GPS Solutions

, Volume 21, Issue 3, pp 1275–1284 | Cite as

Reduced-dynamic and kinematic baseline determination for the Swarm mission

  • Gerardo Allende-AlbaEmail author
  • Oliver Montenbruck
  • Adrian Jäggi
  • Daniel Arnold
  • Franz Zangerl
Original Article


The Swarm mission of the European Space Agency was launched in November 2013 with the objective of performing measurements of the earth’s magnetic field with unprecedented accuracy. At the beginning of data collection, two satellites started to fly in orbits with a separation in ascending nodes of 1°–1.5° at an altitude of about 480 km, and a third satellite has been placed in a higher orbit with an altitude of 530 km. The three spacecraft are equipped with dual-frequency eight-channel GPS receivers for the generation of precise orbits. Although such orbits support the fulfillment of the primary objectives of the mission, precise space baselines may be helpful for studying the earth’s gravity field, a spin-off application of the Swarm mission. Hitherto, a particular challenge for the computation of precise baselines from Swarm has been the presence of half-cycle ambiguities in GPS carrier phase observations, which complicate the implementation of integer ambiguity resolution methods. The present study shows the feasibility of generating carrier phase observations with full-cycle ambiguities, which in turn has been used to improve the performance of reduced-dynamic and kinematic precise baseline determination schemes. The implemented strategies have been tested in a period of 90 days in 2016. The obtained reduced-dynamic and kinematic baseline products were evaluated by inter-product and inter-agency comparisons using two independent software tools.


Swarm Space baseline determination Half-cycle ambiguity resolution GPS 



The present study uses data made available by the European Space Agency (ESA/ESTEC), Noordwijk, the Center for Orbit Determination in Europe (CODE) and the International Laser Ranging Service (ILRS). The support of these institutions is gratefully acknowledged. The authors acknowledge the reviewers for their valuable remarks that helped to improve the original manuscript. GAA wishes to thank the support provided by the Consejo Nacional de Ciencia y Tecnología de México, the Deutscher Akademischer Austauschdienst (Grant No. 213633 - A/10/72692) and the TU München Graduate School.


