Modeling the Earth's gravity field from precise satellite orbit data: the acceleration approach worksDr Pavel Ditmar^{(1)}and Mr Alexis Van Eck van der Sluijs^{(1)} ^{(1)}
Delft University of Technology,
Kluyverweg 1,
2629 HS Delft,
Netherlands
Abstract A technique has been developed for modeling the Earth's gravity field from precise satellite orbit data. The technique makes use of the orbitderived accelerations, which can be related to the gravity field in compliance with Newton's second law. The goals of the presentation is to compare this technique with others in terms of the modeling accuracy and CPU time. We demonstrate that the general opinion about a poor performance of the acceleration approach is nothing but a myth. The key elements of the developed technique are as follows: 1) A clear distinction between the observations and the observation points. It is proposed to take the observation points from the reduced dynamic satellite orbit and to derive the observations (satellite accelerations) from the kinematic orbit. The latter is motivated by the following considerations: (i) the kinematic orbit, contrary to the reduceddynamic one, is not biased towards the reference model; (ii) the stochastic properties of the data can be estimated much easier. 2) Usage of a simple threepoint differentiation scheme for deriving the satellite accelerations. Naturally, such accelerations cannot be treated as pointwise. The functional model, however, can be easily adapted to such data. The motivation for using the 3point scheme: (i) fewer orbit data are lost at the vicinity of gaps and (ii) the noise propagation "orbit > accelerations" is straightforward. 3) Exploitation of the preconditioned conjugate gradient (PCCG) method for computing the Earth's gravity field parameters (spherical harmonic coefficients) from the data. In this way, the explicit computation of the normal matrix can be avoided. Thanks to that, both the CPU time and the required computer memory is reduced. 4) Formation of the preconditioner on the basis of a blockdiagonal approximation of the normal matrix, which is derived under the Colombo's assumptions about the satellite orbit. Thanks to that, the number of PCCG iterations is reduced to only a few (10 to 30). 5) Exact data weighting by means of a lowlevel conjugate gradient scheme (including the case of a data set with gaps). The following situations are distinguished: (i) noise in the accelerations is a propagated noncorrelated nonstationary noise in the orbit data; (ii) noise in the accelerations is stationary and colored (such noise may be caused, e.g., by the accelerometer inaccuracies); (iii) noise in the acceleration is a combination of scenarios (i) and (ii). The developed technique is compared analytically and numerically with: (i) the "classical" approach based on the integration of variational equations; (ii) the energy balance approach (EBA). It is shown that developed technique is as accurate as the classical one but is orders of magnitude faster. Furthermore, the developed technique is more accurate than the EBA. The latter is explained by the fact that the EBA is only sensitive to the alongtrack force component. The other force components, which may also contain valuable information about the Earth's gravity field, are ignored because they do no work and do not contribute to the energy balance.
Keywords: ESA European Space Agency  Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry
