三维坐标转换的通用整体最小二乘算法

A General Total Least Squares Algorithm for Three-dimensional Coordinate Transformations

三维坐标转换模型属于非线性EIV(errors-in-variables)模型,现有整体最小二乘算法均设定了某些特殊的假设条件,如仅适用于小角度或者属于非统计意义上的数值解,并且不能用于结构性的系数矩阵等,算法适用性受到极大限制。本文提出三维坐标转换模型的通用加权整体最小二乘算法,该算法适用于任意旋转角度以及一般性权矩阵的三维坐标转换,并且将结构性系数矩阵,同时包含随机和非随机元素的系数矩阵等情况纳入统一的算法。实例计算表明,本文提出的算法具有通用性,适用于实际应用中的各类三维坐标转换模型。

The model of three‐dimensional coordinate transformation is a nonlinear errors‐in‐variables model .The methods proposed in published literatures are always restricted in practice for their speci al assumptions ,such as size of rotation angles ,structured design matrix and special weight matrix .A general weighted TLS algorithm of a three‐dimensional coordinate transformation is investigated in this paper .The new algorithm can be applied in transformations with an arbitrary rotation angles and any applicable weights of the observations ,as well as the structured design matrix or the design matrix with both random and fixed elements .The example given in this paper illustrates that this algorithmis general and suits to all kinds of three‐dimensional coordinate transformations in practice .