Gauss-Markov模型的广义压缩t型估计  

GENERALIZED SHRUNKEN T-TYPE ESTIMATION IN GUASS-MARKOV MODEL

作　　者：陈轲[1] 归庆明[2] 杨娜[1,3] 

机构地区：[1]解放军信息工程大学测绘学院 [2]解放军信息工程大学理学院 [3]解放军65015部队

出　　处：《大地测量与地球动力学》2009年第3期114-118,共5页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(40474007);国家杰出青年科学基金(40125013);"基础地理信息与数字化技术"山东省重点开放实验室课题(SD040202);河南省自然科学基金(0511010100)

摘　　要：t型估计的基本思想是以t分布刻画误差分布,可从形式上得到t型估计解的等价权形式,但t型估计不能抵抗病态性的缺点。针对这一缺点,利用广义压缩型抗差估计的思想,对t型估计位置参数的解进行压缩,得到了广义压缩t型估计,并讨论了广义压缩t型估计的具体形式、偏参数选取、迭代方案等。算例证实了该方法的有效性。T-type estimation is a new kind of robust estimations, which takes t-distribution as the error distri- bution and has some advantages in some respects. The equivalent weight form of t-type estimation is presented. A disadvantage of t-type estimation that it cannot resist ill-conditioning is analyzed. To overcome this drawback, according to the idea of the generalized shrunken type robust estimation, the generalized shrunken t-type estimation is presented, which shrinks the solution of the location parameters. Some important problems of this estimation are discussed. A numerical example shows the validity of the method presented.

关 键 词：粗差 t型估计 抗差有偏估计 广义压缩型抗差估计 广义压缩t型估计 

分 类 号：P207[天文地球—测绘科学与技术]