一种基于补偿最小二乘的空间直线拟合算法

A spatial linear fitting algorithm based on compensation least squares

针对空间直线拟合的整体最小二乘算法无法顾及模型误差以及空间直线拟合无法直接利用整体最小二乘进行拟合的问题,该文提出了一种基于补偿最小二乘方法的空间直线拟合方法。首先,将待拟合的空间直线分别投影至3个互相垂直的平面得到3条平面直线;然后根据补偿最小二乘方法能同时顾及数据中模型误差和偶然误差的特性,选择合适的方法求取正规化矩阵和平滑因子来平衡误差,分别求解3条平面直线的拟合参数;最后,根据3条平面直线的拟合参数重建空间直线。通过与相关文献的结果进行比较,结果表明采用补偿最小二乘方法进行空间直线拟合具有一定的可行性,可以提高空间直线的拟合精度。

Aiming at the problem that the model error can not be taken into account in total least square spatial linear fitting and the total least squares can not be directly used to fit the spatial line,a spatial linear fitting algorithm based on the compensation least square method was proposed in this paper.Firstly,the spatial lines to be fitted were projected into three perpendicular planes to obtain three plane lines;Then,based on the characteristics that compensation least squares method can consider the model errors and accidental errors simultaneously,appropriate method was selected to get the normalization matrix and smoothing factors to balance the error,and solve the fitting parameters of the three plane straight lines respectively;Finally,the spatial line was reconstructed on the basis of the fitting parameters.The results of comparison with related literature showed that the compensation least square method had certain feasibility and could improve the precision of spatial line fitting.