同伦加权整体最小二乘平差算法  

An algorithm for weighted total least squares adjustment by homotopy method

作　　者：张重阳 胡川[1] 李成洪 范小猛 ZHANG Chongyang;HU Chuan;LI Chenghong;FAN Xiaomeng(School of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学土木工程学院,重庆400074

出　　处：《测绘工程》2022年第6期20-26,共7页Engineering of Surveying and Mapping

基　　金：重庆市基础科学与前沿技术研究(一般)项目(cstc2017jcyjAX0102);重庆市教委科学技术研究(KJ1705132);重庆交通大学高层次人才科研启动项目(16JDKJC-A025,17JDKJC-A207);重庆交通大学研究生科研创新项目资助(CYS21341)。

摘　　要：针对标准最小二乘(SLS)解EIV模型存在算法收敛性受初值影响的问题,提出同伦加权整体最小二乘平差法。首先根据SLS理论,按照整体最小二乘平差准则获得求解EIV模型的法方程,联合同伦理论构建同伦加权整体最小二乘平差模型;然后采用预估-校正法对模型进行求解,并设计对应的计算算法;最后以直线拟合和二维坐标变换为例,对所提算法的可行性进行验证,针对不同初值情况对新旧算法收敛性对比。实验结果表明,在初值离真值较远时,新算法仍然能够收敛,解决SLS-WTLS中出现的发散和奇异问题。Aiming at the problem that the convergence of the standard least squares(SLS) theory for solving EIV model is affected by the initial value, a homotopy weighted total least squares adjustment method is proposed.Firstly, according to the SLS theory and the total least squares adjustment criterion, the normal equation for solving the EIV model is obtained.And the homotopy weighted total least squares adjustment model is constructed combined with the homotopy theory.Then the prediction-correction method is used to solve this model, and the corresponding calculation algorithm is designed.Finally, taking straight-line fitting and two-dimensional coordinate transformation as examples, the feasibility of the proposed algorithm is verified, and the convergence of the new and old algorithms is compared according to different initial values.Numerical experiments results show that the new algorithm is feasible;when the initial value is far from the true value, the algorithm in this paper can still converge and solve the problem of divergence or singularity in SLS-WTLS method.

关 键 词：同伦方法 EIV模型 直线拟合 二维平面坐标变换 

分 类 号：P207[天文地球—测绘科学与技术]