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

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 ad...

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Main Authors:	LIU Zhiping, ZHU Dantong, YU Hang, ZHANG Kefei
Format:	Article
Language:	zho
Published:	Surveying and Mapping Press 2019-09-01
Series:	Acta Geodaetica et Cartographica Sinica
Subjects:	equivalent conditional adjustment model variance-covariance component estimation lsv-ecm method triangulateration network gnss station coordinate time series
Online Access:	http://html.rhhz.net/CHXB/html/2019-9-1088.htm

id	doaj-3714538efcf346b69babd30fea6cfc1f
record_format	Article
spelling	doaj-3714538efcf346b69babd30fea6cfc1f2020-11-25T02:48:57ZzhoSurveying and Mapping PressActa Geodaetica et Cartographica Sinica1001-15951001-15952019-09-014891088109510.11947/j.AGCS.2019.201802272019090227Least-square variance-covariance component estimation method based on the equivalent conditional adjustment modelLIU Zhiping0ZHU Dantong1YU Hang2ZHANG Kefei3School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, ChinaSchool of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, ChinaSchool of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, ChinaSchool of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, ChinaA 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.http://html.rhhz.net/CHXB/html/2019-9-1088.htmequivalent conditional adjustment modelvariance-covariance component estimationlsv-ecm methodtriangulateration networkgnss station coordinate time series
collection	DOAJ
language	zho
format	Article
sources	DOAJ
author	LIU Zhiping ZHU Dantong YU Hang ZHANG Kefei
spellingShingle	LIU Zhiping ZHU Dantong YU Hang ZHANG Kefei Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model Acta Geodaetica et Cartographica Sinica equivalent conditional adjustment model variance-covariance component estimation lsv-ecm method triangulateration network gnss station coordinate time series
author_facet	LIU Zhiping ZHU Dantong YU Hang ZHANG Kefei
author_sort	LIU Zhiping
title	Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model
title_short	Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model
title_full	Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model
title_fullStr	Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model
title_full_unstemmed	Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model
title_sort	least-square variance-covariance component estimation method based on the equivalent conditional adjustment model
publisher	Surveying and Mapping Press
series	Acta Geodaetica et Cartographica Sinica
issn	1001-1595 1001-1595
publishDate	2019-09-01
description	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.
topic	equivalent conditional adjustment model variance-covariance component estimation lsv-ecm method triangulateration network gnss station coordinate time series
url	http://html.rhhz.net/CHXB/html/2019-9-1088.htm
work_keys_str_mv	AT liuzhiping leastsquarevariancecovariancecomponentestimationmethodbasedontheequivalentconditionaladjustmentmodel AT zhudantong leastsquarevariancecovariancecomponentestimationmethodbasedontheequivalentconditionaladjustmentmodel AT yuhang leastsquarevariancecovariancecomponentestimationmethodbasedontheequivalentconditionaladjustmentmodel AT zhangkefei leastsquarevariancecovariancecomponentestimationmethodbasedontheequivalentconditionaladjustmentmodel
_version_	1724745680765845504

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

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