  1. Allende-Alba G, Montenbruck O (2016) Robust and precise baseline determination of distributed spacecraft in LEO. Adv Space Res 57(1):46–63. doi: 10.1016/j.asr.2015.09.034 CrossRefGoogle Scholar
  2. Betz J (2016) Engineering satellite-based navigation and timing—global navigation satellite systems, signals, and receivers. Wiley-IEEE Press, HobokenGoogle Scholar
  3. Bock H, Jäggi A, Meyer U, Visser P, van den IJssel J, van Helleputte T, Heinze M, Hugentobler U (2011) GPS-derived orbits for the GOCE satellite. J Geodesy 85(11):807–818CrossRefGoogle Scholar
  4. Buchert S, Zangerl F, Sust M, André M, Eriksson A, Wahlund JE, Opgenoorth H (2015) SWARM observations of equatorial electron densities and topside GPS track losses. Geophys Res Lett 42(7):2008–2092. doi: 10.1002/2015GL063121 CrossRefGoogle Scholar
  5. Dach R, Lutz S, Walser P, Fridez P (eds) (2015) Bernese GNSS Software version 5.2. User manual. Astronomical Institute, University of Bern, Bern Open Publishing. doi:  10.7892/boris.72297
  6. Dach R, Schaer S, Arnold D, Orliac E, Prange L, Sušnik A, Villiger A, Jäggi A (2016) CODE final product series for the IGS. Published by Astronomical Institute, University of Bern. doi:  10.7892/boris.75876
  7. Flechtner F, Morton P, Watkins P, Webb F (2014) Status of the GRACE Follow-on mission. In: Gravity, geoid and height systems, IAG symposia, vol. 141. pp 117-121. doi:  10.1007/978-3-319-10837-715
  8. Friis-Christensen E, Lühr H, Hulot G (2006) Swarm: a constellation to study the Earth’s magnetic field. Earth Planets Space 58(4):351–358. doi: 10.1186/BF03351933 CrossRefGoogle Scholar
  9. Friis-Christensen E, Lühr H, Knudsen D, Haagmans R (2008) Swarm—an earth observation mission investigating geospace. Adv Space Res 41(1):210–216. doi: 10.1016/j.asr.2006.10.008 CrossRefGoogle Scholar
  10. Gerlach C, Visser PNAM (2006) SWARM and gravity: possibilities and expectations for gravity field recovery. In: Proceedings of the first international science meeting, SWARM, ESA WPP-261Google Scholar
  11. Jäggi A, Hugentobler U, Bock H, Beutler G (2007) Precise orbit determination for GRACE using undifferenced or doubly differenced GPS data. Adv Space Res 39(10):1612–1619. doi: 10.1016/j.asr.2007.03.012 CrossRefGoogle Scholar
  12. Jäggi A, Beutler G, Prange L, Dach R (2009a) Assessment of GPS-only observables for gravity field recovery from GRACE. In: Sideris MG (ed) Observing our changing earth. IAG symposia, vol. 33. pp 113–123. doi:  10.1007/978-3-540-85426-514
  13. Jäggi A, Dach R, Montenbruck O, Hugentobler U, Bock H, Beutler G (2009b) Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination. J Geodesy 83:1145–1162. doi: 10.1007/s00190-009-0333-2 CrossRefGoogle Scholar
  14. Jäggi A, Montenbruck O, Moon Y, Wermuth M, König R, Michalak G, Bock H, Bodenmann D (2012) Inter-agency comparison of TanDEM-X baseline solutions. Adv Space Res 50(2):260–271. doi: 10.1016/j.asr.2012.03.027 CrossRefGoogle Scholar
  15. Jäggi A, Dahle C, Arnold D, Meyer U, Bock H (2014) Kinematic space-baselines and their use for gravity field recovery. Presented at the 40th COSPAR Scientific Assembly, Moscow, Russia, Aug 2014. doi:  10.7892/boris.58970
  16. Jäggi A, Dahle C, Arnold D, Bock H, Meyer U, Beutler G, van den IJssel J (2016) Swarm kinematic orbits and gravity fields from 18 months of GPS data. Adv Space Res 57(1):218–233. doi: 10.1016/j.asr.2015.10.035 CrossRefGoogle Scholar
  17. Kintner PM, Ledvina BM (2005) The ionosphere, radio navigation, and global navigation satellite systems. Adv Space Res 35(5):788–811. doi: 10.1016/j.asr.2004.12.076 CrossRefGoogle Scholar
  18. Kintner PM, Ledvina BM, de Paula ER (2007) GPS and ionospheric scintillations. Space Weather 5:S09003CrossRefGoogle Scholar
  19. Kovach K, Mendicki PJ, Powers E, Renfro B (2016) GPS receiver impact from the UTC Offset (UTCO) Anomaly of 25–26 Jan 2016. In: Proceedings of ION GNSS+, Institute of Navigation, Portland, Oregon, Sept 12–13, pp 2887–2895Google Scholar
  20. Krieger G, Hajnsek I, Papathanassiou KP, Younis M, Moreira A (2010) Interferometric synthetic aperture radar (SAR) missions employing formation flying. Proc IEEE 98(5):816–843CrossRefGoogle Scholar
  21. Kroes R (2006) Precise relative positioning of formation flying spacecraft using GPS. Ph.D. thesis, TU DelftGoogle Scholar
  22. Mackenzie R, Bock R, Kuijper D, Ramos-Bosch P, Sieg D, Ziegler G (2014) A review of Swarm flight dynamics operations from launch to routine phase. In: Proceedings of the 24th international symposium on space flight dynamics, May 2014Google Scholar
