On non-combinatorial weighted total least squares with inequality constraints
Observation systems known as errors-in-variables (EIV) models with model parameters estimated by total least squares (TLS) have been discussed for more than a century, though the terms EIV and TLS were coined much more recently. So far, it has only been shown that the inequality-constrained TLS (ICT...
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| Published in: | Journal of geodesy Vol. 88; no. 8; pp. 805 - 816 |
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| Format: | Journal Article |
| Language: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2014
Springer Nature B.V |
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| ISSN: | 0949-7714, 1432-1394 |
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| Abstract | Observation systems known as errors-in-variables (EIV) models with model parameters estimated by total least squares (TLS) have been discussed for more than a century, though the terms EIV and TLS were coined much more recently. So far, it has only been shown that the inequality-constrained TLS (ICTLS) solution can be obtained by the combinatorial methods, assuming that the weight matrices of observations involved in the data vector and the data matrix are identity matrices. Although the previous works test all combinations of active sets or solution schemes in a clear way, some aspects have received little or no attention such as admissible weights, solution characteristics and numerical efficiency. Therefore, the aim of this study was to adjust the EIV model, subject to linear inequality constraints. In particular, (1) This work deals with a symmetrical positive-definite cofactor matrix that could otherwise be quite arbitrary. It also considers cross-correlations between cofactor matrices for the random coefficient matrix and the random observation vector. (2) From a theoretical perspective, we present first-order Karush–Kuhn–Tucker (KKT) necessary conditions and the second-order sufficient conditions of the inequality-constrained weighted TLS (ICWTLS) solution by analytical formulation. (3) From a numerical perspective, an active set method without combinatorial tests as well as a method based on sequential quadratic programming (SQP) is established. By way of applications, computational costs of the proposed algorithms are shown to be significantly lower than the currently existing ICTLS methods. It is also shown that the proposed methods can treat the ICWTLS problem in the case of more general weight matrices. Finally, we study the ICWTLS solution in terms of non-convex weighted TLS contours from a geometrical perspective. |
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| AbstractList | Observation systems known as errors-in-variables (EIV) models with model parameters estimated by total least squares (TLS) have been discussed for more than a century, though the terms EIV and TLS were coined much more recently. So far, it has only been shown that the inequality-constrained TLS (ICTLS) solution can be obtained by the combinatorial methods, assuming that the weight matrices of observations involved in the data vector and the data matrix are identity matrices. Although the previous works test all combinations of active sets or solution schemes in a clear way, some aspects have received little or no attention such as admissible weights, solution characteristics and numerical efficiency. Therefore, the aim of this study was to adjust the EIV model, subject to linear inequality constraints. In particular, (1) This work deals with