求解球面拟合的改进总体最小二乘算法  

An Improved Total Least Squares Algorithm for Solving Sphere Surface Fitting

作　　者：陶武勇 鲁铁定[2] 吴飞[3] 李丁 

机构地区：[1]江西信息应用职业技术学院测绘工程系,南昌市气象路58号330043 [2]东华理工大学测绘工程学院,南昌市广兰大道418号330013 [3]中国矿业大学环境与测绘学院,江苏省徐州市大学路1号221116

出　　处：《大地测量与地球动力学》2018年第1期92-96,共5页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(41204003;41374007;41464001);测绘地理信息公益性行业科研专项(201512026);江西省教育厅科技项目(KJLD12077;GJJ13457);中国博士后科学基金(2012M511962);江西省中青年教师发展计划访问学者专项(2012132);江西省远航工程计划(2013)~~

摘　　要：在球面拟合中,系数矩阵和观测向量的误差同源,均来源于球面点坐标。不同位置有相同元素存在,从理论上讲,这些相同元素应该有相同的改正数,并且非线性形式出现在观测向量中。为此,本文推导了一种改进的总体最小二乘算法,可以很好地克服上述问题。通过算例分析发现,本文方法得到的参数估值更为可靠,证明了本文方法的有效性。In sphere surface fitting, the errors in the coefficient matrix and observation vector are from the same place, which is the coordinate of the spherical point. The same elements exist in different places. These same elements ought to have the same corrections. The linear form appears in the obser- vation vector. Therefore, an improved total least squares algorithm is deduced which can overcome the above problems. Through analysis of examples, we discover that the parameters obtained from the method in the paper are more reliable. This demonstrates that the method is feasible and effective.

关 键 词：球面拟合 非线性总体最小二乘 线性化 总体最小二乘 

分 类 号：P207[天文地球—测绘科学与技术]