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

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...
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Autor*in:	Jian Xie [verfasserIn] Tianwei Qiu [verfasserIn] Cui Zhou [verfasserIn] Dongfang Lin [verfasserIn] Sichun Long [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional model modification Stochastic model modification Accuracy evaluation

Übergeordnetes Werk:	In: Geodesy and Geodynamics - KeAi Communications Co., Ltd., 2017, 15(2024), 2, Seite 177-188
Übergeordnetes Werk:	volume:15 ; year:2024 ; number:2 ; pages:177-188

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1016/j.geog.2023.06.001

Katalog-ID:	DOAJ100319750

Internformat


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520			\|a 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 traditional LS and TLS estimations.
650		4	\|a Linear structured weighted total least squares
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650		4	\|a Functional model modification
650		4	\|a Stochastic model modification
650		4	\|a Accuracy evaluation
653		0	\|a Geodesy
653		0	\|a Geophysics. Cosmic physics
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700	0		\|a Cui Zhou \|e verfasserin \|4 aut
700	0		\|a Dongfang Lin \|e verfasserin \|4 aut
700	0		\|a Sichun Long \|e verfasserin \|4 aut
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allfields	10.1016/j.geog.2023.06.001 doi (DE-627)DOAJ100319750 (DE-599)DOAJf7a31156b43647c0affb65c3e80791dc DE-627 ger DE-627 rakwb eng QB275-343 QC801-809 Jian Xie verfasserin aut Algorithms and statistical analysis for linear structured weighted total least squares problem 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 traditional LS and TLS estimations. Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional model modification Stochastic model modification Accuracy evaluation Geodesy Geophysics. Cosmic physics Tianwei Qiu verfasserin aut Cui Zhou verfasserin aut Dongfang Lin verfasserin aut Sichun Long verfasserin aut In Geodesy and Geodynamics KeAi Communications Co., Ltd., 2017 15(2024), 2, Seite 177-188 (DE-627)750085827 (DE-600)2719789-X 16749847 nnns volume:15 year:2024 number:2 pages:177-188 https://doi.org/10.1016/j.geog.2023.06.001 kostenfrei https://doaj.org/article/f7a31156b43647c0affb65c3e80791dc kostenfrei http://www.sciencedirect.com/science/article/pii/S1674984723000708 kostenfrei https://doaj.org/toc/1674-9847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2119 GBV_ILN_2129 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2817 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 15 2024 2 177-188
spelling	10.1016/j.geog.2023.06.001 doi (DE-627)DOAJ100319750 (DE-599)DOAJf7a31156b43647c0affb65c3e80791dc DE-627 ger DE-627 rakwb eng QB275-343 QC801-809 Jian Xie verfasserin aut Algorithms and statistical analysis for linear structured weighted total least squares problem 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 traditional LS and TLS estimations. Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional model modification Stochastic model modification Accuracy evaluation Geodesy Geophysics. Cosmic physics Tianwei Qiu verfasserin aut Cui Zhou verfasserin aut Dongfang Lin verfasserin aut Sichun Long verfasserin aut In Geodesy and Geodynamics KeAi Communications Co., Ltd., 2017 15(2024), 2, Seite 177-188 (DE-627)750085827 (DE-600)2719789-X 16749847 nnns volume:15 year:2024 number:2 pages:177-188 https://doi.org/10.1016/j.geog.2023.06.001 kostenfrei https://doaj.org/article/f7a31156b43647c0affb65c3e80791dc kostenfrei http://www.sciencedirect.com/science/article/pii/S1674984723000708 kostenfrei https://doaj.org/toc/1674-9847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2119 GBV_ILN_2129 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2817 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 15 2024 2 177-188
allfields_unstemmed	10.1016/j.geog.2023.06.001 doi (DE-627)DOAJ100319750 (DE-599)DOAJf7a31156b43647c0affb65c3e80791dc DE-627 ger DE-627 rakwb eng QB275-343 QC801-809 Jian Xie verfasserin aut Algorithms and statistical analysis for linear structured weighted total least squares problem 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 traditional LS and TLS estimations. Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional model modification Stochastic model modification Accuracy evaluation Geodesy Geophysics. Cosmic physics Tianwei Qiu verfasserin aut Cui Zhou verfasserin aut Dongfang Lin verfasserin aut Sichun Long verfasserin aut In Geodesy and Geodynamics KeAi Communications Co., Ltd., 2017 15(2024), 2, Seite 177-188 (DE-627)750085827 (DE-600)2719789-X 16749847 nnns volume:15 year:2024 number:2 pages:177-188 https://doi.org/10.1016/j.geog.2023.06.001 kostenfrei https://doaj.org/article/f7a31156b43647c0affb65c3e80791dc kostenfrei http://www.sciencedirect.com/science/article/pii/S1674984723000708 kostenfrei https://doaj.org/toc/1674-9847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2119 GBV_ILN_2129 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2817 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 15 2024 2 177-188
allfieldsGer	10.1016/j.geog.2023.06.001 doi (DE-627)DOAJ100319750 (DE-599)DOAJf7a31156b43647c0affb65c3e80791dc DE-627 ger DE-627 rakwb eng QB275-343 QC801-809 Jian Xie verfasserin aut Algorithms and statistical analysis for linear structured weighted total least squares problem 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 traditional LS and TLS estimations. Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional model modification Stochastic model modification Accuracy evaluation Geodesy Geophysics. Cosmic physics Tianwei Qiu verfasserin aut Cui Zhou verfasserin aut Dongfang Lin verfasserin aut Sichun Long verfasserin aut In Geodesy and Geodynamics KeAi Communications Co., Ltd., 2017 15(2024), 2, Seite 177-188 (DE-627)750085827 (DE-600)2719789-X 16749847 nnns volume:15 year:2024 number:2 pages:177-188 https://doi.org/10.1016/j.geog.2023.06.001 kostenfrei https://doaj.org/article/f7a31156b43647c0affb65c3e80791dc kostenfrei http://www.sciencedirect.com/science/article/pii/S1674984723000708 kostenfrei https://doaj.org/toc/1674-9847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2119 GBV_ILN_2129 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2817 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 15 2024 2 177-188
