圆曲线拟合的总体最小二乘算法分析  

Analysis of total least squares algorithms for circular curve fitting

作　　者：鲁铁定[1] 邓小渊 常晓涛[3] 刘晓忠[2] LU Tieding;DENG Xiaoyuan;CHANG Xiaotao;LIU Xiaozhong(Faculty of Geomatics,East China University of Technology,Nanchang 330013,China;Geomatics Center of Zhejiang, Hangzhou 310012,China;Satellite Surveying and Mapping Application Center,National Administration of Surveying,Mapping and Geoinformation,Beijing 100830,China)

机构地区：[1]东华理工大学测绘工程学院,南昌330013 [2]浙江省地理信息中心,杭州310012 [3]国家测绘地理信息局卫星测绘应用中心,北京100830

出　　处：《测绘科学》2019年第2期33-37,共5页Science of Surveying and Mapping

基　　金：国家自然科学基金项目(41464001;41374007);测绘地理信息公益性行业科技专项(201512026);江西省教育厅科技项目(KJLD12077;GJJ13457);江西省远航工程计划项目(2013);江西省中青年教师发展计划访问学者专项(2012132);国家重点研发计划项目(2016YFB0501405);国家重大科学研究计划项目(2016YFB0502601-04)

摘　　要：针对圆曲线拟合参数求解的问题,该文在分析现有的圆曲线模型构建及其参数求解方法的基础上,以圆曲线的参数方程建立圆曲线拟合模型,采用总体最小二乘算法的求解模型参数。通过实例数据和模拟数据,对比分析现有以一般方程构建的圆曲线拟合模型的最小二乘算法、混合总体最小二算法以及根据协方差传播定率定权的加权总体最小二乘算法计算结果。实验结果表明,采用该文提出的总体最小二乘算法求解由参数方程构建的拟合模型,效率和准确度均有所提高。Aiming at the problem of circular curve fitting,this paper in-depth analyzed the construction method for solving the parameters of the existing model of the circular curve and took total least squares to solve the parameters of circle fitting model established by its parametric equation.Comparing the existing least squares algorithm,mixed total least squares algorithm,weighted total least squares algorithm for circle fitting model established by its standard form,the examples results illustrated that the efficiency and feasibility of the algorithm proposed in this paper were better.

关 键 词：圆曲线拟合 线性参数方程 协方差矩阵 总体二乘算法 

分 类 号：P207[天文地球—测绘科学与技术] P258