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Algorithms and statistical analysis for linear structured weighted total least squares problem

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  • 国家科技期刊平台
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Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the tradi-tional LS and TLS estimations.

Linear structured weighted total least squaresErrors-in-variablesErrors-in-observationsFunctional model modificationStochastic model modificationAccuracy evaluation

Jian Xie、Tianwei Qiu、Cui Zhou、Dongfang Lin、Sichun Long

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School of Earth Science and Spatial Information Engineering,Hunan University of Science and Technology,Xiangtan 411201,China

College of Science,Central South University of Forestry and Technology,Changsha 410018,China

National-Local Joint Engineering Laboratory of Geo-spatial Information Technology,Hunan University of Science and Technology,Xiangtan 411201,China

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaHunan Provincial Natural Science Foundation of ChinaScientific Research Fund of Hunan Provincial Education Department

420740164210402542274057417040072021JJ3024422B0496

2024

10.1016/j.geog.2023.06.001

大地测量与地球动力学(英文版)
中国地震局地震研究所

大地测量与地球动力学(英文版)

EI
影响因子：0.568
ISSN：1674-9847
年,卷(期)：2024.15(2)
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