allfieldsSound	10.1016/j.geog.2023.06.001 doi (DE-627)DOAJ100319750 (DE-599)DOAJf7a31156b43647c0affb65c3e80791dc DE-627 ger DE-627 rakwb eng QB275-343 QC801-809 Jian Xie verfasserin aut Algorithms and statistical analysis for linear structured weighted total least squares problem 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 traditional LS and TLS estimations. Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional model modification Stochastic model modification Accuracy evaluation Geodesy Geophysics. Cosmic physics Tianwei Qiu verfasserin aut Cui Zhou verfasserin aut Dongfang Lin verfasserin aut Sichun Long verfasserin aut In Geodesy and Geodynamics KeAi Communications Co., Ltd., 2017 15(2024), 2, Seite 177-188 (DE-627)750085827 (DE-600)2719789-X 16749847 nnns volume:15 year:2024 number:2 pages:177-188 https://doi.org/10.1016/j.geog.2023.06.001 kostenfrei https://doaj.org/article/f7a31156b43647c0affb65c3e80791dc kostenfrei http://www.sciencedirect.com/science/article/pii/S1674984723000708 kostenfrei https://doaj.org/toc/1674-9847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2119 GBV_ILN_2129 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2817 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 15 2024 2 177-188
language	English
source	In Geodesy and Geodynamics 15(2024), 2, Seite 177-188 volume:15 year:2024 number:2 pages:177-188
sourceStr	In Geodesy and Geodynamics 15(2024), 2, Seite 177-188 volume:15 year:2024 number:2 pages:177-188
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional model modification Stochastic model modification Accuracy evaluation Geodesy Geophysics. Cosmic physics
isfreeaccess_bool	true
container_title	Geodesy and Geodynamics
authorswithroles_txt_mv	Jian Xie @@aut@@ Tianwei Qiu @@aut@@ Cui Zhou @@aut@@ Dongfang Lin @@aut@@ Sichun Long @@aut@@
publishDateDaySort_date	2024-01-01T00:00:00Z
hierarchy_top_id	750085827
id	DOAJ100319750
language_de	englisch
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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. 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callnumber-first	Q - Science
author	Jian Xie
spellingShingle	Jian Xie misc QB275-343 misc QC801-809 misc Linear structured weighted total least squares misc Errors-in-variables misc Errors-in-observations misc Functional model modification misc Stochastic model modification misc Accuracy evaluation misc Geodesy misc Geophysics. Cosmic physics Algorithms and statistical analysis for linear structured weighted total least squares problem
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topic_title	QB275-343 QC801-809 Algorithms and statistical analysis for linear structured weighted total least squares problem Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional model modification Stochastic model modification Accuracy evaluation
topic	misc QB275-343 misc QC801-809 misc Linear structured weighted total least squares misc Errors-in-variables misc Errors-in-observations misc Functional model modification misc Stochastic model modification misc Accuracy evaluation misc Geodesy misc Geophysics. Cosmic physics
topic_unstemmed	misc QB275-343 misc QC801-809 misc Linear structured weighted total least squares misc Errors-in-variables misc Errors-in-observations misc Functional model modification misc Stochastic model modification misc Accuracy evaluation misc Geodesy misc Geophysics. Cosmic physics
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title	Algorithms and statistical analysis for linear structured weighted total least squares problem
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title_full	Algorithms and statistical analysis for linear structured weighted total least squares problem
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title_sort	algorithms and statistical analysis for linear structured weighted total least squares problem
callnumber	QB275-343
title_auth	Algorithms and statistical analysis for linear structured weighted total least squares problem
abstract	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 traditional LS and TLS estimations.
abstractGer	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 traditional LS and TLS estimations.
abstract_unstemmed	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 traditional LS and TLS estimations.
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container_issue	2
title_short	Algorithms and statistical analysis for linear structured weighted total least squares problem
url	https://doi.org/10.1016/j.geog.2023.06.001 https://doaj.org/article/f7a31156b43647c0affb65c3e80791dc http://www.sciencedirect.com/science/article/pii/S1674984723000708 https://doaj.org/toc/1674-9847
remote_bool	true
author2	Tianwei Qiu Cui Zhou Dongfang Lin Sichun Long
author2Str	Tianwei Qiu Cui Zhou Dongfang Lin Sichun Long
ppnlink	750085827
callnumber-subject	QB - Astronomy
mediatype_str_mv	c
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doi_str	10.1016/j.geog.2023.06.001
callnumber-a	QB275-343
up_date	2024-07-03T14:00:30.779Z
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Algorithms and statistical analysis for linear structured weighted total least squares problem

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