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. 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.
 Citation: 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. ## Estimation of Variance Components and Its Application in Divection-distance Network Adjustment

• 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ma2和mb2。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。

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 ma2 and mb2 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 ma2 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. / 下载:  全尺寸图片 幻灯片
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