罗翔, 刘志平.任意旋转角三维坐标转换的微分罗德里格矩阵算法[J].河南理工大学学报（自然科学版）,2020,39(5):30-35.

LUO X, LIU Z P.Differential Rodrigues matrix algorithm for three-dimensional coordinatetransformation of arbitrary rotation angle[J].Journal of Henan Polytechnic University(Natural Science) ,2020,39(5):30-35.

任意旋转角三维坐标转换的微分罗德里格矩阵算法

罗翔1,2, 刘志平1,2

1.中国矿业大学 江苏省资源环境信息工程重点实验室，江苏 徐州 221116;2.中国矿业大学环境与测绘学院，江苏 徐州 221116

摘要:为分析现有小旋转角和任意旋转角三维坐标转换模型存在的问题，利用罗德里格矩阵、反对称矩阵与向量积运算性质将矩阵微分形式转换为参数向量微分形式，从而提出微分罗德里格矩阵算法。该算法避免了现有算法普遍存在的矩阵求导问题，实现了函数模型和随机模型同步迭代更新，以提高精度和迭代效率。最后，通过文献算例和仿真算例对本文算法和3种现有算法进行比较分析。统计结果表明，所提算法在迭代次数、参数真误差等方面改进效果显著。

关键词:任意旋转角;三维坐标转换;微分罗德里格矩阵;反对称矩阵

doi:10.16186/j.cnki.1673-9787.2020.5.5

基金项目:国家自然科学基金重点资助项目（41730109）；国家自然科学基金面上项目（41771416 ）；自然资源部精密工程与工业测量 重点实验室开放基金资助项目（PF2017-12）

收稿日期:2019/11/25

修回日期:2020/02/26

出版日期:2020/09/15

Differential Rodrigues matrix algorithm for three-dimensional coordinatetransformation of arbitrary rotation angle

LUO Xiang1,2, LIU Zhiping1,2

1.Key Laboratory for Resources and Environment Information Engineering of Jiangsu Province， China University of Mining and Technology ，Xuzhou  221116 ， Jiangsu， China;2.School of Environment Science and Spatial Informatics， China University of Mining and Technology， Xuzhou 221116 ， Jiangsu， China

Abstract:In order to analyze the existing problems of three-dimensional coordinate transformation with small and arbitrary rotation angle， the matrix differential form was transformed into parameter vector differential form， and then the differential Rodrigues matrix algorithm was proposed based on the theory of Rodrigues matrix， anti-symmetric matrix and vector product operation. The algorithm avoided the matrix derivation problem which was common in the existing algorithms， and realized synchronous iterative updating of function model and random model to improve the precision and efficiency of iteration. The comparison between the proposed algorithm and the three existing algorithms was carried out through literature examples and simulation examples. The statistical results such as the number of iterations and the true error of parameters showed that the improved algorithm was effective.

Key words:arbitrary rotation angle;three-dimensional coordinate transformation;differential Rodrigues matrix;anti-symmetric matrix

任意旋转角三维坐标转换的微分罗德里格矩阵算法_罗翔.pdf