加权总体最小二乘在铁路曲线正矢拟合的应用

计算机工程与应用 ›› 2014, Vol. 50 ›› Issue (1): 232-234.

加权总体最小二乘在铁路曲线正矢拟合的应用

吴桂清，胡弦，张利民

湖南大学电气与信息工程学院，长沙 410082

出版日期:2014-01-01 发布日期:2013-12-30

Application of weighted total least-square adjustment to the versine fitting of the railway curve

WU Guiqing, HU Xian, ZHANG Limin

College of Electrical and Information Engineering, Hunan University, Changsha 410082, China

Online:2014-01-01 Published:2013-12-30

摘要/Abstract

摘要： 针对铁路线路正矢数据特征，考虑自变量、因变量同时存在误差的情况，提出EIV（Error-in-Variables）模型下的加权总体最小二乘法（WTLS）进行曲线拟合。通过分析拟合点贡献的不等确定度以及修正设计矩阵[A]的列向量分别引入权阵[Py、][Px、][P0]，并给出选权迭代算法。经实例证明，WTLS比传统的LS、TLS方法具有更高的拟合精度。

关键词: 正矢拟合, EIV模型, 加权总体最小二乘法（WTLS）, 选权迭代

Abstract: According to the features of versine data of the railway curve and for the independent variables and the dependent variable both contain random errors, the Weighted Total Least-Square（WTLS） adjustment in curve fitting based on the EIV（Error-in-Variables） model is included. The weighted matrix[Py], [Px] and [P0] are introduced by analyzing fitting point contributions to the uncertainty and amending to the column vectors of the design matrix[A]. In addition, the selecting weight iteration algorithm is given. The calculate example proves that WTLS is greater accurate indeed than?the traditional LS and TLS methods.

Key words: versine fitting, Error-in-Variables（EIV）model, Weighted Total Least-Square（WTLS）;selecting weight?iteration

吴桂清，胡弦，张利民. 加权总体最小二乘在铁路曲线正矢拟合的应用[J]. 计算机工程与应用, 2014, 50(1): 232-234.

WU Guiqing, HU Xian, ZHANG Limin. Application of weighted total least-square adjustment to the versine fitting of the railway curve[J]. Computer Engineering and Applications, 2014, 50(1): 232-234.