Satellite to satellite tracking in the space-wise approach


The launch of the champ mission in 2000 has renewed interest in the recovery of the geopotential field from satellite observations which has been a challenging research issue for decades. It was the first dedicated gravity field mission which was followed by the grace spacecrafts. In the grace mission, the high-low (hl-) and the low-low satellite-to-satellite tracking (ll-sst) observations are combined and the resultant observables are expressed in terms of the gravity gradient at the barycenter of two satellites. Each observation at its respective evaluation point can be written in terms of the spherical harmonic coefficients. Consequently, the observations are a sequence of discrete time series which are mathematically related to the unknown coefficients via the corresponding position of the satellites at the evaluation epoch. In this approach, which is called time-wise approach, the determination of unknown coeficients becomes possible after plugging the observations into the mathematical model. Fulfilling the sampling theorem, however, leads to a huge linear system of equations with a large number of unknowns. As an alternative, one can employ the semi-analytical approach which is derived from the time-wise approach by imposing some approximations. Observations are still considered as discrete time series on an ideal geometry with a constant radius and/or constant inclination. The coeficients are reordered and then computed via the lumped coefficients or using 2d fft.
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