空间直线拟合的整体最小二乘算法

Total Least Squares Algorithm for Fitting Spatial Straight Lines

提出了一种基于整体最小二乘的空间直线拟合方法。首先,对空间直线的标准式方程进行变换,并附加参数转换的过程,将6个参数简化为4个;然后,将方程改写为矩阵形式,由此巧妙地将空间直线拟合的问题转化为整体最小二乘的参数求解问题,利用TLS迭代法求得转换后的空间直线拟合的4个参数,再通过参数回代的方法恢复空间直线的6个基本参数。通过算例比较验证了该方法的可行性和有效性。

To address the problem of fitting a straight line in three-dimensional space, since the equa-tion is a six parameter equation, not a simple linear relationship, the traditional least squares method cannot be used to solve it. In this paper, a new method of space line based on the total least squares is proposed. Firstly, the number of parameters was decreased from six to four by changing the standard equation of the straight line, then re-expressed the equation in the form of a matrix. Therefore, the fitting problem was transformed to the parameter-solving problem in total least squares. Further, the / fitting four parameters were obtained using a TLS iteration, and the six parameters of the space lines were recovered through a backtracking method. An experiment in the paper verifies the effectiveness and applicability of the new method.