方差-协方差分量估计的概括平差因子法

Variance-covariance Component Estimation Method Based on Generalization Adjustment Factor

针对现有方差-协方差分量估计(variance-covariance component estimation,VCE)理论存在的问题,通过引入间接平差的平差因子概念,定义并研究了基于概括平差模型的概括平差因子、概括闭合差及其方差阵,进而利用二次期望公式提出了基于概括平差因子的VCE新方法。该方法适用于概括平差模型所归纳的4种函数模型形式,并通过概括平差因子揭示了平差函数模型与VCE是否存在解析估计形式的关系。实例计算结果表明,现有迭代型VCE方法改变了LS估计量的统计性质,而VCE新方法解析估计具有LS统计性质,且无需初值。

The existing variance-covariance component estimation （VCE） theory and its de- fects are analyzed and briefly described. A generalization adjustment factor was developed from the adiustment factor concept, and both generalization closure error and its covariance matrix are investigated based on the generalization adjustment model. A novel VCE method including four basic function models is presented using the generalization adjustment factor. The relationship between four function models and VCE analytical or iterative solution prop- erties is effectively revealed by the generalization adjustment factor. Triangulateration net- work adiustment results show that the VCE iteration solution lost fewer optimal statistical properties found in the LS criterion. The VCE analytical solution, only for the condition function model provides the optimal statistical properties meeting the LS criterion.