Analysis of the Earth’s Gravitational Field from Semi-Continuous Ephemeris of a Low Earth Orbiting GPS-Tracked Satellite of Type CHAMP, GRACE or GOCE

Austen, G.; Grafarend, Erik W.; Reubelt, T.

doi:10.1007/978-3-662-04709-5_51

Cited by 28 publications

(12 citation statements)

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“…The model error as well as accuracy estimates from error simulations of our method have already been tested in previous papers by Austen and Reubelt (2000), Austen et al (2002) and Reubelt et al (2002). There, a RMS of the geoid for an error-free simulation of a 1-week-arc (modelerror) in the sub-mm range for degree/order 30/30 was obtained, which is sufficient for CHAMP-data analysis.…”

Section: Resultsmentioning

confidence: 80%

“…There, a RMS of the geoid for an error-free simulation of a 1-week-arc (modelerror) in the sub-mm range for degree/order 30/30 was obtained, which is sufficient for CHAMP-data analysis. From an error simulation study with the variance of coordinates σ X = 10 cm and the correlation of ρ = 0.99, which seems to be a realistic for kinematic orbits according to Reubelt et al (2002) a RMS of the geoid of 23 cm was received. Regarding the complete CHAMP-mission, a geoid accuracy of below 10 cm seems to be possible, which is at least a confirmation of present geoid models.…”

Section: Resultsmentioning

confidence: 99%

“…In order to set up an adequate error-simulation function for absolute ephemeris that considers high correlations between adjacent ephemeris, a Gauss-Markov process has been introduced. This process, successfully used by Grafarend and Vanicek (1980) in the weight estimation in levelling and applied to our topic by Austen et al (2002) has the following properties of the simulated errors of absolute coordinates e i : standard deviation σ (e i ) = 10 cm, correlation ρ = 0.99. The simulated errors e n+1,n of baselines are received as differences of position errors e i .…”

Section: Influence Of Gps Measurement Errorsmentioning

confidence: 99%

“…The errors of the Newton interpolated accelerations obtained from a 30 s sampling time lie within an accuracy of a few mGal. Due to the immense amount of observations from a 5 years mission duration of CHAMP this accuracy is sufficient to estimate a long wavelength geoid with an accuracy of at least one dm, as estimated from simulations (Reubelt et al, 2002). More details on the derivation of the vector-valued second order functional of Newton's interpolation formula can be found in Austen and Reubelt (2000) and Austen et al (2002).…”

Section: Influence Of Gps Measurement Errorsmentioning

confidence: 99%

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Space Gravity Spectroscopy - determination of the Earth’s gravitational field by means of Newton interpolated LEO ephemeris Case studies on dynamic (CHAMP Rapid Science Orbit) and kinematic orbits

2003

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Abstract. An algorithm for the (kinematic) orbit analysis of a Low Earth Orbiting (LEO) GPS tracked satellite to determine the spherical harmonic coefficients of the terrestrial gravitational field is presented. A contribution to existing long wavelength gravity field models is expected since the kinematic orbit of a LEO satellite can nowadays be determined with very high accuracy in the range of a few centimeters. To demonstrate the applicability of the proposed method, first results from the analysis of real CHAMP Rapid Science (dynamic) Orbits (RSO) and kinematic orbits are illustrated. In particular, we take advantage of Newton's Law of Motion which balances the acceleration vector and the gradient of the gravitational potential with respect to an Inertial Frame of Reference (IRF). The satellite's acceleration vector is determined by means of the second order functional of Newton's Interpolation Formula from relative satellite ephemeris (baselines) with respect to the IRF. Therefore the satellite ephemeris, which are normally given in a Body fixed Frame of Reference (BRF) have to be transformed into the IRF. Subsequently the Newton interpolated accelerations have to be reduced for disturbing gravitational and non-gravitational accelerations in order to obtain the accelerations caused by the Earth's gravitational field. For a first insight in real data processing these reductions have been neglected. The gradient of the gravitational potential, conventionally expressed in vector-valued spherical harmonics and given in a Body Fixed Frame of Reference, must be transformed from BRF to IRF by means of the polar motion matrix, the precession-nutation matrices and the Greenwich Siderial Time Angle (GAST). The resulting linear system of equations is solved by means of a least squares adjustment in terms of a Gauss-Markov model in order to estimate the spherical harmonics coefficients of the Earth's gravitational field. Key words. space gravity spectroscopy, spherical harmonics series expansion, GPS tracked LEO satellites, kinematicCorrespondence to: T. Reubelt (reubelt@gis.uni-stuttgart.de) orbit analysis, Newton interpolation Reference framesFirst, the beforehand mentioned transformation between the Inertial Reference Frame and the Body Fixed Reference Frame is considered for this contribution more an issue of the operational point of view (software development) since the underlying theoretical aspects are well known, eg. McCarthy (1996). The resulting transformation matrix R(t) contains the parameters of nutation, precession, polar motion and Greenwich siderial time. Corrections for the nutation model and the parameters for polar motion and Greenwich siderial time are delivered by the Bulletins of the International Earth Rotation Service (IERS). Representation of the Earth's gravitational field -the spherical harmonics series expansionFor the description of the gravitational field of the Earth we use a spherical harmonics series expansion. Equation (1) defines this series expansion of the gravitational potential U...