a symmetrical positive-definite cofactor matrix that could otherwise be quite arbitrary. It also considers cross-correlations between cofactor matrices for the random coefficient matrix and the random observation vector. (2) From a theoretical perspective, we present first-order Karush–Kuhn–Tucker (KKT) necessary conditions and the second-order sufficient conditions of the inequality-constrained weighted TLS (ICWTLS) solution by analytical formulation. (3) From a numerical perspective, an active set method without combinatorial tests as well as a method based on sequential quadratic programming (SQP) is established. By way of applications, computational costs of the proposed algorithms are shown to be significantly lower than the currently existing ICTLS methods. It is also shown that the proposed methods can treat the ICWTLS problem in the case of more general weight matrices. Finally, we study the ICWTLS solution in terms of non-convex weighted TLS contours from a geometrical perspective. |
| Author | Fang, Xing |
| Author_xml | – sequence: 1 givenname: Xing surname: Fang fullname: Fang, Xing email: wflsfang1981@hotmail.com organization: School of Geodesy and Geomatics, Wuhan University |
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| Cites_doi | 10.1137/0717073 10.1007/s00190-013-0643-2 10.1002/9780470316665 10.1007/s00190-012-0598-8 10.1007/s00190-006-0026-z 10.1179/003962610X12572516251367 10.1007/s00190-012-0575-2 10.1007/s00190-004-0425-y 10.1017/CBO9780511804441 10.1016/S0377-0427(02)00878-6 10.1007/s00190-010-0431-1 10.1007/s00190-013-0658-8 10.1007/s001900050237 10.1007/s11430-012-4418-z 10.1137/1.9781611971002 10.1007/s00190-012-0552-9 10.1007/s11200-012-0671-z 10.1007/s10543-004-6024-8 10.1007/s00190-012-0560-9 10.1016/j.csda.2004.07.014 10.1007/s11200-009-0001-2 10.1007/s11200-013-1150-x 10.1007/s00190-007-0186-5 10.1007/s00190-007-0190-9 10.1007/978-3-642-70659-2_8 10.1214/aos/1176345330 10.1007/s00190-010-0408-0 10.1007/s001840300272 10.1007/s00190-014-0717-9 10.2478/v10156-011-0036-5 10.1007/11666806_80 10.1007/s00190-014-0692-1 10.1016/j.chemolab.2006.04.003 10.1007/s40328-014-0046-8 10.1007/s00190-011-0524-5 10.1179/1752270613Y.0000000052 10.2478/v10156-011-0028-5 10.1016/j.jspi.2003.12.020 10.1007/BF03655306 10.1007/978-3-642-00860-3_33 10.1007/978-3-642-22078-4_25 10.1007/3-540-27432-4_71 |
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| Keywords | Sequential quadratic programming (SQP) Non-convex optimization Second-order sufficient conditions Linear inequality constraints Weighted total least squares (WTLS) Errors-in-variables (EIV) model Karush–Kuhn–Tucker (KKT) necessary conditions Active set method WTLS contours |
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| References | Kukush, Van Huffel (CR20) 2004; 59 Amiri-Simkooei (CR2) 2013; 87 Shen, Li, Chen (CR47) 2011; 85 CR39 Fang (CR6) 2013; 87 Xu, Liu, Shi (CR55) 2012; 86 CR37 Li, Shen, Lou (CR23) 2013; 27 CR36 CR35 CR33 Xu (CR54) 2003; 155 Zhu, Santerre, Chang (CR58) 2005; 78 Schaffrin, Felus (CR40) 2008; 82 Mahboub, Sharifi (CR26) 2013; 87 Fritsch, Grafarend, Sanso (CR11) 1985 CR4 CR5 CR9 Peng, Zhang, Shong, Guo (CR32) 2006; 79 CR49 CR46 Song, Zhu, Li (CR50) 2010; 42 CR44 Boyd, Vandenberghe (CR3) 2004 CR43 Markovsky, Rastello, Premoli, Kukush, van Huffel (CR28) 2006; 50 Schaffrin, Wieser (CR41) 2008; 82 Schaffrin, Neitzel, Uzun, Mahboub (CR45) 2012; 2 Mahboub (CR27) 2014; 58 Fuller (CR12) 1987 Fletcher (CR10) 1987 Fang (CR8) 2014; 58 CR19 Golub, Van Loan (CR14) 1980; 17 CR18 Lu, Krakiwsky, Lachapelle (CR24) 1993; 1 CR17 CR16 CR56 Li, Shen, Li (CR22) 