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

doi:10.11947/j.AGCS.2019.20180227

Abstract

Abstract: 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.

Key words: equivalent conditional adjustment model, variance-covariance component estimation, LSV-ECM method, triangulateration network, GNSS station coordinate time series

CLC Number:

P207

LIU Zhiping, ZHU Dantong, YU Hang, ZHANG Kefei. Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(9): 1088-1095.

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