方差分量估计理论及其在边角网平差中的应用

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。

Estimation of Variance Components and Its Application in Divection-distance Network Adjustment

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.