Transformation of Cartesian to Geodetic Coordinates without Iterations
Publication: Journal of Surveying Engineering
Volume 126, Issue 1
Abstract
A noniterative transformation of earth-centered, earth-fixed (ECEF) Cartesian coordinates to geodetic coordinates of a point is presented. The transformation is based on ellipsoidal coordinates. The ECEF Cartesian coordinates of a point are first transformed to the ellipsoidal coordinates by closed formulas. Second, the reduced latitude referred to the reference ellipsoid takes the approximation to the reduced latitude referred to a confocal ellipsoid. Third, the approximation can be improved by a correction for the purpose of higher accuracy. The accuracy of the transformation is analyzed in the paper and it is shown that the derived geodetic coordinates are sufficiently accurate for the most geodetic purposes.
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References
1.
Benning, W. (1987). “Iterative ellipsoidische Lotfusspunktberechnung.” AVN, 7/1987, 256–260.
2.
Borkowski, K. M. (1987). “Transformation of geocentric to geodetic coordinates without approximations.” Astrophys. Space Sci., 139, 1–4.
3.
Borkowski, K. M. (1987). “Accurate algorithms to transform geocentric to geodetic coordinates.” Bull. Geod., 63, 50–56.
4.
Bowring, B. R. ( 1976). “Transformation from spatial to geographical coordinates.” Surv. Rev., 23, 323–327.
5.
Bowring, B. R. (1985). “The accuracy of geodetic latitude and height equations.” Surv. Rev., 28, 202–206.
6.
Grafarend, E. W., and Lohse, P. (1991). “The minimal distance mapping of the topographic surface onto the (reference) ellipsoid of revolution.” Manu. Geod., 16, 92–110.
7.
Heck, B. (1987). Rechenverfahren und Auswertemodelle der Landesvermessung. Wichmann Verlag, Karlsruhe, Germany.
8.
Heikkinen, M. (1982). “Geschlossene Formeln zur Berechnung raeumlicher geodaetischer Koordinaten aus rechtwinkligen Koordinaten.” ZfV, 5/1982, 207–211.
9.
Heiskanen, W. A., and Moritz, H. (1967). Physical geodesy. W. H. Freeman and Co., San Francisco.
10.
Hoffman-Wellenhof, B., Lichtenegger, H., and Collins, J. (1992). Global positioning system: Theory and practice. Springer-Verlag, Wien, Austria.
11.
Lapaine, M. ( 1990). “A new direct solution of the transformation problem of Cartesian into ellipsoidal coordinates.” Determination of the geoid: Present and future, R. H. Rapp and F. Sanso, eds., Springer, New York, 395–404.
12.
Ozone, M. I. (1985). “Non-iterative solution of the ϕ equation.” Surv. Map., 45, 169–171.
13.
Penev, P. (1978). “The transformation of rectangular coordinates into geographical by closed formulas.” Geod. Map. Photo., 20, 175–177.
14.
Soler, T., and Hothem, L. D. (1989). “Important parameters used in geodetic transformations.”J. Surv. Engrg., ASCE, 115, 414–417.
15.
Torge, W. (1991). Geodesy. Walter de Gruyter, Berlin.
16.
Vanicek, P., and Krakiwsky, E. (1986). Geodesy: The concepts. North-Holland, Amsterdam.
17.
Vincenty, T. (1978). “Verleich zweier Verfahren zur Berechnung der geodaetischen Breite und Hoehe aus rechwinkligen Koordinaten.” AVN, 7/1978, 269–270.
18.
Vincenty, T. (1980). “Zur raeumlich-ellipsoidischen Koordinaten-Transformation.” ZfV, 11/1980, 519–521.
19.
Wolf, P. R., and Ghilani, Ch.D. (1997). Adjustment computations: Statistics and least squares in surveying and GIS. Wiley, New York.
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Received: Jan 6, 1998
Published online: Feb 1, 2000
Published in print: Feb 2000
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