A strict transformation from Cartesian to geodetic coordinates

Lars Erik Sjöberg

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Historical Geography and Cartography GNSS positioning and interference Mathematics and Applications

Abstract

An algorithm is derived to transform Cartesian coordinates to geodetic coordinates by employing ellipsoidal coordinates in an intermediate step. The algorithm is comparatively simple and stable in all steps for any point in space outside a geocentric sphere of an approximate radius of 43 km.

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References

1989Accurate algorithms to transform geocentric to geodetic coordinates 2002Direct transformation from geocentric coordinates to geodetic coordinates 2004Computing geodetic coordinates from geocentric coordinates 1991A New Direct Solution of the Transformation Problem of Cartesian into Ellipsoidal Coordinates

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2019Cartesian to geodetic coordinates conversion on an oblate spheroid using the bisection method 2022A new algebraic solution for transforming Cartesian to geodetic coordinates

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