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Section: Resultsmentioning

confidence: 80%

Section: Resultsmentioning

confidence: 99%

Section: Influence Of Gps Measurement Errorsmentioning

confidence: 99%

Section: Influence Of Gps Measurement Errorsmentioning

confidence: 99%

See 2 more Smart Citations

Space Gravity Spectroscopy - determination of the Earth’s gravitational field by means of Newton interpolated LEO ephemeris Case studies on dynamic (CHAMP Rapid Science Orbit) and kinematic orbits

2003

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“…Though different groups have derived their method making use of the equation of motion, no detailed description of the method or essentially different methods under the same name has been found (e.g. [1]; [17]). Elaborated description of the method as derived by us and numerical results for CHAMP observations are introduced and discussed in the present study.…”

Section: Introductionmentioning

confidence: 99%

Determination of a CHAMP gravity model based on the Newtonian equation of motion

Földváry

Bokor²

2010

Per. Pol. Civil Eng.

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As the CHAMP has been launched as the first of the gravity satellites of the 2000s, its processing has been a real challenge for the geodetic community. Several methods have been developed for gravity field modelling based on different theoretical backgrounds. In this study the feasibility of the direct use of the Newtonian equation of motion has been studied. Then numerical results for 2 years of CHAMP observations are presented. Though the method failed to provide the best CHAMPonly gravity field model, it has been found to be generally feasible, and worth for using of other gravity satellite data. KeywordsNewtonian equation of motion · gravity satellite · CHAMP · gravity field modelling Acknowledgement This work is connected to the scientific program of the "Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" project.

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The Rotation of the Gravity Potential on the Earth's Gravity Field Recovery

Cheng

Xsu

2006

Chinese J of Geophysics

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We analyze the effect of approximate velocity in the formula of the rotation of the gravitational potential. The effect of the rotation of the gravitational potential is caused by the Earth rotation. The difference between the satellite ephemeris's velocity and numerical integral's velocity is computed. The ephemeris data come from GFZ's Rapid Science Orbit, TUM's Reduced-Dynamic Orbit, GFZ's Post-processed Science Orbit respectively. The integral data are obtained from reference gravity field model EGM96, EIGEN2, EIGEN-CG01C respectively. The fitting between ephemeris velocity and integral velocity from EIGEN2 reference gravity field model is better than that from EGM96 and EIGEN-CG01C model. The variations of velocity difference show obvious periodicity, which coincides with the satellite orbit period. When 1m 2 /s 2 for the disturbing potential, or 2mm/s for the approximate velocity in the formula of the rotation of the gravitational potential is required, only the satellite orbit data not satisfying the potential rotation computing demand need to be rejected in GFZ's Rapid Science Orbit and TUM's Reduced-Dynamic Orbit. If the disturbing potential 0.5m 2 /s 2 is desired at satellite track, the satellite velocity required by the formula of the rotation of the gravitational potential should be re-computed or GFZ's Post-processed Science Orbit is adopted.

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Analysis of the Earth’s Gravitational Field from Semi-Continuous Ephemeris of a Low Earth Orbiting GPS-Tracked Satellite of Type CHAMP, GRACE or GOCE

Cited by 28 publications

References 3 publications

Space Gravity Spectroscopy - determination of the Earth’s gravitational field by means of Newton interpolated LEO ephemeris Case studies on dynamic (CHAMP Rapid Science Orbit) and kinematic orbits

Space Gravity Spectroscopy - determination of the Earth’s gravitational field by means of Newton interpolated LEO ephemeris Case studies on dynamic (CHAMP Rapid Science Orbit) and kinematic orbits

Determination of a CHAMP gravity model based on the Newtonian equation of motion

The Rotation of the Gravity Potential on the Earth's Gravity Field Recovery

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