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- 2017
附有奇异值修正限制的改进的岭估计方法
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Abstract:
最小二乘估计具有无偏性，而岭估计是一种有偏估计，它通过引入偏差降低方差来降低均方误差。在模型出现病态时，岭估计优于最小二乘估计。对岭估计的方差与偏差进行分析发现，岭估计通过修正病态矩阵的奇异值降低均方误差，但对部分较大奇异值的修正不能有效降低均方误差。通过比较修正奇异值的方差下降量与偏差引入量的大小关系确定需要修正的小奇异值，进而改进岭估计方法，实现选择性地修正小奇异值，提出附有奇异值修正限制的改进的岭估计方法，可有效改善岭估计的解算效果和可靠性，实验验证了新方法的可行性和有效性
| [1] | Yang Wencai. A Generalized Inversion Technique for Potential Field Data Processing[J]. Acta Geophysica Sinica,1986,29(3):283-291(杨文采.用于位场数据处理的广义反演技术[J].地球物理学报,1986,29(3):283-291) |
| [2] | Xu Tianhe, Yang Yuanxi. Condition of Regularization Solution Superior to LS Solution Based on MSE Principle[J]. Geomatics and Information Science of Wuhan University, 2004, 29(3):223-226(徐天河,杨元喜. 均方误差意义下正则化解优于最小二乘解的条件[J]. 武汉大学学报·信息科学版, 2004,29(3):223-226) |
| [3] | Shen Y Z, Xu P L, Li B F. Bias-Corrected Regularized Solution to Inverse Ill-Posed Models[J]. Journal of Geodesy, 2012,86:597-608 |
| [4] | Zhu Jianjun, A New Algorithm for Ridge Estimate[J]. Journal of Geomatics, 1997, 3:22-25(朱建军. 岭估计的一种新的算法[J]. 测绘信息与工程,1997,3:22-25) |
| [5] | Golub G H, Heath M, Wahba G. Generalized Gross-Validation as a Method for Choosing a Good Ridge Parameter[J]. Technometrics, 1979, 21,215-223 |
| [6] | Hansen P C. The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems[J]. SIAM J. Sci. Comput, 1993, 14(6):1487-1503 |
| [7] | Ye Songlin, Zhu Jianjun. Application of Singular Value Decomposition and Generalized Ridge Estimation Insurveying[J]. The Chinese Journal of Nonferrous Metals,1998,8(1):163-167(叶松林,朱建军.矩阵奇异值分解与广义岭估计及其在测量中的应用[J]. 中国有色金属学报, 1998, 8(1):163-167) |
| [8] | Cui Xizhang, Yu Zongchou, Tao Benzao. Generalized Surveying Adjustment[M]. Wuhan:Wuhan Technical University of Surveying and Mapping Press,2001(崔希璋, 於倧俦,陶本藻. 广义测量平差[M].武汉:武汉测绘科技大学出版社,2001) |
| [9] | Zhu Jianjun, Tian Yumiao, Tao Xiaojing. United Expression and Solution of Adjustment Criteria with Parameters[J]. Acta Geodaetica et Cartographica Sinica, 2012,41(1):8-13(朱建军,田玉淼,陶肖静.带准则参数的平差准则及其统一与解算[J].测绘学报, 2012,41(1):8-13) |
| [10] | Hoerl A E, Kennard R W. Ridge Regression Biased Estimation for Non-orthogonal Problems[J]. Technimetrics,1970,12:55-58 |
| [11] | Xu P L, Shen Y Z, Fukuda Y, et al. Variance Component Estimation in Linear Inverse Ill-Posed Models[J]. Journal of Geodesy, 2006,80:69-81 |
| [12] | Xu C, Deng C F. Solving Multicollinearity in Dam Regression Model Using TSVD[J].Geo-Spatial Information Science, 2011, 14(3):230-234 |
| [13] | Dai W J, Liu B, Ding X L, et al. Modeling Dam Deformation Using Independent Component Regression Method[J]. Transactions of Nonferrous Metals Society of China,2013, 23:2194-2200 |
| [14] | Himanshu S, Srinivas B, Byron D T. Reducing Errors in the GRACE Gravity Solutions Using Regularization[J]. Journal of Geodesy, 2012, 86:695-711 |
