病态模型改进正则化解的单位权中误差无偏估计  

Truncated Regularized Solution to Ill-Posed Model and Its Unbiased Estimation of Unit Weighted Variance

作　　者：毛云蕾 邹时林 吴星[3] MAO Yunlei;ZOU Shilin;WU Xing(Application Engineering Department,East China University of Technology,Yangtze River College,56 Xuefu Road,Fuzhou 344000,China;Faculty of Geomatics,East China University of Technology,418 Guanglan Road,Nanchang 330013,China;Fuzhou Branch of Prospecting and Designing Institute,East China University of Technology,56 Xuefu Road,Fuzhou 344000,China)

机构地区：[1]东华理工大学长江学院应用工程系,江西省抚州市344000 [2]东华理工大学测绘工程学院,南昌市330013 [3]东华理工大学勘察设计院抚州分院,江西省抚州市344000

出　　处：《大地测量与地球动力学》2020年第4期411-416,共6页Journal of Geodesy and Geodynamics

摘　　要：正则化法通过引入正则化参数对奇异值加以修正,从而改善法矩阵的病态性,然而其不加区别地对所有奇异值进行修正显然是不合理的。本文比较正则化解均方误差和最小二乘解方差的迹谱分解展开式,分析因修正奇异值导致解的均方误差变化与奇异值的关系,确定奇异值修正与否的条件,并基于残差二次型期望公式导出改进正则化解的无偏单位权中误差计算公式,最后用数值算例和病态测边网算例验证公式的正确性。The regularized method improves the ill-posedness of the normal matrix by introducing the regularized parameter to correct the singular values.However,it is obviously unreasonable to correct the singular values without distinction.In this paper,we compare the trajectory decomposition expansions of the regularized mean square error and the least squares solution variance,analyze the relationship between the change of the mean square error of the solution caused by the modified singular value and the singular value,and determine the conditions for singular value correction.Based on the residual quadratic expectation formula,an error calculation formula for unbiased unit weights with improved regularization is derived.Finally,numerical examples and ill-trimmed network examples are used to verify the correctness of the formula.

关 键 词：病态模型 正则化 单位权中误差 无偏估计 

分 类 号：P207[天文地球—测绘科学与技术]