多变量整体最小二乘在激光跟踪仪转站中的应用  

Application of Multivariable Total Least Squares in the Coordinate Transformation of Laser Tracker

作　　者：万鹏[1] 楼立志[1,2] 张帅[1] 

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

出　　处：《测绘与空间地理信息》2016年第12期188-191,共4页Geomatics & Spatial Information Technology

摘　　要：激光跟踪仪转站实质是就是三维坐标转换,转站前后坐标误差必然存在,导致系数矩阵中必然存在随机误差。为消除系数矩阵中携带的随机误差对激光跟踪仪转站精度的影响,提高激光跟踪仪转站的精度,文章采用基于EIV(Error-in-Variable)模型的多变量整体最小二乘求解转换参数。多变量整体最小二乘在考虑观测矩阵结构性的基础上同时对观测矩阵与系数矩阵进行改正,其思路是将旋转参数、尺度参数和平移参数分开求解,避免了计算转换参数循环迭代的过程。实验结果表明,多变量整体最小二乘获得的参数估计值比最小二乘平差法获得的参数估计值更加接近设计值,提高了转站的精度。The essence of laser tracker transformation is 3D coordinate transformation, the coordinate error must exist before and after transformation, leading to the error of coefficient matrix must be exist. In order to eliminatethe influence of random measurement error from the coefficient matrix for laser tracker transformation precision, improve the transformation precision of laser tracker, the paper u- ses muhivariable total least squares（MTLS） base on EIV（ Error- in -Variable）model to solve the parameters of coordinate transfor- mation. Using MTLS method can revise the observation matrix and the coefficient matrix on the basis of the structure of the observation matrix, the idea of MTLS is to solve the rotation parameters, the scale parameter and the translation parameters separately, avoid the process of loop iteration. The result shows that estimated parameter from MTLS is close to the designed value than classical least squares, and improves the precision of coordinate transformation.

关 键 词：激光跟踪仪 多变量整体最小二乘 变量中的误差模型 坐标转换 

分 类 号：P209[天文地球—测绘科学与技术]