| 误差限的病态总体最小二乘解算 |
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| 引用本文： | 葛旭明,伍吉仓.误差限的病态总体最小二乘解算[J].测绘学报,2013,42(2):196-202. |
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| 作者姓名： | 葛旭明 伍吉仓 |
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| 作者单位： | 1. 同济大学测绘与地理信息学院,上海,200092
2. 同济大学测绘与地理信息学院,上海200092;现代工程测量国家测绘地理信息局重点实验室,上海200092 |
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| 基金项目： | 国家自然科学基金，中美国际合作项目 |
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| 摘 要： | 大地测量和地球物理数据解算中时常会涉及病态问题的处理。基于客观的观测精度,利用设计矩阵与观测向量的误差限制,一方面降低了病态性对求解造成的波动;另一方面避免引入正常数,从而提高整个解算过程的客观性与可靠性。计算表明,本文提出的方法可以有效地处理病态总体最小二乘问题,并且具有较高的稳定性。
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| 关 键 词： | 病态性 正则化 总体最小二乘 观测精度 误差限度 |
| 收稿时间： | 2012-04-17 |
A Regularization Method to Ill-posed Total Least Squares with Error Limits |
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| WU Ji-Cang.A Regularization Method to Ill-posed Total Least Squares with Error Limits[J].Acta Geodaetica et Cartographica Sinica,2013,42(2):196-202. |
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| Authors: | WU Ji-Cang |
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| Institution: | 1,2 1.Institute of Surveying and Geo-informatics,Tongji University,Shanghai 200092,China;2.Key Laboratory of Modern Engineering Surveying,SBSM,Shanghai 200092,China |
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| Abstract: | Abstract: Ill-posed problems often appear in geodesy and geophysical. Tikhonov regularization is a well-known tool to resolve ill-posed problems in least squares (LS) and total least squares (TLS). In Tikhonov regularization, solving parameters not only need to satisfy the objective function but also to meet inequality condition, so as to avoid acute oscillation in the result which caused by tiny oscillation in observation. A positive constant should be imported in this approach, but unfortunately the true positive constant is unknown in any solution. Moreover there is no objective criterion to give this constant in each solution. Based on the objective measurement accuracy, we attempt to use the residuals of measurements in both design matrix and observation value to replace the positive constant. A few numerical experiments are carried out to demonstrate the performance and efficiency of the new method. |
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| Keywords: | Key words: Ill-posed problems Regularization Total least squares Measurement accuracy Error limits |
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