Skip to main content
SpringerLink
Log in

Universal Algorithm for Inverting the Cartesian to Geodetic Transformation

  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

A singularity-free solution is presented for inverting the Cartesian to Geodetic transformation. Two rapidly converging generalized continued fraction algorithms are presented for handling applications spanning the LEO to GEO range of applications. Comparisons with state-of-the-art algorithms are provided for solution accuracy and run-time performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. FUKUSHIMA, T. “Fast Transform from Geocentric to Geodetic Coordinate,” Journal of Geodesics, Vol. 73, 1999. pp. 603–610.

    Article  MATH  Google Scholar 

  2. BORKOWSKI, K.M. “Accurate Algorithms to Transform Geocentric to Geodetic Coordinates,” Bulletin for Geodesics, Vol. 63, 1989, pp. 50–56.

    Article  Google Scholar 

  3. POLLARD, J. “Iterative Vector Methods for Computing Geodetic Latitude and Height from Rectangular Coordinates,” Journal of Geodesics, Vol. 76, 2002, pp. 36–40.

    Article  MATH  Google Scholar 

  4. BOWRING, B.R. “Transformation from Spatial to Geographical Coordinates,” Survey Reviews, Vol. 181, 1976, pp. 323–327.

    Article  Google Scholar 

  5. VANICEK, P. and KRAKIWSKI, E.J. (1982). Geodesy: The Concepts, North Holland, Amsterdam, 1982.

    Google Scholar 

  6. PICK, M. “Closed Formulae for Transformation of the Cartesian Coordinate System into a System of Geodetic Coordinates,” Studies in Geophysics and Geodesy, Vol. 29, No. 2, 1985.

  7. FOTIOU, A. “A Pair of Closed Expressions to Transform Geocentric to Geodetic Coordinates,” Zeitschrit fur Vermessungswesen, Vol. 123, No. 4, 1998, pp. 133–135.

    Google Scholar 

  8. VERMEILLE, H. “Direct Transformation from Geocentric Coordinates to Geodetic Coordinates,” Journal of Geodesics, Vol. 76, 2002, pp. 451–454.

    Article  MATH  Google Scholar 

  9. HEISKANEN, W.A. and MORITZ, H. Physical Geodesy, W.H. Freeman and Co., San Francisco, Vol. 181, 1967.

    Google Scholar 

  10. KLEUSBER, A. and TEUNISSEN, P. (editors), GPS for Geodesy, Springer, Berlin, 1996.

    Google Scholar 

  11. HOFMANN-WELLENHOF, B., LICHTENEGGER, H., and COLLINS, J. GPS Theory and Practice, Springer, Berlin, 1997.

    Google Scholar 

  12. TORGE, W. Geodesy. 3rd Edition. De Gruyter, Berlin, 2001.

    Book  MATH  Google Scholar 

  13. LIN, K.C. and WANG, K.C. “Transformations from Geocentric Coordinates using Newton’s Iteration,” Bulletins in Geodesy, Vol. 69, 1995, pp. 14–17.

    Google Scholar 

  14. LUPASH, L.O. “A New Algorithm for the Computation of the Geodetic Coordinates as a Function of Earth-Centered Earth-Fixed Coordinates,” Journal of Guidance, Control and Dynamics, Vol. 8, No. 6, 1985, pp. 787–789.

    Article  Google Scholar 

  15. FELTENS, J. “Vector Methods to Compute Azimuth, Elevation, Ellipsoidal Normal, and the Cartesian (X, Y, Z) to geodetic (ϕ,λ,h) Transformation,” Journal of Geodesics, Vol. 82, No. 8, 2008, pp. 493–504.

    Article  Google Scholar 

  16. ZHANG, C.C., HSU, H.T., WU, X.P., LI, S.S., WANG, Q.B., CHAI, H.Z., and DU, L. “An Alternative Algebraic Algorithm to Transform Cartesian to Geodetic Coordinates,” Journal of Geodesics, Vol. 79, 2005, pp. 413–420.

    Article  MATH  Google Scholar 

  17. SHU, C. and LI, F. “An Iterative Algorithm to Compute Geodetic Coordinate,” Computers & Geosciences, Vol. 36, No. 9, 2010, pp. 1145–1149.

    Article  MathSciNet  Google Scholar 

  18. FUKUSHIMA, T. “Transformation from Cartesian to Geodetic Coordinates Accelerated by Halley’s Method,” Journal of Geodesics, Vol. 79, No. 12, 2006, pp. 689–693.

    Article  Google Scholar 

  19. TURNER, J.D. “A Non-Iterative and Non-Singular Perturbation Solution for Transforming Cartesian to Geodetic Coordinates,” Journal of Geodesics, Vol. 83, No. 2, 2009, pp. 139–145.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aerospace Engineering, Texas A&M University, USA

    James D. Turner (Research Professor) & John L. Junkins (Distinguished Professor)

Authors
  1. James D. Turner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John L. Junkins
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Turner, J.D., Junkins, J.L. Universal Algorithm for Inverting the Cartesian to Geodetic Transformation. J of Astronaut Sci 58, 429–443 (2011). https://doi.org/10.1007/BF03321178

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03321178

Keywords

Search

Navigation