Skip to main content
Top

2013 | OriginalPaper | Chapter

5. GPS Based Relative Navigation

Authors : Oliver Montenbruck, Simone D’Amico

Published in: Distributed Space Missions for Earth System Monitoring

Publisher: Springer New York

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The use of Global Positioning System (GPS) measurements provides the primary technique for determining the relative position of cooperative, formation-flying satellites in low Earth orbit. Similar to terrestrial applications, the relative navigation benefits from a high level of common error cancellation. Furthermore, the integer nature of double-difference carrier phase ambiguities can be exploited in carrier phase differential GPS (CDGPS). Both aspects enable a substantially higher relative accuracy than can be achieved in single-spacecraft navigation. Following an overview of spaceborne GPS receivers, the dynamical and measurement models for relative navigation using single- or dual-frequency measurements are presented along with a discussion of estimation schemes for real-time and offline applications. Actual flight results from the TanDEM-X and PRISMA missions are presented to demonstrate the feasibility of mm-level post-facto baseline determination and cm-level real-time navigation using CDGPS.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Kaplan ED, Hegarty CJ (eds) (2006) Understanding GPS – principles and applications, 2nd edn. Artech House, Boston/London Kaplan ED, Hegarty CJ (eds) (2006) Understanding GPS – principles and applications, 2nd edn. Artech House, Boston/London
2.
go back to reference Bauer FH, Moreau MC, Dahle-Melsaether ME, Petrofski WP, Stanton BJ, Thomason S, Harris GA, Sena RP, Parker Temple L III (2006) The GPS space service volume. ION-GNSS-2006, Fort Worth, 26–29 Sept 2006 Bauer FH, Moreau MC, Dahle-Melsaether ME, Petrofski WP, Stanton BJ, Thomason S, Harris GA, Sena RP, Parker Temple L III (2006) The GPS space service volume. ION-GNSS-2006, Fort Worth, 26–29 Sept 2006
3.
go back to reference Corazzini T, Robertson A, Adams JC, Hassibi, A, How JP (1997) GPS sensing for spacecraft formation flying. ION-GPS-1997, Kansas, Sept 1997 Corazzini T, Robertson A, Adams JC, Hassibi, A, How JP (1997) GPS sensing for spacecraft formation flying. ION-GPS-1997, Kansas, Sept 1997
4.
go back to reference Fehse W (2003) Automated rendezvous and docking of spacecraft. Cambridge University Press, New YorkCrossRef Fehse W (2003) Automated rendezvous and docking of spacecraft. Cambridge University Press, New YorkCrossRef
5.
go back to reference Kelbel D, Lee T, Long A, Carpenter R, Gramling C (2001) Evaluation of relative navigation algorithms for formation-flying satellites using GPS. In: Proceedings of the 2001 flight mechanics symposium. NASA CP-2001-209986, Greenbelt, 19–21 June 2001 Kelbel D, Lee T, Long A, Carpenter R, Gramling C (2001) Evaluation of relative navigation algorithms for formation-flying satellites using GPS. In: Proceedings of the 2001 flight mechanics symposium. NASA CP-2001-209986, Greenbelt, 19–21 June 2001
6.
go back to reference Space Engineering – Space Environment (2008) ECSS-E-ST-10-04C. European cooperation for space standardization, Noordwijk, 15 Nov 2008 Space Engineering – Space Environment (2008) ECSS-E-ST-10-04C. European cooperation for space standardization, Noordwijk, 15 Nov 2008
10.
