坐标转换四参数解算的整体最小二乘新方法

A new method of total least squares algorithm for the plane four parameters coordinate transformation

在平面四参数坐标转换模型中,观测向量和误差方程系数矩阵中部分元素都存在误差。提出一种使用整体最小二乘迭代法求解坐标转换四参数的新方法,只改正系数矩阵中含误差的元素,同时使系数矩阵中不同位置的相同元素具有相同改正数,理论上更严谨。设计了平面四参数模型坐标转换实验数据,通过与经典最小二乘、整体最小二乘、混合整体最小二乘3种方法结果对比,验证了新方法的可行性且解算结果更优。

In plane four parameters coordinate transformation model,both observation vector and part of the error equation coefficient matrix elements can have errors.To solve this problem,this paper proposes a new method to obtain the plane four parameters coordinate transformation using an iterative method of total least squares.The method only corrects the errors elements in the coefficient matrix.At the same time,it adjusts the same elements in different positions of coefficient matrix to the same correction.The experimental data is designed using the new method to solve the plane four parameter coordinate transformation model.By comparing with the results of three methods of classical least squares,total least squares and mixed LS-TLS,the feasibility of new method is proved and the accuracy of this new method is higher than others.