2012; 55 CR52 Grafarend, Awange (CR15) 2012 Schaffrin (CR38) 1981; 88 Neitzel (CR30) 2010; 84 Amiri-Simkooei, Jazaeri (CR1) 2012; 2 Schaffrin, Felus (CR42) 2009; 53 Xu, Cannon, Lachapelle (CR53) 1999; 73 CR29 Zhang, Tong, Zhang (CR57) 2013; 87 Sima, van Huffel, Golub (CR48) 2004; 44 Van Huffel, Vandewalle (CR51) 1991 CR25 CR21 Roese-Koerner, Devaraju, Sneeuw, Schuh (CR34) 2012; 86 Fang (CR7) 2013 Gleser (CR13) 1981; 9 Nocedal, Wright (CR31) 2006 723_CR36 DM Sima (723_CR48) 2004; 44 723_CR35 723_CR37 723_CR39 B Schaffrin (723_CR38) 1981; 88 B Schaffrin (723_CR45) 2012; 2 L Gleser (723_CR13) 1981; 9 723_CR33 L Roese-Koerner (723_CR34) 2012; 86 S Boyd (723_CR3) 2004 X Fang (723_CR6) 2013; 87 S Zhang (723_CR57) 2013; 87 A Amiri-Simkooei (723_CR2) 2013; 87 S Huffel Van (723_CR51) 1991 R Fletcher (723_CR10) 1987 723_CR25 723_CR29 X Fang (723_CR8) 2014; 58 J Peng (723_CR32) 2006; 79 PL Xu (723_CR55) 2012; 86 723_CR21 D Fritsch (723_CR11) 1985 Y Song (723_CR50) 2010; 42 PL Xu (723_CR54) 2003; 155 723_CR16 B Li (723_CR22) 2012; 55 A Amiri-Simkooei (723_CR1) 2012; 2 E Grafarend (723_CR15) 2012 723_CR18 723_CR17 V Mahboub (723_CR26) 2013; 87 723_CR19 B Schaffrin (723_CR41) 2008; 82 723_CR52 J Nocedal (723_CR31) 2006 723_CR56 WA Fuller (723_CR12) 1987 V Mahboub (723_CR27) 2014; 58 G Golub (723_CR14) 1980; 17 I Markovsky (723_CR28) 2006; 50 723_CR5 723_CR4 X Fang (723_CR7) 2013 723_CR9 723_CR46 723_CR49 A Kukush (723_CR20) 2004; 59 F Neitzel (723_CR30) 2010; 84 B Schaffrin (723_CR42) 2009; 53 723_CR43 Y Shen (723_CR47) 2011; 85 B Schaffrin (723_CR40) 2008; 82 723_CR44 B Li (723_CR23) 2013; 27 J Zhu (723_CR58) 2005; 78 G Lu (723_CR24) 1993; 1 PL Xu (723_CR53) 1999; 73 |
| References_xml | – volume: 17 start-page: 883 issue: 6 year: 1980 end-page: 893 ident: CR14 article-title: An analysis of the total least-squares problem publication-title: SIAM J Numer Anal doi: 10.1137/0717073 – volume: 87 start-page: 733 issue: 8 year: 2013 end-page: 749 ident: CR6 article-title: Weighted total least squares: necessary and sufficient conditions, fixed and random parameters publication-title: J Geod doi: 10.1007/s00190-013-0643-2 – year: 2012 ident: CR15 publication-title: Applications of linear and nonlinear models. Fixed effects, random effects, and total least squares – ident: CR49 – ident: CR4 – year: 1987 ident: CR12 publication-title: Measurement error models doi: 10.1002/9780470316665 – volume: 87 start-page: 279 issue: 3 year: 2013 end-page: 286 ident: CR26 article-title: On weighted total least-squares with linear and quadratic constraints publication-title: J Geod doi: 10.1007/s00190-012-0598-8 – volume: 79 start-page: 705 year: 2006 end-page: 713 ident: CR32 article-title: An aggregate constraint method for inequality-constrained least squares problems publication-title: J Geod doi: 10.1007/s00190-006-0026-z – ident: CR39 – ident: CR16 – volume: 42 start-page: 62 issue: 315 year: 2010 end-page: 71 ident: CR50 article-title: The least-squares estimation of adjustment model constrained by some non-negative parameters publication-title: Surv Rev doi: 10.1179/003962610X12572516251367 – volume: 88 start-page: 227 year: 1981 end-page: 238 ident: CR38 article-title: Parameter estimation with inequality constraints publication-title: Allgemeine Vermessungs-Nachrichten – ident: CR35 – ident: CR29 – volume: 87 start-page: 23 issue: 1 year: 2013 end-page: 28 ident: CR57 article-title: A solution to EIV model with inequality constraints and its geodetic applications publication-title: J Geod doi: 10.1007/s00190-012-0575-2 – volume: 27 start-page: 1572 issue: 8 year: 2013 end-page: 