附有约束条件的大旋转角三维坐标转换  

Three dimensional coordinate transformation of large rotation angle with additional constraints

作　　者：马下平 张中成[3] 师芸 李秦政[2] MA Xiaping;ZHANG Zhongcheng;SHI Yun;LI Qinzheng(State Key Laboratory of Rail Transit Engineering Informatization (FSDI)Xi’an 710043,China;College of Geomatics,Xi’an University of Science and Technology,Xi’an 710054,China;Hunan Non-ferrous Metals Geology Investingation Bureau Rows247,Changsha 410129,China)

机构地区：[1]轨道交通工程信息化国家重点实验室(中铁一院),西安710043 [2]西安科技大学测绘科学与技术学院,西安710054 [3]湖南省有色地质勘查局二四七队,长沙410129

出　　处：《测绘科学》2019年第8期13-18,共6页Science of Surveying and Mapping

基　　金：国家自然科学基金面上项目(46134017);西安科技大学博士启动金项目(2016QDJ005);西安科技大学培育基金项目(201714);北斗开放实验室西安分实验室项目(1707);现代工程测量国家测绘地理信息局重点实验室经费资助项目(TJES1810);轨道交通工程信息化国家重点实验室(中铁一院)开放研究课题项目(SKLK19-10)

摘　　要：为了解决大旋转角三维坐标转换方法在误差方程基础上引入13未知参数(3个平移参数、1个尺度参数和旋转矩阵中9个元素)之间的虚拟观测方程存在无法准确定权和若虚拟观测方程作为约束条件引入时构成的约束条件法方程不可逆的问题,该文只建立旋转矩阵中9个元素之间的约束条件,提出了附有约束条件的大旋转角三维坐标转换方法。详细推导了该方法中未知参数(3个平移参数和1个尺度参数与旋转矩阵中9个元素)估计及其精度评定公式。最后用算例对该方法进行了验证。结果表明:该方法适用于任何角度旋转的空间直角坐标转换,其解算理论正确,模型严密,过程简单,易于程序设计。In order to solve the problems that the virtual observation equation of 13 unknown parameters(3 translation parameters,1 scale parameters and 9 elements in the rotation matrix)is introduced on the basis of the error equation in existing method of three dimensional coordinate transformation,which is unable to determine observational weight exactly,and the constraint condition equation will be irreversible if the virtual observation equation is used as the constraint condition,this paper only established the constraints between the 9 elements in the rotation matrix,and proposed a threedimensional coordinate conversion method of the large rotation angle with the constraints.The estimation and its precision evaluation formula of parameters(3 translation parameters and 1 scale parameters and 9 elements of rotation matrix)were deduced.Finally,the method was validated by simulation data.The results showed that this method could be applied to space rectangular coordinate transformation with any angle.The solved model of this method was correct in theory,the model of this method was tight,its process was simple and program design was easy.

关 键 词：约束条件 大旋转角 旋转矩阵 坐标转换 

分 类 号：P226.3[天文地球—大地测量学与测量工程]