  23. Mao X, Visser PNAM, van den IJssel J, Doornbos E (2016) Swarm absolute and relative orbit determination. Presented at: living planet symposium, ESA SP-740, May 2016. Orbit Determination.pdf
  24. Montenbruck O, van Helleputte T, Kroes R, Gill E (2005) Reduced-dynamic orbit determination using GPS code and carrier measurements. Aerosp Sci Technol 9(3):261–271. doi: 10.1016/j.ast.2005.01.003 CrossRefGoogle Scholar
  25. Montenbruck O, Andres Y, Bock H, van Helleputte T, van den IJssel J, Loiselet M, Marquardt C, Silvestrin P, Visser P, Yoon Y (2008) Tracking and orbit determination performance of the GRAS instrument on MetOp-A. GPS Solut 12(4):289–299. doi: 10.1007/s10291-008-0091-2 CrossRefGoogle Scholar
  26. Montenbruck O, Wermuth M, Kahle R (2011–2012) GPS based relative navigation for the TanDEM-X mission—first flight results. Navigation, 58(4):293–304. doi:  10.1002/j.2161-4296.2011.tb02587.x
  27. Pearlman MR, Degnan JJ, Bosworth JM (2002) The international laser ranging service. Adv Space Res 30(2):135–143. doi: 10.1016/S0273-1177(02)00277-6 CrossRefGoogle Scholar
  28. Reigber Ch, Lühr H, Schwintzer P (2002) CHAMP mission status. Adv Space Res 30(2):129–134. doi: 10.1016/S0273-1177(02)00276-4 CrossRefGoogle Scholar
  29. Sieg D, Diekmann FJ (2016) Options for the further orbit evolution of the Swarm mission. In: Proceedings of the living planet symposium, ESA SP-740, AugustGoogle Scholar
  30. Silvestrin P, Cooper J (2000) Method of processing of signals of a satellite positioning system. US Patent 6 157 341, Dec 5Google Scholar
  31. Silvestrin P, Bagge P, Bonnedal M, Carlstrom A, Christensen J, Hagg M, Lindgren T, Zangerl F (2000) Spaceborne GNSS radio occultation instrumentation for operational applications. In: Proceedings ION GPS, Institute of Navigation, Salt Lake City, UT, Sept 19–22, pp 872–880Google Scholar
  32. Sust M, Zangerl F, Montenbruck O, Buchert S, Garcia-Rodriguez A (2014) Spaceborne GNSS receiving system performance prediction and validation. In: NAVITEC: ESA workshop on satellite navigation technologies and GNSS Signals and signal processingGoogle Scholar
  33. Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett. doi: 10.1029/2004GL019920 Google Scholar
  34. Teixeira da Encarnação J, Arnold D, Bezděk A, Dahle C, Doornbos E, van den IJssel J, Jäggi A, Mayer-Gürr T, Sebera J, Visser PNAM, Zehentner N (2016) Gravity field models derived from Swarm GPS data. Earth Planets Space 68:27CrossRefGoogle Scholar
  35. van den IJssel J, Encarnação J, Doornbos E, Visser P (2015) Precise science orbits for the Swarm satellite constellation. Adv Space Res 56(6):1042–1055. doi: 10.1016/j.asr.2015.06.002 CrossRefGoogle Scholar
  36. van den IJssel J, Forte B, Montenbruck O (2016) Impact of swarm GPS receiver updates on POD performance. Earth Planets Space 68(1):1–17. doi: 10.1186/s40623-016-0459-4 CrossRefGoogle Scholar
  37. Wang X, Rummel R (2012) Using Swarm for gravity field recovery: first simulation results. In: Sneeuw N, Novák P, Crespi M, Sansò F (eds) VII Hotine-Marussi symposium on mathematical geodesy, IAG Symposia, vol. 137, pp 301–306. doi:  10.1007/978-3-642-22078-4 45
  38. Woo KT (2000) Optimum semi-codeless carrier phase tracking of L2. Navigation 47(2):82CrossRefGoogle Scholar
  39. Wu SC, Yunck TP, Thornton CL (1991) Reduced-dynamic technique for precise orbit determination of low Earth satellites. J Guid Control Dyn 14(1):24–31CrossRefGoogle Scholar
  40. Xiong C, Stolle C, Lühr H (2016) The Swarm satellite loss of GPS signal and its relation to ionospheric plasma irregularities. Space Weather 14(8):563–577. doi: 10.1002/2016SW001439 CrossRefGoogle Scholar
  41. Yunck TP, Wu SC, Wu JT, Thornton CL (1990) Tracking of remote satellites with the global positioning system. IEEE Trans Geosci Remote Sens 28(1):108–116CrossRefGoogle Scholar
  42. Zangerl F, Griesauer F, Sust M, Montenbruck O, Buchert B, Garcia A (2014) SWARM GPS precise orbit determination receiver initial in orbit performance evaluation. In: Proceedings ION GNSS+, Institute of Navigation, Tampa, Florida, Sept 8–12, pp 1459–1468Google Scholar
  43. Zin A, Landenna S, Conti A (2006) Satellite-to-satellite tracking instrument—design and performance. Presented at the 3rd international GOCE user workshop, Nov 6–8 Nov 2006, ESA-ESRIN, Frascati, ItalyGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Deutsches Zentrum für Luft- und Raumfahrt (DLR)German Space Operations Center (GSOC)WeßlingGermany
  2. 2.Institute for Astronomical and Physical GeodesyTechnische Universität MünchenMunichGermany
  3. 3.Astronomical InstituteUniversität BernBernSwitzerland
  4. 4.RUAG Space GmbHViennaAustria

Personalised recommendations