摘要
在最小二乘平差中,认为只有观测向量中存在误差,因此当有粗差存在时,也只需要考虑观测向量中的粗差,采用抗差最小二乘可达到剔除粗差的目的。而总体最小二乘同时顾及了系数矩阵和观测向量中的误差,这就要求抗差总体最小二乘同时考虑系数矩阵和观测向量中的粗差。为了同时对粗差进行探测和定位,在加权总体最小二乘奇异值分解法的基础上,提出了一种总体最小二乘抗差估计,最后通过2个算例证明了本文提出方法的有效性和可行性。
In least squares,the errors are thought to exist only in observation vector. Therefore,when there are gross errors in observation data,only need to consider the gross errors of observation vector,in order to exclude gross errors the robust least square is adopt. However,total least square take all the errors of coefficient matrix and observation vector into account,thus,It is required that robust total least square take all the gross errors of coefficient matrix and observation vector into account. Considering the random errors and gross errors may exist both in the observation vector and the coefficient matrix the robust total least squares solution is studied in this paper. Finally,two examples are carried out to prove effectiveness and feasibility of the method.
出处
《江西科学》
2015年第1期101-105,共5页
Jiangxi Science
基金
国家自然科学基金资助项目(41204003
41161069)
江西省自然科学基金资助项目(2010GZC0008)
地球空间环境与大地测量教育部重点实验室开放基金资助项目(100106)
江西省科技落地计划项目(KJLD12077)
江西省教育厅科技项目(GJJ13457)
中国博士后基金(94773)
江西省中青年教师发展计划访问学者专项(赣财指2012-132)
关键词
抗差估计
加权总体最小二乘平差
选权迭代
奇异值分解
robust estimation
Weighted total least square
selecting weight iteration
Singular Value Decomposition