go back to reference Renaudie C, Markgraf M, Montenbruck O, Garcia-Fernandez M (2007) Radiation testing of commercial-off-the-shelf GPS technology for use on low earth orbit satellites. RADECS 2007. In: Proceedings of 9th European conference radiation and its effects on components and systems, Deauville, 10–14 Sept 2007 Renaudie C, Markgraf M, Montenbruck O, Garcia-Fernandez M (2007) Radiation testing of commercial-off-the-shelf GPS technology for use on low earth orbit satellites. RADECS 2007. In: Proceedings of 9th European conference radiation and its effects on components and systems, Deauville, 10–14 Sept 2007
11.
go back to reference Virtanen A (2006) The use of particle accelerators for space projects. EPS Euroconference XIX nuclear physics divisional conference. J Phys: Conf Ser 41:101–114. DOI:10.1088/1742-6596/41/1/008 Virtanen A (2006) The use of particle accelerators for space projects. EPS Euroconference XIX nuclear physics divisional conference. J Phys: Conf Ser 41:101–114. DOI:10.1088/1742-6596/41/1/008
12.
go back to reference Zadeh A, Santandrea S, Landstroem S, Markgraf M (2010) DLR Phoenix GPS receiver radiation characterisation campaign proton irradiation testing at PSI – June 2010 test report. TEC-SYV/81/2011/REP/SS, ESA/ESTEC, Noordwijk, 8 Feb 2011 Zadeh A, Santandrea S, Landstroem S, Markgraf M (2010) DLR Phoenix GPS receiver radiation characterisation campaign proton irradiation testing at PSI – June 2010 test report. TEC-SYV/81/2011/REP/SS, ESA/ESTEC, Noordwijk, 8 Feb 2011
13.
go back to reference Helm A, Hess M-P, Minori M, Gribkov A, Yudanov S, Montenbruck O, Beyerle G, Cacciapuoti L, Nasca R (2009) The ACES GNSS subsystem and its potential for radio-occultation and reflectometry from the International Space Station. In: 2nd international colloquium on scientific and fundamental aspects of the Galileo program, Padua, 14–16 Oct 2009 Helm A, Hess M-P, Minori M, Gribkov A, Yudanov S, Montenbruck O, Beyerle G, Cacciapuoti L, Nasca R (2009) The ACES GNSS subsystem and its potential for radio-occultation and reflectometry from the International Space Station. In: 2nd international colloquium on scientific and fundamental aspects of the Galileo program, Padua, 14–16 Oct 2009
14.
go back to reference Markgraf M, Montenbruck O, Santandrea S, Naudet J (2010) Phoenix-XNS navigation system onboard the PROBA-2 spacecraft – first flight results. Small satellites systems and services – the 4S symposium, Madeira, Portugal, 31 May–4 June 2010 Markgraf M, Montenbruck O, Santandrea S, Naudet J (2010) Phoenix-XNS navigation system onboard the PROBA-2 spacecraft – first flight results. Small satellites systems and services – the 4S symposium, Madeira, Portugal, 31 May–4 June 2010
17.
18.
go back to reference Jäggi A, Dach R, Montenbruck O, Hugentobler U, Bock H, Beutler G (2009) Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination. J Geodesy 83(12):1145–1162. doi:10.1007/s00190-009-0333-2 CrossRef Jäggi A, Dach R, Montenbruck O, Hugentobler U, Bock H, Beutler G (2009) Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination. J Geodesy 83(12):1145–1162. doi:10.​1007/​s00190-009-0333-2 CrossRef
19.
go back to reference van Barneveld P, Montenbruck O, Visser P (2008) Differential ionospheric effects in GPS based navigation of formation flying spacecraft. In: Proceedings of 3rd international symposium on formation flying, missions and technology, ESA/ESTEC, Noordwijk, 23–25 Apr 2008 van Barneveld P, Montenbruck O, Visser P (2008) Differential ionospheric effects in GPS based navigation of formation flying spacecraft. In: Proceedings of 3rd international symposium on formation flying, missions and technology, ESA/ESTEC, Noordwijk, 23–25 Apr 2008
20.
