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Transforming Geocentric Cartesian Coordinates to Geodetic Coordinates by a New Initial Value Calculation Paradigm | ||
| فیزیک زمین و فضا | ||
| مقاله 2، دوره 44، شماره 4، دی 1397، صفحه 19-28 اصل مقاله (322.34 K) | ||
| شناسه دیجیتال (DOI): 10.22059/jesphys.2018.246251.1006946 | ||
| نویسندگان | ||
| Norollah Tatar1؛ Saeed Farzaneh* 2 | ||
| 1Ph.D. Student, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Iran | ||
| 2Assistant Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Iran | ||
| چکیده | ||
| Transforming geocentric Cartesian coordinates (X, Y, Z) to geodetic curvilinear coordinates (φ, λ, h) on a biaxial ellipsoid is one of the problems used in satellite positioning, coordinates conversion between reference systems, astronomy and geodetic calculations. For this purpose, various methods including Closed-form, Vector method and Fixed-point method have been developed. In this paper, a new paradigm for calculation of initial values is presented. According to the new initial values, two state of the art iterative methods are modified to calculate the geodetic height and the geodetic latitude accurately and without iteration. The results show that for those points with height values between -10 to 1,000,000 km (30-fold more than the altitude of GPS satellites), the maximum error of the calculated height and geodetic latitude is less than 1.5×10-8 m and 1×10-14 rad (error lower than 0.001 mm in horizontal), respectively. | ||
| کلیدواژه‌ها | ||
| Geodetic coordinate transformation؛ Cartesian geocentric coordinate؛ Curvilinear geodetic coordinate | ||
| عنوان مقاله [English] | ||
| Transforming Geocentric Cartesian Coordinates to Geodetic Coordinates by a New Initial Value Calculation Paradigm | ||
| نویسندگان [English] | ||
| Norollah Tatar1؛ Saeed Farzaneh2 | ||
| 1Ph.D. Student, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Iran | ||
| 2Assistant Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Iran | ||
| چکیده [English] | ||
| Transforming geocentric Cartesian coordinates (X, Y, Z) to geodetic curvilinear coordinates (φ, λ, h) on a biaxial ellipsoid is one of the problems used in satellite positioning, coordinates conversion between reference systems, astronomy and geodetic calculations. For this purpose, various methods including Closed-form, Vector method and Fixed-point method have been developed. In this paper, a new paradigm for calculation of initial values is presented. According to the new initial values, two state of the art iterative methods are modified to calculate the geodetic height and the geodetic latitude accurately and without iteration. The results show that for those points with height values between -10 to 1,000,000 km (30-fold more than the altitude of GPS satellites), the maximum error of the calculated height and geodetic latitude is less than 1.5×10-8 m and 1×10-14 rad (error lower than 0.001 mm in horizontal), respectively. | ||
| کلیدواژه‌ها [English] | ||
| Geodetic coordinate transformation, Cartesian geocentric coordinate, Curvilinear geodetic coordinate | ||
| مراجع | ||
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Borkowski, K. M., 1989, Accurate algorithms to transform geocentric to geodetic coordinates. Bulletin géodésique, 63, 50-56. Bowring, B. R., 1976, Transformation from spatial to geographical coordinates. Survey review, 23, 323-327. Civicioglu, P., 2012, Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Computers & Geosciences, 46, 229-247. Featherstone, W. and Claessens, S., 2008, Closed-form transformation between geodetic and ellipsoidal coordinates. Studia geophysica et geodaetica, 52, 1-18. Feltens, J., 2008, Vector methods to compute azimuth, elevation, ellipsoidal normal, and the Cartesian (X, Y, Z) to geodetic (φ, λ, h) transformation. Journal of Geodesy, 82, 493-504. Fukushima, T., 1999, Fast transform from geocentric to geodetic coordinates. Journal of Geodesy, 73, 603-610. Fukushima, T., 2006, Transformation from Cartesian to geodetic coordinates accelerated by Halley’s method. Journal of Geodesy, 79, 689-693. Heiskanen, W. A. and Moritz, H., 1967, Physical Geodesy. San Francisco: Freeman. Jones, G., 2002, New solutions for the geodetic coordinate transformation. Journal of Geodesy, 76, 437-446. Kumi-Boateng, B. and Ziggah, Y. Y., 2016, Accuracy assessment of cartesian (X, Y, Z) to geodetic coordinates (φ, λ, h) transformation procedures in precise 3D coordinate transformation–A case study of Ghana geodetic reference network. Journal of Geosciences and Geomatics, 4, 1-7. Laskowski, P., 1991, Is Newton's iteration faster than simple iteration for transformation between geocentric and geodetic coordinates? Bulletin Géodésique, 65, 14-17. Ligas, M. and Banasik, P., 2011, Conversion between Cartesian and geodetic coordinates on a rotational ellipsoid by solving a system of nonlinear equations. Geodesy and Cartography, 60, 145-159. Lin, K.-C. and Wang, J., 1995, Transformation from geocentric to geodetic coordinates using Newton's iteration. Bulletin Géodésique, 69, 300-303. Pollard, J., 2002, Iterative vector methods for computing geodetic latitude and height from rectangular coordinates. Journal of Geodesy, 76, 36-40. Shu, C. and Li, F., 2010, An iterative algorithm to compute geodetic coordinates. Computers & Geosciences, 36, 1145-1149. Turner, J. D., 2009, A non-iterative and non-singular perturbation solution for transforming Cartesian to geodetic coordinates. Journal of Geodesy, 83, 139-145. Vaniček, P. and Krakiwsky, E. J., 1986, Geodesy: The Concepts. Amsterdam: North Holland. Vermeille, H., 2002, Direct transformation from geocentric coordinates to geodetic coordinates. Journal of Geodesy, 76, 451-454. Vermeille, H., 2004, Computing geodetic coordinates from geocentric coordinates. Journal of Geodesy, 78, 94-95. Vermeille, H., 2011, An analytical method to transform geocentric into geodetic coordinates. Journal of Geodesy, 85, 105-117. Zhang, C., Hsu, H., Wu, X., Li, S., Wang, Q., Chai, H. and Du, L., 2005, An alternative algebraic algorithm to transform Cartesian to geodetic coordinates. Journal of Geodesy, 79, 413-420. | ||
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