1592 ident: CR23 article-title: Seamless multivariate affine error-in-variables transformation and its application to map rectification publication-title: Int J GIS – volume: 78 start-page: 528 year: 2005 end-page: 534 ident: CR58 article-title: A bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning publication-title: J Geod doi: 10.1007/s00190-004-0425-y – year: 1987 ident: CR10 publication-title: Practical methods of optimization – year: 2004 ident: CR3 publication-title: Convex optimization doi: 10.1017/CBO9780511804441 – ident: CR25 – ident: CR21 – ident: CR46 – ident: CR19 – volume: 155 start-page: 423 issue: 2 year: 2003 end-page: 446 ident: CR54 article-title: A hybrid global optimization method: the multi-dimensional case publication-title: J Comput Appl Math doi: 10.1016/S0377-0427(02)00878-6 – volume: 85 start-page: 229 issue: 4 year: 2011 end-page: 238 ident: CR47 article-title: An iterative solution to weighted total least squares adjustment publication-title: J Geod doi: 10.1007/s00190-010-0431-1 – volume: 87 start-page: 935 year: 2013 end-page: 944 ident: CR2 article-title: Application of least squares variance component estimation to errors-in-variables models publication-title: J Geod doi: 10.1007/s00190-013-0658-8 – volume: 2 start-page: 98 issue: 2 year: 2012 end-page: 106 ident: CR45 article-title: Modifying Cadzow’s algorithm to generate the optimal TLS-solution for the structured EIV-model of a similarity transformation publication-title: J Geod Sci – year: 2006 ident: CR31 publication-title: Numerical optimization – year: 2013 ident: CR7 publication-title: A global solution to the inequality constrained total least squares problem – ident: CR9 – volume: 73 start-page: 204 year: 1999 end-page: 213 ident: CR53 article-title: Stabilizing ill-conditioned linear complementarity problems publication-title: J Geod doi: 10.1007/s001900050237 – ident: CR36 – ident: CR5 – volume: 55 start-page: 2099 issue: 12 year: 2012 end-page: 2108 ident: CR22 article-title: The seamless model for three-dimensional datum transformation publication-title: Sci China Earth Sci doi: 10.1007/s11430-012-4418-z – volume: 1 start-page: 124 year: 1993 end-page: 130 ident: CR24 article-title: Application of inequality constrained least squares to GPS navigation under selective availability publication-title: Manuscr Geod – year: 1991 ident: CR51 publication-title: The total least -squares problem doi: 10.1137/1.9781611971002 – volume: 86 start-page: 661 issue: 8 year: 2012 end-page: 675 ident: CR55 article-title: Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis publication-title: J Geod doi: 10.1007/s00190-012-0552-9 – volume: 58 start-page: 1 issue: 1 year: 2014 end-page: 16 ident: CR8 article-title: A structured and constrained Total Least-Squares solution with cross-covariances publication-title: Studia Geophysica et Geodaetica doi: 10.1007/s11200-012-0671-z – ident: CR18 – ident: CR43 – volume: 44 start-page: 793 year: 2004 end-page: 812 ident: CR48 article-title: Regularized total least-squares based on quadratic eigenvalue problem solver publication-title: BIT doi: 10.1007/s10543-004-6024-8 – volume: 86 start-page: 1005 year: 2012 end-page: 1018 ident: CR34 article-title: A stochastic framework for inequality constrained estimation publication-title: J Geod doi: 10.1007/s00190-012-0560-9 – ident: CR37 – ident: CR33 – ident: CR56 – volume: 50 start-page: 181 year: 2006 end-page: 209 ident: CR28 article-title: The element-wise weighted total least-squares problem publication-title: Comput Stat Data Anal doi: 10.1016/j.csda.2004.07.014 – volume: 