加权总体最小二乘在铁路曲线正矢拟合的应用

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。

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

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.