| 大地测量中法方程病态性问题的初探 |
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| 引用本文： | 张俊,文鸿雁,刘立龙.大地测量中法方程病态性问题的初探[J].海洋测绘,2006,26(5):1-3. |
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| 作者姓名： | 张俊 文鸿雁 刘立龙 |
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| 作者单位： | 桂林工学院,土木工程系,广西,桂林541004 |
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| 基金项目： | 国家自然科学基金;广西自然科学基金 |
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| 摘 要： | 在大地测量中,法方程病态问题大量存在。由于病态性的存在,致使按最小二乘法解算参数估值精度变差发生扭曲,最终使所得结果不能使用。重点研究奇异值分解法(SVD)和误差转移法解决病态问题的思想、途径、对关键问题的处理、适用范围等。最后通过GPS实测数据来验证这两种方法的有效性,其解算的结果表明:这两种方法能解决法方程病态性问题,且算法简便、易懂,有较强的应用价值。
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| 关 键 词： | 大地测量 法方程 奇异值分解 误差转移 |
| 文章编号： | 1671-3044（2006）05-0001-03 |
| 收稿时间： | 2006-03-29 |
| 修稿时间： | 2006-05-14 |
Discussion on the Ill-conditioned Problems in Normal Equation of Geodesy |
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| ZHANG Jun,WEN Hong-yan,LIU Li-long.Discussion on the Ill-conditioned Problems in Normal Equation of Geodesy[J].Hydrographic Surveying and Charting,2006,26(5):1-3. |
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| Authors: | ZHANG Jun WEN Hong-yan LIU Li-long |
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| Institution: | Department of Civil Engineering, Guilin Insititute of Technology, Guilin, Guangxi ,541004 |
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| Abstract: | The ill-conditioned problems are widely being in the GPS surveying and because of it,accuracy of the parameters obtained by least square estimation become worse,sometimes even distorted.As a result,these estimate values may be in vain for use.Consequently,singular value deeomposition(SVD) and error transformation methods are mainly presented in the paper and the theory,methods,suitable use range and the key approaches of the methods are described respectively in detail.In the end,the feasibility of the two methods in solving the ill-conditioned equation are checked with the real data of GPS.The results show that these two methods can solve the ill-conditioned problems and are easy to understand and use,and of a high usable value in practice. |
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| Keywords: | geodesy normal equation singular value decomposition(SVD) error transfer |
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