中文摘要：

分析指出现有方差一协方差分量估计（VCE）方法在计算效率与χ2统计性质两方面的固有缺陷。利用零空间算子消去概括平差模型中的参数向量，建立等价条件平差模型。由此定义等价条件闭合差（ECM），并导出了以ECM表示的χ2统计量计算式。顾及对称性和可逆性构造了新的方差分量模型，进而基于等价条件闭合差提出方差一协方差分量估计的无偏解析法，简称为VCE—ECM法。同时，给出对应4种基本平差模型的VCE—ECM法简化计算式。实例与仿真结果表明，VCE—ECM法与现有残差型VCE方法的估计效果相当，并有效地克服了现有VCE方法的固有缺陷。

英文摘要：

The defects of the existed methods for variance-covariance component estimation （VCE）, including both computational efficiency and statistical properties of Chi-squared test statistic, are analyzed and investigated in this paper. The equivalent condition adjustment model is established from the generalized adjustment model by null-space operator, based on which both the equivalent condition misclosure （ECM） and the formula of Chi-squared test statistic are given. Moreover, theinvertiblevariance-covariancecomponent model instead of thenoninvertible variance-covariancecomponent model is constructed creatively and the analytical method for VCE is proposed using both ECM and invertiblevariance-covariancecomponent model （short for VCE-ECM method）. Meantime, the simplified formulas of VCE-ECM method are provided for four basic adjustment models correspondingly. Finally, Theoretical and computational results show there was no statistically significant difference in variance-covariance components between proposed method and existed VCE methods, and the analytical method presented here could overcome the inherent defects in existed VCE methods.