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

• 工程与应用 • 上一篇    下一篇

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   

  1. 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   

  1. College of Electrical and Information Engineering, Hunan University, Changsha 410082, China
  • Online:2014-01-01 Published:2013-12-30

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