Journal of Geodesy

, Volume 89, Issue 2, pp 99–110 | Cite as

Gravity field processing with enhanced numerical precision for LL-SST missions

  • Ilias DarasEmail author
  • Roland Pail
  • Michael Murböck
  • Weiyong Yi
Original Article


On their way to meet the augmenting demands of the Earth system user community concerning accuracies of temporal gravity field models, future gravity missions of low-low satellite-to-satellite tracking (LL-SST) type are expected to fly at optimized formations and make use of the latest technological achievements regarding the on-board sensor accuracies. Concerning the main measuring unit of an LL-SST type gravity mission, the inter-satellite measuring instrument, a much more precise interferometric laser ranging system is planned to succeed the K-band ranging system used by the Gravity Recovery and Climate Experiment (GRACE) mission. This study focuses on investigations concerning the potential performance of new generation sensors such as the laser interferometer within the gravity field processing chain. The sufficiency of current gravity field processing accuracies is tested against the new sensor requirements, via full-scale closed-loop numerical simulations of a GRACE Follow-On configuration scenario. Each part of the processing is validated separately with special emphasis on numerical errors and their impact on gravity field solutions. It is demonstrated that gravity field processing with double precision may be a limiting factor for taking full advantage of the laser interferometer’s accuracy. Instead, a hybrid processing scheme of enhanced precision is introduced, which uses double and quadruple precision in different parts of the processing chain, leading to system accuracies of only 17 nm in terms of geoid height reconstruction errors. Simulation results demonstrate the ability of enhanced precision processing to minimize the processing errors and thus exploit the full precision of a laser interferometer, when at the same time the computational times are kept within reasonable levels.


Future gravity missions Extended precision Gravity field simulations Numerical investigations 



The quadruple precision linear algebra libraries which were used in Version 3 (QP) of the simulator, were kindly provided to us by the Numerical Algorithms Group (NAG). We would like to thank three anonymous reviewers and Prof. Pavel Ditmar as the handling editor, for their useful reviews which helped in improving the manuscript significantly.


