| 病态平差模型直接解算方法的研究 |
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| 引用本文： | 归庆明,郭建峰. 病态平差模型直接解算方法的研究[J]. 大地测量与地球动力学, 2004, 24(3): 15-18 |
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| 作者姓名： | 归庆明 郭建峰 |
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| 作者单位： | 1. 信息工程大学理学院,郑州,450001
2. 信息工程大学理学院,郑州,450001;中国科学院测量与地球物理研究所,武汉,430077 |
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| 基金项目： | 国家杰出青年科学基金项目 (4 0 12 5 0 13 )，国家自然科学基金项目 (4 0 0 740 0 6) |
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| 摘 要： | 基于矩阵的SVD理论，通过修改设计阵的奇异值，提出了若干种直接解算病态(满秩或秩亏)观测方程的方法，以改善设计阵的病态性，提高参数估值的稳定性和准确性。理论分析和数值计算的结果验证了这些解算方法的优良性。
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| 关 键 词： | 平差模型 SVD理论 观测方程 奇异值分解 解算方法 |
| 文章编号： | 1671-5942(2004)03-0015-04 |
| 修稿时间： | 2004-03-14 |
STUDY ON METHODS FOR SOLVING ILL-CONDITIONED EQUATIONS |
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| Gui Qingming and Guo Jianfeng,) Institute of Science,Information Engineering University,Zhengzhou ) Institute of Geodesy and Geophysics,CAS,Wuhan. STUDY ON METHODS FOR SOLVING ILL-CONDITIONED EQUATIONS[J]. Journal of Geodesy and Geodynamics, 2004, 24(3): 15-18 |
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| Authors: | Gui Qingming Guo Jianfeng ) Institute of Science Information Engineering University Zhengzhou ) Institute of Geodesy Geophysics CAS Wuhan |
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| Affiliation: | Gui Qingming1 and Guo Jianfeng1,21) Institute of Science,Information Engineering University,Zhengzhou 450001 2) Institute of Geodesy and Geophysics,CAS,Wuhan 430077 |
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| Abstract: | Based on Singular Value Decomposition (SVD), several methods for directly solving ill conditioned equations with full rank or not full rank are proposed by modifying the singular values of the design matrix. The numerical results show that the proposed methods can resist the ill conditioned effect and improve the numerical stability and accuracy of parameter estimation. |
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| Keywords: | surveying equation ill-conditioned singular-value decomposition adjustment model solving method |
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