整体最小二乘和最小二乘拟合空间直线的比较  

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

作　　者：胡川[1] 陈义[1,2] 朱卫东[3] 钱承军[1] 

机构地区：[1]同济大学测绘与地理信息学院,上海市四平路1239号200092 [2]现代工程测量国家测绘地理信息局重点实验室,上海市四平路1239号200092 [3]上海海洋大学海洋科学学院

出　　处：《大地测量与地球动力学》2015年第4期689-692,701,共5页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(41074017)

摘　　要：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。In this contribution, an iterative algorithm of total least squares is organized for fitting spa- tial 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.

关 键 词：整体最小二乘 最小二乘 空间直线 三维激光扫描 拟合 

分 类 号：P207[天文地球—测绘科学与技术]