Journal of Geodesy

, Volume 92, Issue 11, pp 1299–1312 | Cite as

A Terrestrial Reference Frame realised on the observation level using a GPS-LEO satellite constellation

  • Daniel KoenigEmail author
Original Article


Applying a one-step integrated process, i.e. by simultaneously processing all data and determining all satellite orbits involved, a Terrestrial Reference Frame (TRF) consisting of a geometric as well as a dynamic part has been determined at the observation level using the EPOS-OC software of Deutsches GeoForschungsZentrum. The satellite systems involved comprise the Global Positioning System (GPS) as well as the twin GRACE spacecrafts. Applying a novel approach, the inherent datum defect has been overcome empirically. In order not to rely on theoretical assumptions this is done by carrying out the TRF estimation based on simulated observations and using the associated satellite orbits as background truth. The datum defect is identified here as the total of all three translations as well as the rotation about the z-axis of the ground station network leading to a rank-deficient estimation problem. To rectify this singularity, datum constraints comprising no-net translation (NNT) conditions in x, y, and z as well as a no-net rotation (NNR) condition about the z-axis are imposed. Thus minimally constrained, the TRF solution covers a time span of roughly a year with daily resolution. For the geometric part the focus is put on Helmert transformations between the a priori and the estimated sets of ground station positions, and the dynamic part is represented by gravity field coefficients of degree one and two. The results of a reference solution reveal the TRF parameters to be estimated reliably with high precision. Moreover, carrying out a comparable two-step approach using the same data and models leads to parameters and observational residuals of worse quality. A validation w.r.t. external sources shows the dynamic origin to coincide at a level of 5 mm or better in x and y, and mostly better than 15 mm in z. Comparing the derived GPS orbits to IGS final orbits as well as analysing the SLR residuals for the GRACE satellites reveals an orbit quality on the few cm level. Additional TRF test solutions demonstrate that K-Band Range-Rate observations between both GRACE spacecrafts are crucial for accurately estimating the dynamic frame’s orientation, and reveal the importance of the NNT- and NNR-conditions imposed for estimating the components of the dynamic geocenter.


Integrated Geodesy Terrestrial Reference Frame Geocenter Datum defect GPS GRACE 



Through funding of the projects GGOS-D (BMBF, grant 03F0425A) and TOBACO-CHAMP/GRACE (BMBF, grant 03G0728A) the underlying Ph.D. thesis Koenig (2013) was made possible. Data have been provided by the IAG services IGS (Dow et al. 2009) and ILRS (Pearlman et al. 2002) as well as by GFZ and JPL. Some plots were created using Generic Mapping Tools (Wessel and Smith 1991). Some technical support provided by Thomas Grombein and Kurt Seitz of Karlsruhe Institute of Technology (KIT) is highly appreciated. Various reviewers helped to improve this article.


