平面坐标转换的稳健总体最小二乘算法  

A solution to plane coordinate transformation based on robust total least squares

作　　者：陶叶青[1] 高井祥[1] 姚一飞[1] 

机构地区：[1]中国矿业大学国土环境与灾害监测国家测绘局重点实验室,江苏徐州221116

出　　处：《中国矿业大学学报》2014年第3期534-539,共6页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(41074010);安徽省优秀青年人才基金重点项目(2013SQRL085ZD)

摘　　要：为解决控制点坐标在原坐标系与目标坐标系中均含有误差的情况下求解模型参数的问题,对应用基于奇异值分解(SVD)与拉格朗日方法的总体最小二乘算法(TLS)建立高斯-马尔可夫(G-M)模型求解转换参数的方法进行了讨论.通过算例对TLS算法与最小二乘算法(LS)进行了比较,TLS算法较LS算法更合理.应用稳健估计的方法,解决了由于控制点含有粗差导致控制点坐标精度不等,对参数求解有影响的问题;对基于稳健估计方法的TLS迭代定权算法进行了讨论,并通过算例与其它两种算法进行了比较.基于稳健估计的TLS算法能更好的解决含有误差的控制点已知坐标对坐标系统转换影响的问题.The control points in both original coordinate system and target coordinate system have error, which will bring serious difficulties in computation parameters. To solve the above problem, this paper introduced the total least squares （TLS） algorithm. The Gauss-Markov （G-M） model is established for computation conversion parameters based on singular value de- composition（SVD） and Lagrange approach. Taking an instance to compare the TLS algorithm with LS algorithm, the result proves that the method of computation parameters based on TLS algorithm is more accurate than the method based on LS algorithm. Besides, the fact that accuracy of control points coordinates is different which is the reason for gross error existing in control points is concerned, and robust estimation is applied to get over influence that the fact has on computaton parameters. At last, we discussed the TLS algorithm of applying iteration method to fix weight based on robust estimation and compared with the other two algorithms through the instance. The numerical results demonstrate that the method of applying TLS algorithm based on robust estimation is more suitable to solve the problem that the known coor- dinates of control points with error have influence on coordinate transformation.

关 键 词：坐标系统转换 稳健估计 总体最小二乘算法 

分 类 号：P221[天文地球—大地测量学与测量工程]