Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere |
| |
| Authors: | A Albertella F Sansò N Sneeuw |
| |
| Institution: | DIIAR – Politecnico di Milano, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy e-mail: alberta@ipmtf4.topo.polimi.it; Tel.: +39 2 2399 6504; Fax: +39 2 2399 6530, IT
Institut für Astronomische und Physikalische Geod?sie, Technische Universit?t München, D-80290 München, Germany e-mail: sneeuw@step.iapg.verm.tu-muenchen.de; Tel.: +48 89 28923193, Fax: +48 89 28923178, DE
|
| |
| Abstract: | The Slepian problem consists of determining a sequence of functions that constitute an orthonormal basis of a subset of ℝ
(or ℝ2) concentrating the maximum information in the subspace of square integrable functions with a band-limited spectrum. The same
problem can be stated and solved on the sphere. The relation between the new basis and the ordinary spherical harmonic basis
can be explicitly written and numerically studied. The new base functions are orthogonal on both the subspace and the whole
sphere. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case
of polar data gaps, even in the presence of aliasing. This tool turns out to be a natural solution to the polar gap problem
in satellite geodesy. It enables capture of the maximum amount of information from non-polar gravity field missions.
Received: 10 June 1998 / Accepted: 20 May 1999 |
| |
| Keywords: | , Slepian,Polar gap,Spherical harmonics |
| 本文献已被 SpringerLink 等数据库收录！ |
|