53 start-page: 1 issue: 1 year: 2009 end-page: 16 ident: CR42 article-title: An algorithmic approach to the total least-squares problem with linear and quadratic constraints publication-title: Studia Geophysica et Geodaetica doi: 10.1007/s11200-009-0001-2 – volume: 58 start-page: 17 issue: 1 year: 2014 end-page: 40 ident: CR27 article-title: Variance component estimation in errors-in-variables models and a rigorous total least-squares approach publication-title: Studia Geophysica et Geodaetica doi: 10.1007/s11200-013-1150-x – ident: CR44 – volume: 82 start-page: 373 year: 2008 end-page: 383 ident: CR40 article-title: On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms publication-title: J Geod doi: 10.1007/s00190-007-0186-5 – volume: 82 start-page: 415 year: 2008 end-page: 421 ident: CR41 article-title: On weighted total least-squares adjustment for linear regression publication-title: J Geod doi: 10.1007/s00190-007-0190-9 – start-page: 169 year: 1985 end-page: 184 ident: CR11 article-title: Some additional informations on the capacity of the linear complementarity algorithm publication-title: Optimization and design of geodetic networks doi: 10.1007/978-3-642-70659-2_8 – ident: CR52 – volume: 9 start-page: 24 issue: 1 year: 1981 end-page: 44 ident: CR13 article-title: Estimation in a multivariate ‘errors in variables’ regression model: large sample results publication-title: Ann Stat doi: 10.1214/aos/1176345330 – ident: CR17 – volume: 84 start-page: 751 year: 2010 end-page: 762 ident: CR30 article-title: Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation publication-title: J Geod doi: 10.1007/s00190-010-0408-0 – volume: 2 start-page: 113 issue: 2 year: 2012 end-page: 124 ident: CR1 article-title: Weighted total least squares formulated by standard least squares theory publication-title: J Geod Sci – volume: 59 start-page: 75 issue: 1 year: 2004 end-page: 97 ident: CR20 article-title: Consistency of element wise weighted total least squares estimator in a multivariate errors-in-variables model AX = B publication-title: Metrika doi: 10.1007/s001840300272 – volume-title: Measurement error models year: 1987 ident: 723_CR12 doi: 10.1002/9780470316665 – volume: 58 start-page: 17 issue: 1 year: 2014 ident: 723_CR27 publication-title: Studia Geophysica et Geodaetica doi: 10.1007/s11200-013-1150-x – ident: 723_CR56 doi: 10.1007/s00190-014-0717-9 – volume: 42 start-page: 62 issue: 315 year: 2010 ident: 723_CR50 publication-title: Surv Rev doi: 10.1179/003962610X12572516251367 – ident: 723_CR44 – volume: 73 start-page: 204 year: 1999 ident: 723_CR53 publication-title: J Geod doi: 10.1007/s001900050237 – volume: 2 start-page: 113 issue: 2 year: 2012 ident: 723_CR1 publication-title: J Geod Sci doi: 10.2478/v10156-011-0036-5 – volume: 155 start-page: 423 issue: 2 year: 2003 ident: 723_CR54 publication-title: J Comput Appl Math doi: 10.1016/S0377-0427(02)00878-6 – start-page: 169 volume-title: Optimization and design of geodetic networks year: 1985 ident: 723_CR11 doi: 10.1007/978-3-642-70659-2_8 – ident: 723_CR29 doi: 10.1007/11666806_80 – volume: 53 start-page: 1 issue: 1 year: 2009 ident: 723_CR42 publication-title: Studia Geophysica et Geodaetica doi: 10.1007/s11200-009-0001-2 – volume: 59 start-page: 75 issue: 1 year: 2004 ident: 723_CR20 publication-title: Metrika doi: 10.1007/s001840300272 – ident: 723_CR36 doi: 10.1007/s00190-014-0692-1 – volume: 79 start-page: 705 year: 2006 ident: 723_CR32 publication-title: J Geod doi: 10.1007/s00190-006-0026-z – ident: 723_CR19 – volume-title: Numerical optimization year: 2006 ident: 723_CR31 – ident: 