加权总体最小二乘在铁路曲线正矢拟合的应用  

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

作　　者：吴桂清[1] 胡弦[1] 张利民[1] 

机构地区：[1]湖南大学电气与信息工程学院,长沙410082

出　　处：《计算机工程与应用》2014年第1期232-234,共3页Computer Engineering and Applications

基　　金：广东省教育部产学研结合项目(No.2010B090400213)

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P y、P x、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。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.

关 键 词：正矢拟合 EIV模型 加权总体最小二乘法(WTLS) 选权迭代 WEIGHTED TOTAL Least-Square(WTLS) 

分 类 号：TP39[自动化与计算机技术—计算机应用技术] U216.68[自动化与计算机技术—计算机科学与技术]