| 基于信噪比检验的部分奇异值双参数修正估计 |
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| 引用本文： | 李豪,顾勇为,郭淑妹.基于信噪比检验的部分奇异值双参数修正估计[J].测绘科学技术学报,2017,34(4). |
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| 作者姓名： | 李豪 顾勇为 郭淑妹 |
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| 作者单位： | 信息工程大学,河南 郑州,450001 |
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| 基金项目： | 国家自然科学基金项目，信息工程大学自主科研课题项目 |
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| 摘 要： | 从分析LS估计和岭估计的奇异值展开式出发,研究了病态性问题的解算方法。岭估计中岭参数对较大奇异值的修正不能有效降低估计的方差,却增大了估计的偏差,这是导致岭估计有时效果不好的重要原因。首先借鉴TSVD思想,保留展式中较大奇异值所对应的项,然后修正展式中较小奇异值所对应的项。在修正前,利用信噪比检验,将各个参数按受到复共线性危害的大小分为两类,据此作出不同强度的双参数修正,提出了基于信噪比检验的部分奇异值双参数修正估计。实验结果表明,新方法的解算精度较高。
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| 关 键 词： | 信噪比 复共线性 岭估计 奇异值 双参数 |
Partial Singular Value Correction Estimation with Double Parameters Based on Signal-to-Noise Ratio Test |
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| LI Hao,GU Yongwei,GUO Shumei.Partial Singular Value Correction Estimation with Double Parameters Based on Signal-to-Noise Ratio Test[J].Journal of Zhengzhou Institute of Surveying and Mapping,2017,34(4). |
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| Authors: | LI Hao GU Yongwei GUO Shumei |
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| Abstract: | Embarking from the analysis of the singular values expansions of LS estimation and ridge estimation, the methods of solving ill-posed problems are studied in this paper. The correction of ridge parameter to singular value in ridge estimation cannot effectively reduce the variance of estimation, but increase the deviation of estimation, which is an important reason that the effect of ridge estimation is sometimes not good. First, according to the idea of TSVD estimation, the items corresponding to larger singular values in the expansion are retain, and the items cor-responding to smaller singular values are fixed. Before the revision, utilizing the method of signal-to-noise ratio test, all the parameters are divided into two parts according to the influence extent each parameter suffers from col-linearity. Accordingly, the correction of different intensity with double parameters are made. This method is named partial singular value correction estimationwith double parameters based on signal-to-noise ratio test. Experimental results show that the new method has higher calculation precision. |
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| Keywords: | signal-to-noise ratio multicollinearity ridge estimation singular value double parameters |
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