Modeling the Earth's gravity field from precise satellite orbit data: the acceleration approach works
Dr Pavel Ditmar(1)and Mr Alexis Van Eck van der Sluijs(1)
Delft University of Technology,
2629 HS Delft,
A technique has been developed for modeling the Earth's gravity
field from precise satellite orbit data. The technique makes use of the
orbit-derived 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
reduced-dynamic 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 three-point differentiation scheme for deriving
the satellite accelerations. Naturally, such accelerations cannot be
treated as point-wise. The functional model, however, can be easily
adapted to such data. The motivation for using the 3-point 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 pre-conditioned 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 pre-conditioner on the basis of a block-diagonal
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 low-level 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 non-correlated non-stationary 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 along-track 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,