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On the Numerical Implementation of a Perturbation Method for Satellite Gravity Mapping

  • Christopher Jekeli
  • Nlingi Habana
Chapter
Part of the International Association of Geodesy Symposia book series

Abstract

In 2008 P. Xu (Celest Mech Dyn Astron, 100:231–249) proposed a strictly kinematic perturbation method for determining the Earth’s gravitational field from continuous satellite tracking. The main idea is to process orbital arcs of arbitrary length, thus minimizing superfluous parameter estimation associated with stitching together short-arc solutions, and at the same time formulating the problem in terms of standard linear parameter estimation. While the original formulation appears mathematically robust, its nested quadruple along-track integrations are computationally challenging. We reduce the formulation to double integrals and show that the method is numerically not feasible as originally envisaged. On the other hand, by abandoning the rigorous Gauss-Markov formalism, we show the numerical feasibility of processing multiple-day orbital arcs. The methodology lends itself to high-low and low-low satellite-to-satellite tracking, or combinations thereof, as for GRACE-like systems.

Keywords

GNSS satellite tracking Gravitational field estimation Numerical orbit integration Satellite perturbation theory 

Notes

Acknowledgments

The authors wish to thank Prof. Torsten Mayer-Gürr and an anonymous reviewer for valuable comments that improved the manuscript.

References

  1. Kondo J (1991) Integral equations. Clarendon Press, OxfordGoogle Scholar
  2. Krogh FT (1970) VODQ/SVDQ/DVDQ - variable order integrators for the numerical solution of ordinary differential equations. Tech. Util. Doc. No. CP-2308, NPO-11643, JPL, PasadenaGoogle Scholar
  3. Mayer-Gürr T (2006) Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE. Dissertation, Friedrich-Wilhelms-Universität, Bonn, GermanyGoogle Scholar
  4. Naeimi M, Flury J (eds) (2017) Global gravity field modeling from satellite-to-satellite tracking. Lecture Notes in Earth System Sciences. Springer, BerlinGoogle Scholar
  5. Xu P (2008) Position and velocity perturbations for the determination of geopotential from space geodetic measurements. Celest Mech Dyn Astron 100:231–249Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Christopher Jekeli
    • 1
  • Nlingi Habana
    • 1
  1. 1.Division of Geodetic ScienceSchool of Earth Sciences, Ohio State UniversityColumbusUSA

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