等价条件平差模型的方差-协方差分量最小二乘估计方法

Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model

提出等价条件闭合差的方差-协方差分量最小二乘估计方法,简称LSV-ECM法。首先,利用等价条件平差模型建立了基于等价条件闭合差二次型的方差-协方差分量估计方程,由矩阵半拉直算子将其变换为线性Gauss-Markov形式,进而通过最小二乘准则导出了具有模型通用性、形式简洁性且满足无偏性和最优性的方差-协方差分量估计公式。其次,证明了LSV-ECM方法与残差型VCE方法的等价性,并在此基础上通过计算复杂度定量分析了所提方法的计算高效性。最后,通过边角网平差和中国区域GNSS站坐标时序建模及其结果分析,验证了所提新方法的正确性和计算高效性。

A VCE method termed the least-square variance-covariance component estimation method based on the equivalent conditional misclosure (LSV-ECM) is developed. Three steps are involved. First, the equivalent conditional misclosure is extracted using the projection matrix in the equivalent conditional adjustment model, of which the quadratic equations are established for variance-covariance component estimation. The quadratic equations in the form of matrix are then transformed to the linearized Gauss-Markov form using the half-vectorization operator. A simplified and generalized LSV-ECM method is derived using the least-square principle with an unbiased and optimal estimation.Furthermore, the equivalence between the LSV-ECM and the existing VCE methods is proven mathematically, and computational complexities of the LSV-ECM and the existing VCE methods are quantitatively analyzed and investigated in the indirect adjustment model. It is shown that the new method gives the highest computational efficiency. Finally, the performance and superiority of the new method is evaluated through an adjustment of a triangulateration network and an analysis of a coordinate time series of GNSS stations.