TSVD正则化解法的单位权方差无偏估计  

Unbiased Estimation of Unit Weight Variance by TSVD Regularization

作　　者：嵇昆浦 沈云中 JI Kunpu;SHEN Yunzhong(College of Surveying and Geo-Informatics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学测绘与地理信息学院,上海200092

出　　处：《武汉大学学报（信息科学版）》2020年第4期626-632,共7页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41731069)。

摘　　要：截断奇异值(truncated singular value decomposition,TSVD)法通过截掉病态观测方程系数矩阵的小奇异值来改善模型的病态性,提高参数估值的稳定性和精度。然而,截除小奇异值后,改变了观测方程的结构,不仅参数估值有偏,残差估值也是有偏的;因此,其单位权方差不能用传统的估计公式计算。针对此,导出了TSVD正则化解的单位权方差无偏公式,并以第一类Fredholm积分方程和病态测边网为算例验证了公式的正确性。The truncated singular value method(TSVD) improves the morbidity of model by truncating small singular values of the ill-posed observational equation matrix and increases the stability and accuracy of the parameter estimation. However, the structure of observation equation has been changed after truncating small singular value, which makes parameter valuation and residual biased, the unit weight variance cannot be calculated by using traditional estimation formula. This paper derives the unbiased formula of unit weight variance for TSVD regularization, and uses the first Fredholm integral equation and ill-posed trilateration network as examples to verify the correctness of the formula.

关 键 词：病态观测方程 截断奇异值 单位权方差 TSVD正则化 无偏估计 

分 类 号：P207[天文地球—测绘科学与技术]