整体最小二乘和最小二乘拟合空间直线的比较

给出整体最小二乘法拟合空间直线的一种迭代算法。将空间直线垂直投影到坐标平面，分别采用整体最小二乘法和最小二乘法拟合直线。对坐标点等精度观测、非等精度观测和坐标分量非等精度观测3种场景进行模拟计算，比较两种方法估计的参数和验后单位权方差，并对三维激光扫描仪实测数据拟合结果进行分析。

Comparisons of Total Least Squares and Least Squares for Fitting Spatial Lines

In this contribution, an iterative algorithm of total least squares is organized for fitting spatial lines. We projected spatial straight lines to coordinate planes perpendicularly, and then total least squares (TLS) and least squares (LS) are employed to fit the plane's lines. A simulated experiment with three scenarios is designed to compare the estimated parameters and the variance of unit weight from TLS and LS, respectively. In scenario one, the error of all points is normally distributed with zero mean and identical standard deviation. In the second scenario, the error of each point is normally distributed with zero mean and different standard deviation. In scenario three, the error of point coordinate components is normally distributed with zero mean and different standard deviation. In addition, in a second experiment, a set of laser scanned data points are fitted by TLS and LS, respectively.