| 基于中位参数法相关观测的抗差加权整体最小二乘算法 |
| |
| 引用本文： | 刘春阳,王坚,王彬,刘超,刘纪平.基于中位参数法相关观测的抗差加权整体最小二乘算法[J].武汉大学学报(信息科学版),2019,44(3):378-384. |
| |
| 作者姓名： | 刘春阳 王坚 王彬 刘超 刘纪平 |
| |
| 作者单位： | 1.中国矿业大学国土环境与灾害监测国家测绘地理信息局重点实验室, 江苏 徐州, 221116 |
| |
| 基金项目： | 国家重点研发计划2016YFC0803103 |
| |
| 摘 要： | 在抗差加权整体最小二乘算法中，抗差模型的抗差性与初值的好坏关系极大，若以最小二乘或整体最小二乘估值作为初值，必定会受到粗差污染而影响其抗差性。考虑到观测向量和系数矩阵存在相关性，首先推导了部分变量误差（partial errors-in-variables，Partial EIV）模型的加权整体最小二乘算法，在此基础上提出了一种利用中位参数法求解抗差迭代初值的相关观测抗差加权整体最小二乘算法。然后采用中位参数法确定抗差初值，考虑到可能出现的粗差对观测空间与结构空间的综合影响，基于标准化残差构造权因子函数，实现其抗差解法。仿真实验结果表明，此算法具有良好的抗差性能，其参数估计结果比传统算法精度更高，且随着粗差个数的增加，其抗差稳定性较好。
|
| 关 键 词： | 抗差加权整体最小二乘 中位参数法 Partial EIV模型 相关观测 标准化残差 |
| 收稿时间： | 2017-03-16 |
Robust Weight Total Least Squares Algorithm of Correlated Observation Based on Median Parameter Method |
| |
| Affiliation: | 1.Key Laboratory of Land Environment and Disaster Monitoring, NASG, China University of Mining and Technology, Xuzhou, 221116, China2.School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China3.School of Geodesy and Geomatics, Anhui University of Science and Technology, Huainan 232001, China4.Chinese Academy of Surveying and Mapping, Beijing 100830, China |
| |
| Abstract: | In the robust weighted total least squares(RWTLS) algorithm, its robustness of the robust model is highly related to the initial values. If the least squares or total least squares estimates is used as the initial value, it will be affected by gross error, and certainly impacted the robust characteristics of RWTLS estimates. Considering the correlation between the observed vector and the coefficient matrix, we first deduce the weighted least-squares solution of Partial-EIV model, and a new RWTLS algorithm of correlated observation is proposed to solve the initial values of robust iterations by using the median parameter method. Then the median parameter method is used to determine the initial value, and on this basis we propose a new robust estimated method, which is based on the standardized residual error and considered the influence of gross error both on observation and structure spaces. The experiment results show that the proposed estimated method has a good performance to resist gross error, and the presented solution is more accurate than the traditional method for line fitting, and with the increase of the number of gross errors, the stability of the algorithm is superior to the traditional method. |
| |
| 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)》下载全文 |
|
