NDLI: A non-iterative and non-singular perturbation solution for transforming Cartesian to geodetic coordinates

Content Provider	Springer Nature Link
Author	Turner, James D.
Copyright Year	2008
Abstract	The Cartesian-to-Geodetic coordinate transformation is re-cast as a minimization algorithm for the height of the Satellite above the reference Earth surface. Optimal necessary conditions are obtained that fix the satellite ground track vector components in the Earth surface. The introduction of an artificial perturbation variable yields a rapidly converging second order power series solution. The initial starting guess for the solution provides 3–4 digits of precision. Convergence of the perturbation series expansion is accelerated by replacing the series solution with a Padé approximation. For satellites with heights < 30,000 km the second-order expansions yields ~mm satellite geodetic height errors and ~10−12 rad errors for the geodetic latitude. No quartic or cubic solutions are required: the algorithm is both non-iterative and non-singular. Only two square root and two arc-tan calculations are required for the entire transformation. The proposed algorithm has been measured to be ~41% faster than the celebrated Bowring method. Several numerical examples are provided to demonstrate the effectiveness of the new algorithm.
Starting Page	139
Ending Page	145
Page Count	7
File Format	PDF
ISSN	09497714
Journal	Journal of Geodesy
Volume Number	83
Issue Number	2
e-ISSN	14321394
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-08-06
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geodetic coordinates Coordinate transformation Constrained minimization Artificial perturbation parameter Padé approximant Non-singular Mathematical Applications in Earth Sciences Geophysics/Geodesy
Content Type	Text
Resource Type	Article
Subject	Geophysics Geochemistry and Petrology Computers in Earth Sciences

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