Satellite-to-Satellite Tracking (Low–Low/High–Low SST)

Living reference work entry

Abstract

This contribution reviews the mathematical ideas behind the most frequently used techniques for the processing of satellite-to-satellite tracking data. Its emphasis is on the model part rather than on all necessary technicalities in data preprocessing and numerical implementation. The main outcomes of these data-processing strategies, when applied to data of the satellite missions CHAMP and GRACE, are reviewed.

Keywords

Spherical Harmonic Orbital System Repeat Orbit Gravity Field Model Nonconservative Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Antoni M (2012) Nichtlineare Optimierung regionaler Graviationsfeldmodelle aus SST Daten. PhD thesis, Universität StuttgartGoogle Scholar
  2. Badura T, Sakulin C, Gruber T, Klostius R (2006) Derivation of the CHAMP-only gravity field model TUG-CHAMP04 applying the energy integral approach. Stud Geophys Geod 50:57–74CrossRefGoogle Scholar
  3. Ballani L (1988) Partielle Ableitungen und Variationsgleichungen zur Modellierung von Satellitenbahnen und Parameterbestimmung. Vermessungstechnik 36:192–194Google Scholar
  4. Bettadpur S (2012) Level-2 gravity field product user handbook rev. 3.0, May 29. ftp://podaac-ftp.jpl.nasa.gov/GeodeticsGravity/grace/L1B/JPL/RL01/docs/L2-UserHandbook_v3.0.pdf
  5. Beutler G, Jäggi A, Mervart L, Meyer U (2010a) The celestial mechanics approach: theoretical foundations. J Geodesy 84:65–624CrossRefGoogle Scholar
  6. Beutler G, Jäggi A, Mervart L, Meyer U (2010b) The celestial mechanics approach: application to data of the GRACE mission. J Geodesy 84:661–681CrossRefGoogle Scholar
  7. Bjerhammar A (1976) On the energy integral for satellites. Technical report, Report of the Royal Institute of Technology, StockholmGoogle Scholar
  8. Blaha G (1992) Refinement of the satellite-to-satellite line-of-sight model in residual gravity field. Manuscr Geod 17:321–333Google Scholar
  9. Chao BF, Gross RS (1987) Changes in the Earth’s rotation and low-degree gravitational field induced by earthquakes. J R Astron Soc 91:569–596CrossRefGoogle Scholar
  10. Colombo O (1984) Global mapping of gravity with two satellites. Technical report vol 7 Nr 3, Netherlands Geodetic CommissionGoogle Scholar
  11. Eicker A (2012) Gravity field Refinement by radial basis functions from in-situ satellite data. Technical report, DGK Reihe C, Bd. 676Google Scholar
  12. Fengler MJ, Freeden W, Kohlhaas A, Michel V, Peters T (2007) Wavelet modeling of regional variations of the Earth’s gravitational potential observed by GRACE. J Geodesy 81:5–15CrossRefMATHGoogle Scholar
  13. Gerlach CL, Földvary L, Švehla D, Gruber T, Wermut M, Sneeuw N, Frommknecht B, Oberhofer H, Peters T, Rothacher M, Rummel R, Steigenberger P (2003) A CHAMP-only gravity field model from kinematic orbits using the energy integral. Geophys Res Lett, doi:10.1029/2003GLO18025Google Scholar
  14. Han D, Wahr J (1995) The viscoelastic relaxation of a realistic stratified Earth and further analysis of post-glacial rebound. Geophys J Int 120:287–311CrossRefGoogle Scholar
  15. Han S-C (2004) Efficient determination of global gravity field from satellite-to-satellite tracking mission. Celest Mech Dyn Astron 88:69–102CrossRefGoogle Scholar
  16. Heß D, Keller W (1999) Gradiometrie mit GRACE. Z Vermess 124:137–144Google Scholar
  17. Jekeli C (1999) The determination of gravitational potential differences from satellite-to-satellite tracking. Celest Mech Dyn Astron 75:85–101CrossRefMATHGoogle Scholar
  18. Kaula WM (2000) Theory of satellite geodesy. Applications of satellites to geodesy. Dover, New YorkMATHGoogle Scholar
  19. Keller W, Sharifi MA (2005) Satellite gradiometry using a satellite pair. J Geodesy 78:544–557CrossRefGoogle Scholar
  20. Klees R, Liu X, Wittwer T, Gunter BC, Revtona EA, Tenzer R, Ditmar P, Winsemius HC, Savanije HHG (2008) A comparison of global and regional GRACE models for land hydrology. Surv Geophys 29:335–359CrossRefGoogle Scholar
  21. Kostelec PJ, Rockmore DN (2008) FFTs on the rotation group. J Fourier Anal Appl 14:145–179MathSciNetCrossRefMATHGoogle Scholar
  22. Kusche J, Schmidt R, Petrovic S, Rietbroeck R (2009) Decorrelated GRACE time-variable gravity field solutions by GFZ, and their validation using a hydrological model. J Geodesy 83:903–913CrossRefGoogle Scholar
