摘要
在文献〔1〕中，给出了适用于各种平差方法的Helmert型方差—协方差分量估计的通用公式，同时还给出了Helmert型方差分量估计以及简化的方差分量估计的通用公式。本文按最优二次无偏估计理论（BQUE）导出了另一种形式的方差—协方差分量估计的通用公式，而国外学者C．R．Rao所给出的方差分量最小范数二次无偏估计式（MINQUE）以及由Lars E．Sjoberg所给出的方差—协方差分量最优二次无偏估计式，都是该通用公式的特例。此外，本文还证明了Helmert型方差—协方差分量估计与BQUE估计，两者是彼此等价的。
The General Formulas of estimation of variance and covariance components of
Helmert type which are adequate for all adjustment methods. have been derived and the
corresponding simplified formula has also been given[1]. Based on the best quadratic
unbiased estimation theory(BQUE). a new form of general formula for estimating
variance-covariance components has been derived in this paper. It is shown that
MINQUE of variance components(C. R. Rao. 1973) and the best quadratic unbiased
estimates (Lars E. Sjoberg. 1983) only are as special cases of the general formula.
Final1y. it is proved that in the case of block structured covariance matrix. the esti-
mation of variance-covariance components of Helmert type is equivalent to BQUE.
出处
《测绘学报》
EI
CSCD
北大核心
1991年第3期161-171,共11页
Acta Geodaetica et Cartographica Sinica
基金
国家自然科学基金资助项目
