空间直线拟合的PEIV模型的构建与解法

Model and Solution of PEIV Model for Spatial Straight Line Fitting

针对空间直线拟合不宜直接采用总体最小二乘算法和混合总体最小二乘算法的问题,提出一种基于PEIV模型的总体最小二乘法的空间直线拟合算法。首先将空间直线的标准方程进行变换,改写为总体最小二乘的EIV模型;然后针对系数矩阵的特点,将模型转换为更加合理的PEIV模型,线性化成类似于最小二乘间接平差形式,采用迭代的方法求解拟合参数。平差过程保证了系数矩阵重复元素的改正数一致,常数元素的改正数为零,符合实际理论;最后,通过算例比较验证了该方法的可行性和优越性。

In spatial linear fitting,it is not possible to directly adopt the method of total least squares algorithm and mixed total least squares.This paper proposes a space linear fitting algorithm based on the PEIV model of the total least squares method.The standard equation of space straight line is transformed and the equation is rewritten as the overall least squares EIV model.Then,according to the characteristics of the coefficient matrix,the model is transformed into a more reasonable PEIV model,linearly similar to the least squares indirect adjustment form,and the iterative method is used to solve the fitting parameters.The adjustment process ensures that the correction number of the elements of the coefficient matrix is the same,and the correction number of the constant element is zero,which is in accordance with the actual theory.Finally,the feasibility and superiority of the method are verified by an example.