  1. Anselmi A, Cesare S, Visser P, Van Dam T, Sneeuw N, Gruber T, Altes B, Christophe B, Cossu F, Ditmar P, Murböck M, Parisch M, Renard M, Reubelt T, Sechi G, Teixeira da Encarnação (2010) Assessment of a next generation gravity mission to monitor the variations of Earth’s gravity field. ESA Contract No. 22643/09/NL/AF, Final report, issue 2, Thales Alenia Space report SDRP-AI-0688Google Scholar
  2. Ditmar P, Klees R, Liu X (2007) Frequency-dependent data weighting in global gravity field modeling from satellite data contaminated by non-stationary noise. J Geod 81(1):81–96. doi: 10.1007/s00190-006-0074-4 CrossRefGoogle Scholar
  3. Ditmar P, Teixeira da Encarnação J, Hashemi Farahani H (2012) Understanding data noise in gravity field recovery on the basis of inter-satellite ranging measurements acquired by the satellite gravimetry mission GRACE. J Geod 86(6):441–465. doi: 10.1007/s00190-011-0531-6 CrossRefGoogle Scholar
  4. Elsaka B, Kusche J, Ilk KH (2012) Recovery of the Earth’s gravity field from formation-flying satellites: Temporal aliasing issues. Adv Space Res 50(11):1534–1552. doi: 10.1016/j.asr.2012.07.016 CrossRefGoogle Scholar
  5. Elsaka B, Raimondo JC, Brieden P, Reubelt T, Kusche J, Flechtner F, Pour SI, Sneeuw N, Müller J (2014) Comparing seven candidate mission configurations for temporal gravity field retrieval through full-scale numerical simulation. J Geod 88(1):31–43. doi: 10.1007/s00190-013-0665-9 CrossRefGoogle Scholar
  6. Ettl M (2013) Hochgenaue numerische lösung von bewegungsproblemen mit frei wählbarer stellengenauigkeit. Ph.D. thesis, Technische Universität München, Munich.
  7. Kim J (2000) Simulation study of a low-low satellite-to-satellite tracking mission. Ph.D. thesis, University of Texas at Austin, AustinGoogle Scholar
  8. Loomis BD, Nerem RS, Luthcke SB (2012) Simulation study of a follow-on gravity mission to GRACE. J Geod 86(5):319–335. doi: 10.1007/s00190-011-0521-8 CrossRefGoogle Scholar
  9. Mayer-Gürr T (2006) Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE. Ph.D. thesis.
  10. Meyer U, Flechtner F, Schmidt R, Frommknecht B (2010a) A simulation study discussing the GRACE baseline accuracy. In: Mertikas SP (ed) Gravity, geoid and earth observation. International association of geodesy symposia, no 135. Springer, Berlin, pp 171–176. doi: 10.1007/978-3-642-10634-7_23
  11. Meyer U, Frommknecht B, Flechtner F (2010b) Global gravity fields from simulated level-1 GRACE data. In: Flechtner FM, Gruber T, Güntner A, Mandea M, Rothacher M, Schöne T, Wickert J (eds) System earth via geodetic-geophysical space techniques. Advanced technologies in earth sciences. Springer, Berlin, pp 143–158. doi: 10.1007/978-3-642-10228-8_12
  12. Murböck M, Pail R, Daras I, Gruber T (2014) Optimal orbits for temporal gravity recovery regarding temporal aliasing. J Geod 88(2):113–126. doi: 10.1007/s00190-013-0671-y CrossRefGoogle Scholar
  13. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res Solid Earth 117(B4). doi: 10.1029/2011JB008916
  14. Schall J, Eicker A, Kusche J (2014) The ITG-Goce02 gravity field model from GOCE orbit and gradiometer data based on the short arc approach. J Geod 88(4):403–409. doi: 10.1007/s00190-014-0691-2
  15. Schneider M (1969) Outline of a general orbit determination method. In: Champion KSW, Smith PA, Smith-Rose RL (eds) Space research IX, Proceedings of open meetings of working groups (OMWG) on physical sciences of the 11th plenary meeting of the committee on space research (COSPAR), Tokyo. North-Holland Publishing Company, Amsterdam, pp 37–40, mitteilungen aus dem Institut für Astronomische und Physikalische Geodäsie, Nr. 51Google Scholar
  16. Shampine LF, Gordon MK (1975) Computer solution of ordinary differential equations: the initial value problem. W.H. Freeman, San FranciscoGoogle Scholar
  17. Sheard BS, Heinzel G, Danzmann K, Shaddock DA, Klipstein WM, Folkner WM (2012) Intersatellite laser ranging instrument for the GRACE follow-on mission. J Geod 86(12):1083–1095. doi: 10.1007/s00190-012-0566-3 CrossRefGoogle Scholar
  18. Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31(9). doi: 10.1029/2004GL019920
  19. Watkins M, Flechtner F, Morton P, Webb F (2013) Status of the grace follow-on mission. In: EGU general assembly conference abstracts, vol 15. p 6024Google Scholar
  20. Wiese DN, Nerem RS, Han SC (2011a) Expected improvements in determining continental hydrology, ice mass variations, ocean bottom pressure signals, and earthquakes using two pairs of dedicated satellites for temporal gravity recovery. J Geophys Res Solid Earth 116(B11405). doi: 10.1029/2011JB008375
  21. Wiese DN, Visser P, Nerem RS (2011) Estimating low resolution gravity fields at short time intervals to reduce temporal aliasing errors. Adv Space Res 48:1094–1107. doi: 10.1016/j.asr.2011.05.027 CrossRefGoogle Scholar
  22. Yi W (2012) The Earth’s gravity field from GOCE. Ph.D. thesis, Technische Universität München.

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ilias Daras
    • 1
    Email author
  • Roland Pail
    • 1
  • Michael Murböck
    • 1
  • Weiyong Yi
    • 1
  1. 1.Institut für Astronomische und Physikalische Geodäsie (IAPG) Technische Universität MünchenMunichGermany

Personalised recommendations