CAJ | 학술논문

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y2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。
선형의합재궤도적조정중구유비상중요적작용，고필도철로궤도측량실측점적평면좌표x화y중균포함오차，제출기우정교거리최단적직선화원곡선선형의합방법，병대이용해방법진행의합적원리진행천술。목전상용적선형의합방법시보통최소이승법，주요고필x혹y모일개방향상적오차。안조정교거리최단화최소이승2개준칙，론증료동시고필x화y2개방향오차적정교거리최소이승법요우우보통최소이승법。통과실례계산분석，2충방법대우동일조선형측량수거적의합결과표명，정교거리최소이승법적험후정도고우혹접근보통최소이승법，이차잔차즉위궤도점지의합선형적발도량，동시전자구유경소적원도，설명조정량구간경소。이상내용증명료재철로기유선선형정정우화중정교거리최소이승법우우보통최소이승법。
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 paper prove that the orthogonal distance least squares method has advantages over the ordinary least squares in stand-ardization and optimization of existing railway lines.