Details

Title

Conversion between Cartesian and geodetic coordinates on a rotational ellipsoid by solving a system of nonlinear equations

Journal title

Geodesy and Cartography

Yearbook

2011

Volume

vol. 60

Numer

No 2

Publication authors

Keywords

Cartesian and geodetic coordinates ; rotational ellipsoid ; Newton’s method ; coordinate transformation

Divisions of PAS

Nauki Techniczne

Abstract

A new method to transform from Cartesian to geodetic coordinates is presented. It is based on the solution of a system of nonlinear equations with respect to the coordinates of the point projected onto the ellipsoid along the normal. Newton’s method and a modification of Newton’s method were applied to give third-order convergence. The method developed was compared to some well known iterative techniques. All methods were tested on three ellipsoidal height ranges: namely, (-10 – 10 km) (terrestrial), (20 – 1000 km), and (1000 – 36000 km) (satellite). One iteration of the presented method, implemented with the third-order convergence modified Newton’s method, is necessary to obtain a satisfactory level of accuracy for the geodetic latitude ( σ φ < 0.0004”) and height ( σ h < 10 − 6 km, i.e. less than a millimetre) for all the heights tested. The method is slightly slower than the method of Fukushima (2006) and Fukushima’s (1999) fast implementation of Bowring’s (1976) method.

Publisher

Commitee on Geodesy PAS

Date

2011

Type

Artykuły / Articles

Identifier

ISSN 2080-7636

References

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DOI

10.2478/v10277-012-0013-x

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