| 方差分量估计理论及其在边角网平差中的应用 |
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| 引用本文： | 张万鹏. 方差分量估计理论及其在边角网平差中的应用[J]. 武汉大学学报 ( 信息科学版),1988,13(1): 9-21. |
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| 作者姓名： | 张万鹏 |
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| 摘 要： | 本文从理论上阐明了MINQE(I,U)(最小范数二次不变无偏估计)方差分量估计出现负方差的原因;论述了存在MINQE(U,NND)估计量的充要条件;对边角网平羞问题而言,MINQE(I,U)估计法不可能同时准确地求出边长误差模型中的m a 2 和m b 2 。文章从边角网误差模型的特点出发,提出了一种新的方差分量估计模型(改进的方差分量估计模型),该模型能合理地确定方向和边长的方差分量,从而较好地解决了边角网平差中的定权问题。
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| 关 键 词： | 方差分量估计 最小范数二次不变无偏估计 非负定最小范数二次无偏估计 改进的方差分量估计模型 边角网平差 |
| 收稿时间： | 1987-05-31 |
Estimation of Variance Components and Its Application in Divection-distance Network Adjustment |
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| Zhang Wanpong. Estimation of Variance Components and Its Application in Divection-distance Network Adjustment[J]. Geomatics and Information Science of Wuhan University ,1988,13(1): 9-21. |
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| Authors: | Zhang Wanpong |
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| Affiliation: | Zhang Wanpong |
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| Abstract: | This paper discusses the necessary and sufficient condition for the existence of a non-negative definite quadratic unbiased estimator (MINQE(U,NND)) of variance components, and explains theoretically why some negative estimators arise in MINQE (I,U) at times. From this conclusion variance components m_a~2 and m_b~2 of distance observations cannot be determined simultaneously and accurately by the MINQE in the direction-distance net adjustment. Furthermore, the analysis of some examples in the paper gives the same result. Therefore, considering the ease that m_a~2 is known generally, an improved variance component estimation model is provided for the direction-distance net adjustment, according to which we can obtain unbiased estimates of both direction and distance variance components and arrive at a reasonable solution to the above examples. In orther words, we can determine more appropriate and reasonable weights in the direction-distance net adjustment. |
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| Keywords: | variance component estimation MINQE(I U) MINQE(U NND) improved variance component estimation model direction-distance network adjustmeet |
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