多元总体最小二乘在三维坐标转换中的应用  

Application of Multivariate Total Least Square in Three-Dimensional Coordinate Transformation

作　　者：黄令勇[1,2] 吕志平[1] 任雅奇 陈正生[1] 王宇谱[1] 

机构地区：[1]信息工程大学地理空间信息学院 [2]海洋测绘研究所 [3]63883部队

出　　处：《武汉大学学报（信息科学版）》2014年第7期793-798,共6页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41274015;41274045);国家863计划资助项目(2013AA122501)~~

摘　　要：为解决总体最小二乘(TLS)解算三维坐标转换时旋转矩阵线性化导致解算精度降低的问题,提出了能够直接求解旋转矩阵的多元总体最小二乘(MTLS)模型。为了验证多元总体最小二乘坐标转换解算效果,设置了各种坐标转换实验,并与总体最小二乘法进行比较。分析了旋转角度和尺度因子对解算精度的影响,并根据实验结果得出了以下结论:在大角度及独立等权观测条件下,多元总体最小二乘坐标转换解算精度优于总体最小二乘,且算法简单无需迭代,能够实现任意尺度的坐标转换。For avoiding loss of accuracy caused by the linearization of rotation matrix in three-dimensional coordinate transformation by the total least square（TLS）method,the multivariate total least square（MTLS）model is advanced.In order to evaluate the effect of MTLS on coordinate transformation,various experiment schemes set compared with the TLS algorithm.he impacts of rotation angle and scale factor on solution precision are analyzed,and conclusions based on the experimentresults as following：In the condition of coordinate transformation with a bigger rotation angle or under independent equal precision observation,the solution precision of MTLS is better than the one of TLS,especially the MTLS method does not need iterative calculation and can be used for coordinate transformation with any scale factor.

关 键 词：总体最小二乘 多元总体最小二乘 坐标转换 尺度因子 

分 类 号：P207[天文地球—测绘科学与技术]