Open Access

ARTICLE

Continued Fraction Cartesian to Geodetic Coordinate Transformation

J.D. Turner¹ , A. Alnaqeb¹, A. Bani Younes¹

1 Khalifa University, Abu Dhabi, UAE.

Computer Modeling in Engineering & Sciences 2016, 111(3), 257-268. https://doi.org/10.3970/cmes.2016.111.257

Abstract

A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation. Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates, this work explores the use of the satellite ground-track vector as the differential correction variable. The geodetic latitude is recovered by well-known elementary means. A high-accuracy highperformance 3D vector-valued continued fraction iteration is constructed. Rapid convergence is achieved because the starting guess for the ground-track vector provides a maximum error of 30 m for the satellite height above the Earth's surface, throughout the LEO-GEO range of applications. As a result, a single iteration of the continued fraction iteration yields a maximum error for the satellite height of 10

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Keywords

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