go back to reference Julien O, Cannon ME, Alves P, Lachapelle G (2004) Triple frequency ambiguity resolution using GPS/Galileo. Eur J Navig 2(2):51–57 Julien O, Cannon ME, Alves P, Lachapelle G (2004) Triple frequency ambiguity resolution using GPS/Galileo. Eur J Navig 2(2):51–57
21.
go back to reference Van der Marel H (2010) Combining GNSS signals – bias and calibration issues. IGS analysis workshop, Newcastle, June 28–July 1, 2010 Van der Marel H (2010) Combining GNSS signals – bias and calibration issues. IGS analysis workshop, Newcastle, June 28–July 1, 2010
22.
go back to reference GPS World Receiver Survey. GPS World. Jan 2012, 1–23 GPS World Receiver Survey. GPS World. Jan 2012, 1–23
23.
go back to reference García-Rodríguez A (2008) Onboard radio navigation receivers. Technical Dossier – European Space Technology Harmonization, TEC-ETN/2007.65, 16 Apr 2008 García-Rodríguez A (2008) Onboard radio navigation receivers. Technical Dossier – European Space Technology Harmonization, TEC-ETN/2007.65, 16 Apr 2008
24.
go back to reference Roselló Guasch J, Silvestrin P, Aguirre M, Massotti L (2010) Navigation needs for ESA’s earth observation missions. In: Sandau R, Röser H-P, Valenzuela A (eds) Small satellite missions for earth observation – new developments and trends. Springer, Berlin, Heidelberg, pp 457–466. doi:10.1007/978-3-642-03501-2_41 Roselló Guasch J, Silvestrin P, Aguirre M, Massotti L (2010) Navigation needs for ESA’s earth observation missions. In: Sandau R, Röser H-P, Valenzuela A (eds) Small satellite missions for earth observation – new developments and trends. Springer, Berlin, Heidelberg, pp 457–466. doi:10.​1007/​978-3-642-03501-2_​41
25.
go back to reference Montenbruck O, Yoon Y, Ardaens J-S, Ulrich D (2008) In-flight performance assessment of the single frequency MosaicGNSS receiver for satellite navigation. In: Proceedings of 7th international ESA conference on guidance, navigation and control systems, ESA WPP-288, Tralee, 2–5 June 2008 Montenbruck O, Yoon Y, Ardaens J-S, Ulrich D (2008) In-flight performance assessment of the single frequency MosaicGNSS receiver for satellite navigation. In: Proceedings of 7th international ESA conference on guidance, navigation and control systems, ESA WPP-288, Tralee, 2–5 June 2008
26.
go back to reference Föckersperger S, Hollmann R, Dick G, Reigber C (1997) On board MIR: orienting remote images with MOMSNAV. GPS World 8:32–39 Föckersperger S, Hollmann R, Dick G, Reigber C (1997) On board MIR: orienting remote images with MOMSNAV. GPS World 8:32–39
27.
go back to reference Ebinuma T, Rooney E, Gleason S, Unwin M (2005) GPS receiver operations on the disaster monitoring constellation satellites. J Navig 58:227–240CrossRef Ebinuma T, Rooney E, Gleason S, Unwin M (2005) GPS receiver operations on the disaster monitoring constellation satellites. J Navig 58:227–240CrossRef
28.
go back to reference Pinard D, Reynaud S, Delpy P, Strandmoe SE (2007) Accurate and autonomous navigation for the ATV. Aerosp Sci Technol 11:490–498CrossRef Pinard D, Reynaud S, Delpy P, Strandmoe SE (2007) Accurate and autonomous navigation for the ATV. Aerosp Sci Technol 11:490–498CrossRef
29.
go back to reference Hwang Y, Lee B-S, Kim J, Jung O-C, Chung D-W, Kim H (2010) KOMPSAT-2 orbit determination status report. AIAA 2010–8260; AIAA guidance, navigation, and control conference, Toronto, 2–5 Aug 2010 Hwang Y, Lee B-S, Kim J, Jung O-C, Chung D-W, Kim H (2010) KOMPSAT-2 orbit determination status report. AIAA 2010–8260; AIAA guidance, navigation, and control conference, