顾及位置关系的直线参数整体最小估计算法  

An algorithm for total least squares of line parameters considering the position relationship

作　　者：颜晓于 刘宇凡 鲁子洋 张重阳 YAN Xiaoyu;LIU Yufan;LU Ziyang;ZHANG Chongyang(School of Smart City,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学智慧城市学院,重庆400074

出　　处：《甘肃科学学报》2025年第1期1-7,15,共8页Journal of Gansu Sciences

基　　金：重庆市自然科学基金项目(CSTB2022NSCQ-MSX1527);重庆市大学生创新创业训练计划(S202310618080);重庆交通大学大创培育项目(157)。

摘　　要：针对直线间平行、垂直和斜交的3种位置关系,提出将直线间的位置关系转化为等式约束条件,结合加权整体最小二乘法进行直线拟合。首先,将直线间的3种位置关系表达为直线斜率的关系,对其线性化,得到3种约束模型;其次,根据加权整体最小二乘准则确定附有等式约束的加权整体最小二乘法平差模型,推导其解算方程,并建立平差算法;最后,针对3种约束模型进行拟合实验。实验结果表明:新算法具有可行性,拟合精度较高,且能确保直线间的平面位置关系正确。Position relationships between lines can be divided into parallel,perpendicular and intersecting,and these relationships can be transformed into constraints in line fitting.For taking advantage of this constraint,the weighted total least squares estimation method with equation constraint is introduced for line fitting.Position relationship between lines is expressed as the relationship between slopes of lines,and is linearized to obtain three constraint models,which together with the weighted total least squares criterion determine the equality constrained weighted total least squares model.Then the solution formula of the model is derived and an iterative algorithm is proposed.Finally,three simulation experiments demonstrated the feasibility and effectiveness of the developed algorithm.The result shows that the new algorithm is feasible with a higher fitting accuracy,and can ensure the correct plane position relationship between straight lines.

关 键 词：平面位置关系 直线拟合 加权整体最小二乘 等式约束 

分 类 号：P207[天文地球—测绘科学与技术]