In this paper, we propose a novel distributed orientation estimation strategy, which is based on the measurements of relative orientations of neighbors, in $d$-dimensional space, where $d \geq 3$. Since agents do not share a common reference frame, local reference frames are not aligned with each other. Under the proposed orientation estimation law, a rotation matrix that identifies the orientation of a local frame with respect to a common frame is obtained by auxiliary variables. The proposed estimation strategy is applied to formation control and network localization in 3-D space. Since the orientation of each agent is estimated in a global sense, formation control strategy ensures that the formation globally exponentially converges to the desired formation in 3-D space.

中文翻译：

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SO（d）中的分布式方向估计及其在地层控制和网络本地化中的应用

在本文中，我们提出了一种新颖的分布式方向估计策略，该策略基于邻居的相对方向的测量值。 $ d $维空间，其中 $ d \ geq 3 $。由于代理不共享公共参考框架，因此本地参考框架彼此不对齐。在提出的方向估计定律下，通过辅助变量获得标识局部框架相对于公共框架的方向的旋转矩阵。所提出的估计策略被应用于3-D空间中的编队控制和网络定位。由于在全局意义上估计了每个代理的方向，因此编队控制策略可确保整个编队以指数方式收敛至3-D空间中所需的编队。