基于等价条件闭合差的VCE通用解析法

分析指出了现有方差-协方差分量估计(VCE)方法在计算效率与?2统计量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，建立了等价条件平差模型。由此定义了等价条件闭合差(ECC)，并导出了以ECC表示的?2统计量计算式。进而，基于等价条件闭合差与新构造的可逆方差分量模型提出了方差-协方差分量估计的通用解析法，简称为VCE-ECC法。同时，给出了对应四种基本平差模型的VCE-ECC法简化计算式。实例与仿真结果表明：VCE-ECC法与现有VCE方法的方差-协方差分量估计值在统计意义上无明显差异，并有效地克服了现有VCE方法的固有缺陷。

Analytical Method for VCE Using Equivalent Condition Closure

The defect of the existed methods for variance - covariance component estimation (VCE), including computational efficiency and statistical properties of Chi-square statistic, are analyzed and pointed out in this paper. The equivalent condition adjustment model is established from the generalized adjustment model by null-space operator, based on which the equivalent condition closure (ECC) and the formula of Chi-square statistic is derived. Moreover, the variance-covariance component model characterized with invertibility is constructed effectively and the analytical method used for VCE is proposed using ECC and invertible variance covariance component model (short for VCE-ECC method). Meantime, simplification formulas of VCE-ECC method are provided for four basic adjustment models correspondingly. Finally, results show there was no significant difference for estimated value of variance - covariance component between proposed method and existed VCE methods in the statistical significance, and the analytical method presented here could overcome the inherent defect in existed VCE methods.