Efficient transformation from Cartesian to geodetic coordinates
The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational spee...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Claessens, S.J. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019transfer abstract |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Ultrafast acquirement of combined time and frequency spectroscopic data - 2012transfer abstract, an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets : an official journal of the International Association for Mathematical Geology, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:133 ; year:2019 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.cageo.2019.104307 |
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ELV048604429 |
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| 520 | |a The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. | ||
| 520 | |a The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. | ||
| 650 | 7 | |a Coordinate transformation |2 Elsevier | |
| 650 | 7 | |a Geodetic coordinates |2 Elsevier | |
| 650 | 7 | |a Cartesian coordinates |2 Elsevier | |
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10.1016/j.cageo.2019.104307 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000822.pica (DE-627)ELV048604429 (ELSEVIER)S0098-3004(18)31132-4 DE-627 ger DE-627 rakwb eng 530 VZ 580 VZ AFRIKA DE-30 fid BIODIV DE-30 fid 42.38 bkl Claessens, S.J. verfasserin aut Efficient transformation from Cartesian to geodetic coordinates 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. Coordinate transformation Elsevier Geodetic coordinates Elsevier Cartesian coordinates Elsevier Enthalten in Elsevier Science Ultrafast acquirement of combined time and frequency spectroscopic data 2012transfer abstract an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets : an official journal of the International Association for Mathematical Geology Amsterdam [u.a.] (DE-627)ELV021566380 volume:133 year:2019 pages:0 https://doi.org/10.1016/j.cageo.2019.104307 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-AFRIKA FID-BIODIV GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_130 42.38 Botanik: Allgemeines VZ AR 133 2019 0 |
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10.1016/j.cageo.2019.104307 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000822.pica (DE-627)ELV048604429 (ELSEVIER)S0098-3004(18)31132-4 DE-627 ger DE-627 rakwb eng 530 VZ 580 VZ AFRIKA DE-30 fid BIODIV DE-30 fid 42.38 bkl Claessens, S.J. verfasserin aut Efficient transformation from Cartesian to geodetic coordinates 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. Coordinate transformation Elsevier Geodetic coordinates Elsevier Cartesian coordinates Elsevier Enthalten in Elsevier Science Ultrafast acquirement of combined time and frequency spectroscopic data 2012transfer abstract an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets : an official journal of the International Association for Mathematical Geology Amsterdam [u.a.] (DE-627)ELV021566380 volume:133 year:2019 pages:0 https://doi.org/10.1016/j.cageo.2019.104307 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-AFRIKA FID-BIODIV GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_130 42.38 Botanik: Allgemeines VZ AR 133 2019 0 |
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10.1016/j.cageo.2019.104307 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000822.pica (DE-627)ELV048604429 (ELSEVIER)S0098-3004(18)31132-4 DE-627 ger DE-627 rakwb eng 530 VZ 580 VZ AFRIKA DE-30 fid BIODIV DE-30 fid 42.38 bkl Claessens, S.J. verfasserin aut Efficient transformation from Cartesian to geodetic coordinates 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. Coordinate transformation Elsevier Geodetic coordinates Elsevier Cartesian coordinates Elsevier Enthalten in Elsevier Science Ultrafast acquirement of combined time and frequency spectroscopic data 2012transfer abstract an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets : an official journal of the International Association for Mathematical Geology Amsterdam [u.a.] (DE-627)ELV021566380 volume:133 year:2019 pages:0 https://doi.org/10.1016/j.cageo.2019.104307 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-AFRIKA FID-BIODIV GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_130 42.38 Botanik: Allgemeines VZ AR 133 2019 0 |
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10.1016/j.cageo.2019.104307 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000822.pica (DE-627)ELV048604429 (ELSEVIER)S0098-3004(18)31132-4 DE-627 ger DE-627 rakwb eng 530 VZ 580 VZ AFRIKA DE-30 fid BIODIV DE-30 fid 42.38 bkl Claessens, S.J. verfasserin aut Efficient transformation from Cartesian to geodetic coordinates 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. Coordinate transformation Elsevier Geodetic coordinates Elsevier Cartesian coordinates Elsevier Enthalten in Elsevier Science Ultrafast acquirement of combined time and frequency spectroscopic data 2012transfer abstract an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets : an official journal of the International Association for Mathematical Geology Amsterdam [u.a.] (DE-627)ELV021566380 volume:133 year:2019 pages:0 https://doi.org/10.1016/j.cageo.2019.104307 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-AFRIKA FID-BIODIV GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_130 42.38 Botanik: Allgemeines VZ AR 133 2019 0 |
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10.1016/j.cageo.2019.104307 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000822.pica (DE-627)ELV048604429 (ELSEVIER)S0098-3004(18)31132-4 DE-627 ger DE-627 rakwb eng 530 VZ 580 VZ AFRIKA DE-30 fid BIODIV DE-30 fid 42.38 bkl Claessens, S.J. verfasserin aut Efficient transformation from Cartesian to geodetic coordinates 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. Coordinate transformation Elsevier Geodetic coordinates Elsevier Cartesian coordinates Elsevier Enthalten in Elsevier Science Ultrafast acquirement of combined time and frequency spectroscopic data 2012transfer abstract an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets : an official journal of the International Association for Mathematical Geology Amsterdam [u.a.] (DE-627)ELV021566380 volume:133 year:2019 pages:0 https://doi.org/10.1016/j.cageo.2019.104307 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-AFRIKA FID-BIODIV GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_130 42.38 Botanik: Allgemeines VZ AR 133 2019 0 |
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The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. |
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The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. |
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The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97–108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232–251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by ~3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323–327) is derived, and it is shown to improve the computation speed of Bowring's method by ~12%–~27% compared to the conventional formulation. |
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