- 1999 (2) (entfernen)
- Multiscale Gravitational Field Recovery from GPS-Satellite-to-Satellite Tracking (1999)
- 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 Posittioning 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. 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. As an appropriate solution method regularization in terms of spherical wavelets is proposed based on the knowledge of the singular system. Finally, the extension of this method is generalized to a non-spherical earth and a non-spherical orbital surface based on combined terrestrial and satellite data material.
- A General Hilbert Space Approach to Wavelets and Its Application in Geopotential Determination (1999)
- A general approach to wavelets is presented within a framework of a separable functional Hilbert space H. Basic tool is the construction of H-product kernels by use of Fourier analysis with respect to an orthonormal basis in H. Scaling function and wavelet are defined in terms of H-product kernels. Wavelets are shown to be 'building blocks' that decorrelate the data. A pyramid scheme provides fast computation. Finally, the determination of the earth's gravitational potential from single and multipole expressions is organized as an example of wavelet approximation in Hilbert space structure.