  1. Altamimi Z, Boucher C, Sillard P (2002) New trends for the realization of the international terrestrial reference system. Adv Space Res 30(2):175–184CrossRefGoogle Scholar
  2. Altamimi Z, Collilieux X, Métivier L (2011) ITRF2008: an improved solution of the international terrestrial reference frame. J Geod 85(8):457–473CrossRefGoogle Scholar
  3. Altamimi Z, Rebischung P, Métivier L, Collilieux X (2016) A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J Geophys Res Solid Earth 121(8):6109–6131. CrossRefGoogle Scholar
  4. Blewitt G (2003) Self-consistency in reference frames, geocenter definition, and surface loading of the solid Earth. J Geophys Res 108(B2).
  5. Blossfeld M, Müller H, Gerstl M, Štefka V, Bouman J, Göttl F, Horwarth M (2015) Second-degree Stokes coefficients from multi-satellite SLR. J Geod. CrossRefGoogle Scholar
  6. Boehm J, Werl B, Schuh H (2006) Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data. J Geophys Res 111(B02406). CrossRefGoogle Scholar
  7. Cheng MK, Tapley BD, Ries JC (2010) Geocenter variations from analysis of SLR data. In: IAG commission 1 symposium 2010, reference frames for applications in geosciences (REFAG2010), IAGGoogle Scholar
  8. Collilieux X, Métivier L, Altamimi Z, van Dam T, Ray J (2011) Quality assessment of GPS reprocessed Terrestrial Reference Frame. GPS Solut 15:219–231. CrossRefGoogle Scholar
  9. Dahle C, Flechtner F, Gruber C, Koenig D, König R, Michalak G, Neumayer KH (2012) GFZ GRACE level-2 processing standards document for level-2 product release 0005 (Scientific technical report—data , 12/02). Tech. rep., GFZ, Potsdam., p 20
  10. Dong D, Dickey JO, Chao Y, Cheng MK (1997) Geocenter variations caused by atmosphere, ocean and surface ground water. Geophys Res Lett 24:1867–1870CrossRefGoogle Scholar
  11. Dow J, Neilan R, Rizos C (2009) The international GNSS service in a changing landscape of global navigation satellite systems. J Geod 83(3–4):191–198CrossRefGoogle Scholar
  12. Flechtner F, Dahle C, Neumayer KH, König R, Förste C (2010) The release 04 CHAMP and GRACE EIGEN gravity model. Springer, Heidelberg, pp 41–58Google Scholar
  13. Förste C, Bruinsma S, Shako R, Marty J, Flechtner F, Abrikosov O, Dahle C, Lemoine JM, Neumayer H, Biancale R, Barthelmes F, König R, Balmino G (2011) EIGEN-6—a new combined global gravity field model including GOCE data from the collaboration of GFZ-Potsdam and GRGS-Toulouse. Geophys Res Abstr 13, EGU2011-3242-2Google Scholar
  14. GGOS (2012) Global geodetic observing system internet site.
  15. Haines BJ, Bar-Sever Y, Bertiger WI, Desai SD, Harvey N, Sibois AE, Weiss JP (2015) Realizing a terrestrial reference frame using the Global Positioning System. J Geophys Res Solid Earth 120:5911–5939. CrossRefGoogle Scholar
  16. Heiskanen WA, Moritz H (1967) Physical geodesy. W.H. Freeman and Company, San FranciscoGoogle Scholar
  17. Hofmann-Wellenhof B, Lichtenegger H, Collins J (2001) Global positioning system—theory and practice, 5th edn. Springer, WienCrossRefGoogle Scholar
  18. IGS (2012a) International GNSS service internet site.
  19. IGS (2012b) IGS08 Terrestrial Reference System coordinates file.
  20. IGS (2012d) Products quality overview.
  21. JPL (2012) Planetary and lunar ephemeris DE421.
  22. Kang Z, Tapley B, Chen J, Ries J, Bettadpur S (2009) Geocenter variations derived from GPS tracking of the GRACE satellites. J Geod 83(10):895–901. CrossRefGoogle Scholar
  23. Koenig D (2013) Determining a Terrestrial Geodetic Reference Frame following the integrated approach of space geodesy. Ph.D. thesis, Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany., 157 p
  24. Koenig D (2015) Determining a Terrestrial Geodetic Reference Frame following the integrated approach of space geodesy. Ph.D. thesis, Deutsche Geodätische Kommission, München, second publication, p 143Google Scholar
