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_a² and m_b² 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_a² 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.