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Polynomial approximation for fast generation of associated Legendre functions
Arak University of Technology, Department of Surveying Engineering, Arak, Iran.
University of Tehran, School of Surveying and Geospatial Engineering, College of Engineering, Tehran, Iran.
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0003-0067-8631
2018 (English)In: Acta Geodaetica et Geophysica, ISSN 2213-5812, Vol. 53, no 2, p. 275-293Article in journal (Refereed) Published
Abstract [en]

Today high-speed computers have simplified many computational problems, but fast techniques and algorithms are still relevant. In this study, the Hermitian polynomial approximation is used for fast evaluation of the associated Legendre functions (ALFs). It has lots of applications in geodesy and geophysics. This method approximates the ALFs instead of computing them by recursive formulae and generate them several times faster. The approximated ALFs by the Newtonian polynomials are compared with Hermitian ones and their differences are discussed. Here, this approach is applied for computing a global geoid model point-wise from EGM08 to degree and order 2160 and in propagating the orbit of a low Earth orbiting satellite. Our numerical results show that the CPU-time decreases at least two times for orbit propagation, and five times for geoid computation comparing to the case where recursive formulae for generation of ALFs are used. The approximation error in the orbit computation is at a sub-millimeter level over two weeks and that the computed geoid 0.01 mm, with a maximum of 1 mm

Place, publisher, year, edition, pages
Springer, 2018. Vol. 53, no 2, p. 275-293
Keywords [en]
Orbits, Approximation errors; Associated Legendre functions; Computational problem; Hermite polynomials; High speed computers; Low earth orbiting satellites; Newton polynomials; Orbit propagation, Polynomial approximation
National Category
Geophysics
Research subject
ENGINEERING, Geodesy
Identifiers
URN: urn:nbn:se:hv:diva-12479DOI: 10.1007/s40328-018-0216-1ISI: 000445505100007Scopus ID: 2-s2.0-85047242977OAI: oai:DiVA.org:hv-12479DiVA, id: diva2:1219158
Note

First Online: 28 April 2018

Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2019-10-22Bibliographically approved

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Eshagh, Mehdi

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