| 基于单位四元数的任意旋转角度的三维坐标转换 |
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| 引用本文： | 李志伟,李克昭,赵磊杰,王云凯,梁晓庆.基于单位四元数的任意旋转角度的三维坐标转换[J].大地测量与地球动力学,2017,37(1):81-85. |
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| 作者姓名： | 李志伟 李克昭 赵磊杰 王云凯 梁晓庆 |
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| 摘 要： | 针对三维空间坐标转换模型的参数求解问题，引入四元数构造旋转矩阵，证明了坐标转换旋转矩阵等价于四元数的正交变换，并利用单位四元数理论推导了一种直接进行空间坐标转换的算法。通过模拟数据进行仿真实验表明，该算法无需线性化，计算简便，且适用于任意旋转角度的坐标转换。
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| 关 键 词： | 坐标转换 旋转矩阵 正交变换 单位四元数 |
Three-Dimensional Coordinate Transformation Adapted to Arbitrary Rotation Angles Based on Unit Quaternion |
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| LI Zhiwei,LI Kezhao,ZHAO Leijie,WANG Yunkai,LIANG Xiaoqing.Three-Dimensional Coordinate Transformation Adapted to Arbitrary Rotation Angles Based on Unit Quaternion[J].Journal of Geodesy and Geodynamics,2017,37(1):81-85. |
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| Authors: | LI Zhiwei LI Kezhao ZHAO Leijie WANG Yunkai LIANG Xiaoqing |
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| Abstract: | In this paper, to solve the parameter of the three-dimensional spatial coordinate transformation model, quaternion is introduced to construct a rotation matrix. This paper proves that the coordinate transformation rotation matrix is equivalent to the orthogonal transformation of quaternion. Using unit quaternion theory derivates a direct algorithm for solving spatial coordinate transformations. A simulation test using analogue data and numerical examples show that the method is feasible and simple, does need not linearization, and can adapt to arbitrary rotation angle rotation transformations. |
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