基于正交距离最短的平面线形拟合方法及应用.docx

第 11 卷 第 5 期 2014 年 10 月 铁道科学与工程学报 Journal of Ｒailway Science and Engineering Volume 11 Number 5 Octoter 2014 基于正交距离最短的平面线形拟合方法及应用* 王利朋，刘成龙，杨雪峰 ( 西南交通大学 地球科学与环境工程学院，四川 成都 611756) 摘 要: 线形拟合在轨道的调整中具有非常重要的作用，考虑到铁路轨道测量实测点的平面坐标 x 和 y 中均包含误差，提 出基于正交距离最短的直线和圆曲线线形拟合方法，并对利用该方法进行拟合的原理进行阐述。目前常用的线形拟合方 法是普通最小二乘法，主要考虑 x 或 y 某一个方向上的误差。按照正交距离最短和最小二乘 2 个准则，论证了同时考虑 x 和 y 2 个方向误差的正交距离最小二乘法要优于普通最小二乘法。通过实例计算分析，2 种方法对于同一组线形测量数据 的拟合结果表明，正交距离最小二乘法的验后精度高于或接近普通最小二乘法，而且残差即为轨道点至拟合线形的拨道 量，同时前者具有更小的圆度，说明调整量区间更小。以上内容证明了在铁路既有线线形整正优化中正交距离最小二乘法 优于普通最小二乘法。 关键词: 线形拟合; 正交距离最小二乘; 圆度; 整正优化; 验后精度 中图分类号: P207 文献标志码: A 文章编号: 1672 － 7029( 2014) 05 － 0125 － 06 Method and application of plane linear fitting based on shortest orthogonal distance WANG Lipeng，LIU Chenglong，YANG Xuefeng ( School of Geosciences and Environmental Engineering，Southwest Jiaotong University，Chengdu 611756，China) Abstract: Linear fitting is very important in track adjustment． Given the error of horizontal coordinates in meas- ured points of tracks，the method of line － fitting and circular curve － fitting was proposed based on shortest or- thogonal distance． Then the principle of the method was introduced． The main method in linear fitting is ordinary least squares at the moment，which mainly considers the error of a specific direction． According to two norms， shortest orthogonal distance and least squares，this paper proved that the method of orthogonal distance least squares considered the error of horizontal coordinates and was more effective than ordinary least squares on whole． The results of data fitting，according to different methods，show that orthogonal distance least squares method has higher posteriori precision，and the residual errors represent variation of track lining． Meanwhile， the former method has a smaller roundness，which shows the small interval of adjustment． The results in this pa- per prove that the orthogonal distance least squares