等价于TLS的非线性最小二乘直线参数估计模型  

A nonlinear least squares model being equivalent to TLS for estimating straight-line parameter

作　　者：范小猛 张重阳 李成洪 胡川[1] Fan Xiaomeng;Zhang Chongyang;Li Chenghong;Hu Chuan(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：《工程勘察》2021年第11期48-53,共6页Geotechnical Investigation & Surveying

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);2016年重庆交通大学高层次人才科研启动项目(16JDKJC-A025)。

摘　　要：在研究了整体最小二乘法和正交距离法等价性的基础上,提出一种与它们等价的非线性最小二乘直线参数估计模型。首先推导整体最小二乘法和正交距离法估计直线参数的计算公式,并给出它们等价时误差改正数应该满足的条件函数式;然后将该条件与传统最小二乘法相结合,建立了估计直线参数的非线性最小二乘模型,并采用拉格朗日乘数法推导其估计直线参数的公式;最后设计了估计参数的迭代计算流程,采用模拟数据和实测数据对提出的方法进行测试。实验结果表明,新方法与正交距离法、整体最小二乘法估计的直线参数值相等,具有等价性。A nonlinear least squares model for straight line parameter estimation is proposed, which is equivalent to TLS and ODR. Firstly, the formulae for linear parameters estimated by TLS and ODR are derived, and the corrected error condition function of equivalence between two approaches is given. Subsequently, following with the condition and LS, a nonlinear least squares model for estimating straight-line is defined, and the formula for computing the optimal parameters are derived by using Lagrange multiplier method. Finally, the iterative calculation process of the parameter estimation is designed, and the proposed method is tested with simulated data and measured data. The results show that the linear parameter estimated by the suggested method equal to TLS and ODR.

关 键 词：整体最小二乘 正交距离法 非线性最小二乘 直线参数估计模型 

分 类 号：O141.4[理学—数学]