基于整体最小二乘法的任意旋转角度三维坐标转换

摘要

In the process for researching three-dimensional coordination transformation adapted to arbitrary ro tation angle, with the case of only three control points , an improved constrained weighted total least squares meth od (ICWTLS) was proposed to solve the model of control points in the two sets having random errors ( EIV model). If the control points are rich ( four or more) , we put forward the multivariate total least squares method (observation equation has not only one row, MTLS) to solve the parameters, and the problem of the repeated random elements of coefficient matrix' s corrections being not equal,and to improve the accuracy of the parameter values.%在研究任意旋转角度三维坐标转换的过程中,针对控制点在两套坐标系下均存在随机误差(EIV模型)的情况,提出在只有三个控制点的情况下采用改进的附有约束条件的加权整体最小二乘法进行解算,在控制点较丰富(四个及以上)的情况下采用多元整体最小二乘法(观测方程的观测值不只一列的整体最小二乘法)进行解算,解决系数矩阵中重复随机元素改正数不相等的问题,提高参数值的精度.