723_CR46 doi: 10.1016/j.chemolab.2006.04.003 – ident: 723_CR9 doi: 10.1007/s40328-014-0046-8 – ident: 723_CR25 doi: 10.1007/s00190-011-0524-5 – volume-title: A global solution to the inequality constrained total least squares problem year: 2013 ident: 723_CR7 – volume: 87 start-page: 279 issue: 3 year: 2013 ident: 723_CR26 publication-title: J Geod doi: 10.1007/s00190-012-0598-8 – volume: 82 start-page: 415 year: 2008 ident: 723_CR41 publication-title: J Geod doi: 10.1007/s00190-007-0190-9 – volume: 87 start-page: 935 year: 2013 ident: 723_CR2 publication-title: J Geod doi: 10.1007/s00190-013-0658-8 – ident: 723_CR16 doi: 10.1179/1752270613Y.0000000052 – volume: 2 start-page: 98 issue: 2 year: 2012 ident: 723_CR45 publication-title: J Geod Sci doi: 10.2478/v10156-011-0028-5 – ident: 723_CR5 – volume: 55 start-page: 2099 issue: 12 year: 2012 ident: 723_CR22 publication-title: Sci China Earth Sci doi: 10.1007/s11430-012-4418-z – ident: 723_CR33 – volume-title: Applications of linear and nonlinear models. Fixed effects, random effects, and total least squares year: 2012 ident: 723_CR15 – ident: 723_CR37 – ident: 723_CR17 – volume: 50 start-page: 181 year: 2006 ident: 723_CR28 publication-title: Comput Stat Data Anal doi: 10.1016/j.csda.2004.07.014 – volume-title: Convex optimization year: 2004 ident: 723_CR3 doi: 10.1017/CBO9780511804441 – volume: 9 start-page: 24 issue: 1 year: 1981 ident: 723_CR13 publication-title: Ann Stat doi: 10.1214/aos/1176345330 – ident: 723_CR21 doi: 10.1016/j.jspi.2003.12.020 – volume: 88 start-page: 227 year: 1981 ident: 723_CR38 publication-title: Allgemeine Vermessungs-Nachrichten – volume: 1 start-page: 124 year: 1993 ident: 723_CR24 publication-title: Manuscr Geod doi: 10.1007/BF03655306 – volume: 84 start-page: 751 year: 2010 ident: 723_CR30 publication-title: J Geod doi: 10.1007/s00190-010-0408-0 – volume: 86 start-page: 661 issue: 8 year: 2012 ident: 723_CR55 publication-title: J Geod doi: 10.1007/s00190-012-0552-9 – ident: 723_CR43 doi: 10.1007/978-3-642-00860-3_33 – volume: 87 start-page: 23 issue: 1 year: 2013 ident: 723_CR57 publication-title: J Geod doi: 10.1007/s00190-012-0575-2 – ident: 723_CR4 – volume: 17 start-page: 883 issue: 6 year: 1980 ident: 723_CR14 publication-title: SIAM J Numer Anal doi: 10.1137/0717073 – volume: 87 start-page: 733 issue: 8 year: 2013 ident: 723_CR6 publication-title: J Geod doi: 10.1007/s00190-013-0643-2 – volume: 86 start-page: 1005 year: 2012 ident: 723_CR34 publication-title: J Geod doi: 10.1007/s00190-012-0560-9 – volume: 58 start-page: 1 issue: 1 year: 2014 ident: 723_CR8 publication-title: Studia Geophysica et Geodaetica doi: 10.1007/s11200-012-0671-z – ident: 723_CR35 doi: 10.1007/978-3-642-22078-4_25 – volume-title: Practical methods of optimization year: 1987 ident: 723_CR10 – ident: 723_CR18 – volume: 44 start-page: 793 year: 2004 ident: 723_CR48 publication-title: BIT doi: 10.1007/s10543-004-6024-8 – volume: 27 start-page: 1572 issue: 8 year: 2013 ident: 723_CR23 publication-title: Int J GIS – volume: 82 start-page: 373 year: 2008 ident: 723_CR40 publication-title: J Geod doi: 10.1007/s00190-007-0186-5 – ident: 723_CR39 doi: 10.1007/3-540-27432-4_71 – ident: 723_CR49 – volume-title: The total least -squares problem year: 1991 ident: 723_CR51 doi: 10.1137/1.9781611971002 – volume: 85 start-page: 229 issue: 4 year: 2011 ident: 723_CR47 publication-title: J Geod doi: 10.1007/s00190-010-0431-1 – volume: 78 start-page: 528 year: 2005 ident: 723_CR58 publication-title: J Geod doi: 10.1007/s00190-004-0425-y – ident: 723_CR52 |
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