Covariance Propagation of Latitude-Dependent Orbit Errors Within the Energy Integral Approach
The satellite mission GOCE (Gravity and steady-state Ocean Circulation Explorer) has the demanding task to map the Earth’s gravity field with unprecedented accuracy by using state-of-the-art observation technologies. The processing strategy of the orbit d
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Covariance Propagation of Latitude-Dependent Orbit Errors Within the Energy Integral Approach H. Goiginger and R. Pail
Abstract The satellite mission GOCE (Gravity and steady-state Ocean Circulation Explorer) has the demanding task to map the Earth’s gravity field with unprecedented accuracy by using state-of-the-art observation technologies. The processing strategy of the orbit data is based on the energy integral approach to determine the long wavelength structure of the gravity field. The final product will consist of the gravity field model in terms of estimated spherical harmonic coefficients and the corresponding error description. The study about covariance propagation of latitudedependent orbit errors is driven by the fact that the GPS receiver used for GOCE might not have full performance in the case of low-elevation GPS satellites, which might lead to a reduced number of observable satellites in higher latitudes. Therefore, the adjustment procedure is extended by a covariance propagation taking this fact into account. The studies have shown that the consistent error propagation can not significantly improve the coefficient solution itself but it rather provides a correct error description of the result.
in the framework of the ESA-funded project “GOCE High-Level Processing Facility” (HPF; Rummel et al., 2004). In the frame of this contract, the “Subprocessing Facility (SPF) 6,000”, a co-operation of TU Graz, Austrian Academy of Sciences, University of Bonn, and TU Munich, under the lead of TU Graz, is responsible for the processing of a spherical harmonic Earth’s gravity field model and the corresponding full variance-covariance matrix from the precise GOCE orbit and from satellite gravity gradiometry (SGG) data. The long wavelength part of the gravity field recovery is based on the energy integral approach (Jekeli, 1999; Visser et al., 2003) where the velocity of the satellite serves as basic input. Since the satellite velocity is not directly observed but derived from the measured satellite position, a suitable numerical differentiation technique should be applied. Results of the investigations on numerical differentiation applying the Taylor-MacLaurin and the Newton-Gregory method can be found in Goiginger and Pail (2006).
21.1 Introduction
21.2 Mathematical Formulation
The scientific data processing of the GOCE mission (ESA, 1999) is performed by the “European GOCE Gravity Consortium” (EGG-C), a consortium of 10 European universities and research institutes,
To derive the velocity of the satellite from the kinematic orbit positions, numerical differentiation methods can be applied. In the following, the TaylorMacLaurin differentiator is introduced, which is based on a Taylor series expansion in each position. Let us consider a set of differentials j at a certain sampling point k,
H. Goiginger () Institute of Navigation and Satellite Geodesy, Graz University of Technology, Graz A8010, Austria e-mail: [email protected]
j
k =
xk+j − xk−j 2jδ
S.P. Mertikas (ed.), Gravity, Geoid and Earth
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