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| 基于矩阵分解的平差解算方法研究 | |
| 引用本文： | 冯遂亮,宁德阳,黄令勇,徐广袖.基于矩阵分解的平差解算方法研究[J].海洋测绘,2014,34(5):20-23. |
| 作者姓名： | 冯遂亮 宁德阳 黄令勇 徐广袖 |
| 作者单位： | 1. 61175部队,江苏南京,210049 2. 广州军区空军勘察设计院,广东广州,510000 3. 解放军信息工程大学地理空间信息学院,河南郑州450001;海军海洋测绘研究所,天津300061 4. 海军海洋测绘研究所,天津,300061 |
| 摘 要： | 首先分析了法方程稳定性对平差解算结果的影响。为减弱法方程对平差解算结果的影响,采用矩阵分解方法直接对系数矩阵进行矩阵分解,以求解最小二乘最小范数解替代原来最小二乘的法矩阵求逆运算,从而克服法方程求逆造成的解算稳定性差和病态性问题。实验分析结果表明基于矩阵分解的平差解算精度和可靠性较优。 |
| 关 键 词： | 法方程 矩阵QR分解 SVD分解 最小二乘 |
Adjustment Calculating Method Based on Matrix Decomposition |
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| FNEG Suiliang,NING Deyang,HUANG Lingyong,XU Guangxiu.Adjustment Calculating Method Based on Matrix Decomposition[J].Hydrographic Surveying and Charting,2014,34(5):20-23. | |
| Authors: | FNEG Suiliang NING Deyang HUANG Lingyong XU Guangxiu |
| Institution: | FNEG Suiliang,NING Deyang,HUANG Lingyong,XU Guangxiu( 1.61175 Troops, Nanjing 210049, China; 2.Guangzhou Military Area Air Force Institute of Survey and Design, Guangzhou 510000, China; 3.Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450001, China;Naval Institute of Hydrographic Surveying and Charting, Tianjin 300061, China;) |
| Abstract: | The effect of the normal equation stability on adjustment results is analyzed based on the least squares algorithm.In order to weaken this influence,the matrix decomposition method is used to obtain the least squares minimum norm solution instead of the least squares solution.By this way,the ill-posed and unstable problem of solution caused by normal equation solution can be solved.The experiment results show that the solution precision and reliability of this new method is better. |
| Keywords: | normal equation matrix QR decomposition singular value decomposition least squares |
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