| 多变量稳健总体最小二乘平差方法 |
| |
| 引用本文： | 李思达,柳林涛,刘志平,艾青松.多变量稳健总体最小二乘平差方法[J].武汉大学学报(信息科学版),2019,44(8):1241-1248. |
| |
| 作者姓名： | 李思达 柳林涛 刘志平 艾青松 |
| |
| 作者单位： | 1.中国科学院测量与地球物理研究所大地测量与地球动力学国家重点实验室, 湖北 武汉, 430077 |
| |
| 基金项目： | 国家重大科学仪器设备开发专项2011YQ120045国家自然科学基金41074050国家自然科学基金41204011国家自然科学基金41504032国家重点研发计划2016YFC0803103国家重点研发计划2016YFB0502102精密工程与工业测量国家测绘地理信息局重点实验室开放基金PF2017-12 |
| |
| 摘 要： | 分析指出了在总体最小二乘解下，含有多列独立变量的(以下简称为多变量)变量含误差(errors-invariables，EIV)模型，其各列变量的改正数受对应的参数估值与观测向量先验精度的联合影响，参数估值与观测向量先验精度的乘积越大，则该列变量的改正数越大。因此，现有稳健总体最小二乘方法采用同一个单位权中误差对多变量EIV模型进行降权处理时，会优先对模型中的某一列变量进行降权处理，从而造成平差结果不合理甚至错误，称之为虚假稳健估计现象。鉴于此，提出了多变量稳健总体最小二乘平差方法，并导出了相应的参数估计与精度评定公式。该方法对含有粗差的多变量EIV模型的各列独立变量分别进行降权处理，从而避免虚假稳健估计现象的发生。仿真算例结果表明，当观测值含有粗差时，该方法能够有效避免虚假稳健估计现象的发生，并能够定位出粗差所对应的误差方程；相较于总体最小二乘和稳健最小二乘方法，该方法的参数估计结果更接近真值。
|
| 关 键 词： | 多变量EIV模型 虚假稳健估计 多变量稳健估计策略 多变量稳健总体最小二乘 |
| 收稿时间： | 2018-12-06 |
Robust Total Least Squares Method for Multivariable EIV Model |
| |
| Institution: | 1.State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China2.University of Chinese Academy of Sciences, Beijing 100049, China3.School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China |
| |
| Abstract: | The reliability of the solution to the errors-in-variables (EIV) model can be improved through robust total least square method. The false robust estimation problem that the existed robust total least squares method gives priority to reduce the weights of some columns which have large product of estimated parameters and prior cofactors in the multivariable EIV model is pointed out in detail. To tackle this problem, a new robust estimation strategy is presented based on Huber weight function. This new robust estimation strategy copes with each column variable respectively to avoid the false robust estimation problem. Based on this new robust estimation strategy, a multivariate robust total least squares method is proposed and the corresponding estimation results of parameters and variance-covariance matrix are deduced. Experiment results verify the analysis about false robust estimation problem and show the validity of proposed method in coping with false robust estimation problem and detecting the gross error in multivariable EIV model. And compared with the total least squares method and traditional robust least squares method, the proposed method in this paper gets the nearest parameter estimation results to the real value. |
| |
| Keywords: | |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《武汉大学学报(信息科学版)》浏览原始摘要信息 |
| 点击此处可从《武汉大学学报(信息科学版)》下载免费的PDF全文 |
