基于中位数法的抗差总体最小二乘估计

针对现有总体最小二乘抗差算法存在的缺陷,应用中位数法确定模型参数的初值,提出了对模型的观测向量与系数矩阵中的观测元素进行分类定权的思想,避免了中误差估计偏差与随机模型误差对等价权函数抗差性的影响。基于中位数法建立总体最小二乘抗差迭代算法,并结合算例对算法进行验证。结果表明,在相同观测样本条件下,本文提出的算法拟合的精度高于传统算法拟合的精度。...

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Bibliographic Details
Published inCe hui xue bao Vol. 45; no. 3; pp. 297 - 301
Main Author 陶叶青 高井祥 姚一飞
Format Journal Article
LanguageChinese
English
Published Beijing Surveying and Mapping Press 01.03.2016
淮海工学院测绘工程学院,江苏 连云港,222005%中国矿业大学环境与测绘学院,江苏 徐州,221008
Subjects
Algorithms
Computation
Iterative algorithms
Iterative methods
Least squares
Robustness (mathematics)
中位数
总体最小二乘
抗差估计
总体最小二乘
抗差估计
totalleast squares
robust estimation
median method
中位数
Online AccessGet full text
ISSN1001-1595
1001-1595
DOI10.11947/j.AGCS.2016.20150234

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Summary:针对现有总体最小二乘抗差算法存在的缺陷,应用中位数法确定模型参数的初值,提出了对模型的观测向量与系数矩阵中的观测元素进行分类定权的思想,避免了中误差估计偏差与随机模型误差对等价权函数抗差性的影响。基于中位数法建立总体最小二乘抗差迭代算法,并结合算例对算法进行验证。结果表明,在相同观测样本条件下,本文提出的算法拟合的精度高于传统算法拟合的精度。
Bibliography:total least squares; robust estimation; median method
11-2089/P
Because the present algorithms of total least squares for robust estimation have disadvantages,solution for computation primary model parameters based on median method is proposed.And to get over the influence that estimation error of random model and error of mean square has,computation weight matrix of observation vector and coefficient matrix separately are proposed.Iterative algorithm of robust total least squares is established based on median method,and to prove the proposed solution to be feasible,an instance is cited.The numerical results of the instance clearly demonstrate that the presented solution is more accurate than the traditional method for line fitting.
TAO Yeqing ,GAO Jingxiang ,YAO Yifei（ 1. Department of Geomatic Engineering, Huaihai Institute of Technology, Lianyungang 222005, China~ 2. School of Environment Science and Spatial Informatics, China University of Mining ＆ Technology, Xuzhou 221008, China）
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ISSN:1001-1595
1001-1595
DOI:10.11947/j.AGCS.2016.20150234