旋转矩阵表达方式对大旋转角三维基准转换的影响  

Three-dimensional Reference Transformation of Large Rotation Angle Effects of Rotation Matrix Expression

作　　者：符宏伟 陈义 黄高峰[1] FU Hongwei;CHEN Yi;HUANG Gaofeng(College of Surveying and Geo-informatics,Tongji University,Shanghai 200092,China;Key Laboratory of Modern Engineering Surveying of NAMSG,Shanghai 200092,China)

机构地区：[1]同济大学测绘与地理信息学院,上海200092 [2]现代工程测量国家测绘地理信息局重点实验室,上海200092

出　　处：《测绘与空间地理信息》2018年第10期203-206,210,共5页Geomatics & Spatial Information Technology

摘　　要：大旋转角三维基准转换算法可采用不同的旋转矩阵表达方式。本文研究了欧拉角法、方向余弦法、单位四元素法、罗德里格矩阵法等4种算法的旋转矩阵表达方式。从转换参数精度、迭代稳定性、单位权中误差、左右手坐标系之间的适用性等方面分析了不同旋转矩阵表达方式对大旋转角三维基准转换的影响。模拟和实际数据表明,迭代法比解析法获得的转换参数精度高,且方向余弦法能够适用左右手坐标系之间的转换。The difference of the large rotation angle 3D datum transformation algorithm lies in the difference of expression of the rotationmatrix. The rotation matrices of Euler angle method, direction cosine method, unit quaternion method, and Lodrigues matrix methodare studied. From the aspects of transformation parameter accuracy, iterative stability, mean square error of unit weight and applicability of transformation between left-hand and right-hand coordinate systems, we analyses the influence of different rotation matrix expression modes on the three-dimensional datum transformation of large rotation angle. Simulation and actual data show that the iterativealgorithm has higher accuracy than the analytical method, and the direction cosine method can be applied to transformation betweenleft-hand and right-hand coordinate systems.

关 键 词：三维基准转换 旋转矩阵 方向余弦 单位四元素 罗德里格矩阵 

分 类 号：P226[天文地球—大地测量学与测量工程]