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Solving the Direct and Inverse Geodetic Problems on the Ellipsoid by Numerical Integration
KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
2012 (English)In: Journal of Surveying Engineering, ISSN 0733-9453, E-ISSN 1943-5428, Vol. 138, no 1, 9-16 p.Article in journal (Refereed) Published
Abstract [en]

Taking advantage of numerical integration, we solve the direct and inverse geodetic problems on the ellipsoid. In general, the solutions are composed of a strict solution for the sphere plus a correction to the ellipsoid determined by numerical integration. Primarily the solutions are integrals along the geodesic with respect to the reduced latitude or azimuth, but these techniques either have problems when the integral passes a vertex (i.e., point with maximum/minimum latitude of the arc) or a singularity at the equator. These problems are eliminated when using Bessel's idea of integration along the geocentric angle of the great circle of an auxiliary sphere. Hence, this is the preferred method. The solutions are validated by some numerical comparisons to Vincenty's iterative formulas, showing agreements to within 2 x 10(-10) of geodesic length (or 3.1 mm) and 4 x 10(-5) as seconds of azimuth and position for baselines in the range of 19,000 km.

Place, publisher, year, edition, pages
American Society of Civil Engineers (ASCE), 2012. Vol. 138, no 1, 9-16 p.
Keyword [en]
Geodetic surveys, Numerical analysis
National Category
Geophysics
Identifiers
URN: urn:nbn:se:kth:diva-93403DOI: 10.1061/(ASCE)SU.1943-5428.0000061ISI: 000301675500002Scopus ID: 2-s2.0-84858142300OAI: oai:DiVA.org:kth-93403DiVA: diva2:515798
Note
QC 20120416Available from: 2012-06-13 Created: 2012-04-16 Last updated: 2017-12-07Bibliographically approved

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