  23. Levenberg KA (1944) A method for the solution of certain problems in least squares. Q Appl Math 2:164–168MathSciNetMATHGoogle Scholar
  24. Luthcke SB, Arendt AA, Rowlands DD, McCarthy JJ, Larsen CF (2008) Recent glacier mass changes in the Gulf of Alaska region from GRACE mascons solutions. J Glaciol 54:767–777CrossRefGoogle Scholar
  25. Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–443MathSciNetCrossRefMATHGoogle Scholar
  26. Mayer-Gürr T (2012) Gravitationsfeldbestimmung ausn der Analyse kurzer bahnbögen am eispiel der Satellitenmissionen CHAMP und GRACE. Technical report, DGK Reihe C, Bd. 675Google Scholar
  27. Mayer-Gürr T, Eicker A, Ilk K-H (2007) ITG-Grace02s: a GRACE gravity field derived from range measurements of short arcs. In: Gravity field of the Earth, proceedings of the 1st international symposium of the international gravity field service (IGFS), IstanbulGoogle Scholar
  28. Mayer-Gürr T, Ilk H, Eicker A, Feuchtinger M (2005) ITG-CHAMP01: a CHAMP gravity field model from short kinematic arcs over a one-year observation period. J Geodesy 78:462–480CrossRefMATHGoogle Scholar
  29. Mayer-Gürr T, Kurtenbach E, Eicker A (2010) ITG-grace2010 gravity field model. http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010
  30. Muller PM, Sjogren WL (1968) Mascons: lunar mass concentrations. Science 161:680–684CrossRefGoogle Scholar
  31. O’Keefe JA (1957) An application of Jacobi’s integral to the motion of an Earth satellite. Astron J 62:265–266CrossRefGoogle Scholar
  32. Petit G, Luzum B (2010) IERS conventions (2010) (IERS technical note 36). Technical report, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am MainGoogle Scholar
  33. Reigber C (1969) Zur Bestimmung des Gravitationsfeldes der Erde aus Satellitenbeobachtungen. Technical report, DGK Reihe C, Bd. 137Google Scholar
  34. Reigber C, Jochmann H, Wünsch J, Petrovic S, Schwintzer P, Barthelmes F, Neumayer K-H, König R, Förste C, Balmino G, Biancale R, Lemoine J-M, Loyer S, Perosanz F (2004) Earth gravity field and seasonal variability from CHAMP. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds) Earth observation with CHAMP – results from three years in orbit. Springer, Berlin, pp 25–30Google Scholar
  35. Reigber C, Lühr H, Grunwald L, Förste C, König R (2006) CHAMP mission 5 years in orbit. In: Flury J, Rummel R, Reigber C, Rothacher M, Boedecker G, Schreiber U (eds) Observation of the Earth system from space. Springer, Berlin/Heidelberg/New YorkGoogle Scholar
  36. Reubelt T (2009) Harmonische Gravitationsfeldanalyse aus GPS-vermessenen kinematischen Bahnen niedrig fliegender Satelliten vom Typ CHAMP, GRACE, GOCE mit einem hochauflösenden Beschleunigungsansatz. Technical report, DGK Reihe C, Bd. 632Google Scholar
  37. Reubelt T, Austen G, Grafarend EW (2003) Harmonic analysis of the Earth’s gravitational field by means of semi-continuous ephemerides of a low Earth orbiting GPS-tracked satellite. Case study: CHAMP. J Geodesy 77:257–278MATHGoogle Scholar
  38. Rowlands DD, Luthcke SB, McCarthy JJ, Klosko SM, Chinn DS, Lemoine FG, Boy J-P, Sabaka TS (2010) Global mass-flux solutions from grace: a comparison of parameter estimation strategies – mass concentrations versus Stokes coefficients. J Geophys Res 115:B01403Google Scholar
  39. Rummel R (2003) How to climb the gravity wall. Space Sci Rev 108:1–14CrossRefGoogle Scholar
  40. Schmidt M, Han S-C, Kusche J, Sanchez L, Shum CK (2006) Regional high-resolution spatiotemporal gravity modeling from GRACE data using spherical wavelets. Geophys Res Lett 33:L08403Google Scholar
  41. Schneider M (1968) A general method of orbit determination. Technical report, Library Translations, Aircraft Establishment, Ministry of Technology, FarnboroughGoogle Scholar
  42. Sneeuw N (2000) A semi-analytical approach to gravity field analysis from satellite observations. Technical report, DGK Reihe C, Bd. 527Google Scholar
  43. Visser PNAM, Sneeuw N, Gerlach C (2003) Energy integral method for gravity field determination from satellite orbit coordinates. J Geodesy 77:207–216CrossRefMATHGoogle Scholar
  44. Weisstein E Wolfram mathworld. http:mathworld.wolfram.com, 2014
  45. Wolff M (1969) Direct measurements of the Earth’s gravitational field using a satellite pair. J Geophys Res 74:5295–5300CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Geodätisches Institut, Universität StuttgartStuttgartGermany

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