ISSN:
1573-1626
Keywords:
GPS-satellite-to-satellite tracking
;
uniqueness
;
formulation as integral equation
;
regularization by wavelets
Source:
Springer Online Journal Archives 1860-2000
Topics:
Architecture, Civil Engineering, Surveying
,
Geosciences
,
Physics
Notes:
Abstract The purpose of GPS-satellite-to-satellite tracking (GPS-SST) is to determine the gravitational potential at the earth's surface from measured ranges (geometrical distances) between a low-flying satellite and the high-flying satellites of the Global Positioning System (GPS). In this paper, GPS-satellite-to-satellite tracking is reformulated as the problem of determining the gravitational potential of the earth from given gradients at satellite altitude. The uniqueness and stability of the solution are investigated. The essential tool is to split the gradient field into a normal part (i.e. the first-order radial derivative) and a tangential part (i.e. the surface gradient). Uniqueness is proved for polar, circular orbits corresponding to both types of data (first radial derivative and/or surface gradient). In both cases gravity recovery based on satellite-to-satellite tracking turns out to be an exponentially ill-posed problem. Regularization in terms of spherical wavelets is proposed as an appropriate solution method, based on the knowledge of the singular system. Finally, the extension of this method is generalized to a nonspherical earth and a non-spherical orbital surface, based on combined terrestrial and satellite data.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1023365209883
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