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

journal contribution
posted on 2023-06-07, 22:31 authored by W Freeden, K Hesse
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).

History

Publication status

  • Published

Journal

Studia Scientiarum Mathematicarum Hungarica

ISSN

0081-6906

Issue

1-2

Volume

39

Page range

37-74

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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