On the multiscale solution of satellite problems by use of locally supported kernel functions corresponding to equidistributed data on spherical orbits

Freeden, W and Hesse, K (2002) On the multiscale solution of satellite problems by use of locally supported kernel functions corresponding to equidistributed data on spherical orbits. Studia Scientiarum Mathematicarum Hungarica, 39 (1-2). pp. 37-74. ISSN 0081-6906

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Abstract

Being interested in (rotation-)invariant pseudodifferential equations of satellite problems corresponding to spherical orbits, we are reasonably led to generating kernels that depend only on the spherical distance, i.e., in the language of modern constructive approximation form spherical radial basis functions. In this paper approximate identities generated by such (rotation-invariant) kernels which are additionally locally supported are investigated in detail from theoretical as well as numerical point of view. So-called spherical difference wavelets are introduced. The wavelet transforms are evaluated by the use of a numerical integration rule, that is based on Weyl's law of equidistribution. This approximate formula is constructed such that it can cope with millions of (satellite) data. The approximation error is estimated on the orbital sphere. Finally, we apply the developed theory to the problems of satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG).

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Kerstin Hesse
Date Deposited: 06 Feb 2012 19:18
Last Modified: 04 Apr 2012 08:44
URI: http://sro.sussex.ac.uk/id/eprint/20028
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