratory localization); as a result, the proposed method can be scaled to the localization of large-scale networked agents. Finally, several simulation examples are given to validate the effectiveness of the proposed algorithm in different scenarios.

中文翻译：

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一种基于3D重心坐标的探索性分布式定位算法


本文研究了在 GPS 拒绝的 3D 环境中仅使用距离测量的网络移动代理的探索性分布式定位。为了解决这个具有挑战性的问题，首先提供了一种解析解决方案来计算锚点形成的凸包之外的主体的 3D 重心坐标。然后，开发了分布式雅可比欠松弛迭代 (JURI) 算法来解决噪声环境中的静态 3D 定位问题。所提出的算法被扩展用于移动目标的定位，特别是当移动代理无法获得足够邻居的支持时。由于所提出的算法不受凸包的约束（探索性定位）；因此，所提出的方法可以扩展到大规模网络代理的本地化。最后给出了几个仿真例子来验证所提算法在不同场景下的有效性。