  25. Koenig D, König R (2012) Possibilities and limits for estimating a dynamic and a geometric reference frame origin by the integrated approach applied to the CHAMP-GRACE-GPS constellation. In: Sneeuw N et al (eds) Proceedings VII Hotine-Marussi symposium 2009, Springer, Heidelberg, pp 313–318. Google Scholar
  26. Kuang D, Bar-Sever Y, Haines B (2015) Analysis of orbital configurations for geocenter determination with GPS and low-Earth orbiters. J Geod 89:471–481. CrossRefGoogle Scholar
  27. Meindl M, Beutler G, Thaller D, Jäggi A (2013) Geocenter coordinates estimated from GNSS data as viewed by perturbation theory. Adv Space Res 51:1047–1064CrossRefGoogle Scholar
  28. Pavlis EC (2002) Dynamical determination of origin and scale in the Earth system from satellite laser ranging. In: Proceedings 2001 IAG scientific assembly, Budapest, Hungary, September 2–7, Vistas for Geodesy in the New Millennium, International Association of Geodesy, electronic publication (CD)Google Scholar
  29. Pearlman MR, Degnan JJ, Bosworth JM (2002) The international laser ranging service. Adv Space Res 30:135–143. CrossRefGoogle Scholar
  30. Petit G, Luzum B (2010) IERS conventions 2010. Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, IERS technical note 36, p 179, ISBN 3-89888-989-6Google Scholar
  31. Plag HP (2005) The GGOS as the backbone for global observing and local monitoring: a user driven perspective. J Geodyn 40:479–486. CrossRefGoogle Scholar
  32. Plag HP, Pearlman MR (eds) (2009) Global geodetic observing system—meeting requirements of a global geodetic society on a changing planet in 2020. Springer.
  33. Rebischung P, Altamimi Z, Springer T (2014) A collinearity diagnosis of the GNSS geocenter determination. J Geod 88:65–85. CrossRefGoogle Scholar
  34. Reigber C, Schwintzer P, Lühr H (1999) The CHAMP geopotential mission. Boll Geof Teor Appl 40:285–289Google Scholar
  35. Rietbroek R, Fritsche M, Brunnabend SE, Daras I, Kusche J, Schroeter J, Flechtner F, Dietrich R (2012) Global surface mass from a new combination of GRACE, modelled OBP and reprocessed GPS data. J Geodyn 59–60:64–71. CrossRefGoogle Scholar
  36. Schmid R, Steigenberger P, Gendt G, Ge M, Rothacher M (2007) Generation of a consistent absolute phase center correction model for GPS receiver and satellite antennas. J Geod 81(12):781–798. CrossRefGoogle Scholar
  37. Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31(L09607). CrossRefGoogle Scholar
  38. Thaller D, Dach R, Seitz M, Beutler G, Mareyen M, Richter B (2011) Combination of GNSS and SLR observations using satellite co-locations. J Geod 85(5):257–272. CrossRefGoogle Scholar
  39. Thaller D, Sośnica K, Dach R, Jäggi A, Beutler G, Mareyen M, Richter B (2014) Geocenter coordinates from GNSS and combined GNSS-SLR solutions using satellite co-locations. In: Rizos C, Willis P (eds), Earth on the edge: science for a sustainable planet. International Association of Geodesy Symposia, vol 139. Springer, Berlin. Google Scholar
  40. Torge W (2001) Geodesy, third completely revised and extended edition. de Gruyter, BerlinGoogle Scholar
  41. Wessel P, Smith W (1991) Free software helps map and display data. EOS trans AGU 72:441CrossRefGoogle Scholar
  42. Wu X, Ray J, van Dam T (2012) Geocenter motion and its geodetic and geophysical implications. J Geodyn 58:44–61CrossRefGoogle Scholar
  43. Wu X, Kusche J, Landerer FW (2017) A new unified approach to determine geocentre motion using space geodetic and GRACE gravity data. Geophys J Int 209(3):1398–1402. CrossRefGoogle Scholar
  44. Zhu S, Reigber C, König R (2004) Integrated Adjustment of CHAMP, GRACE and GPS Data. J Geod 78(1–2):103–108. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Joint Center for Earth Systems Technology (JCET)University of Maryland, Baltimore County (UMBC)BaltimoreUSA
  2. 2.Bundesamt für Kartographie und Geodäsie (BKG)Frankfurt am MainGermany

Personalised recommendations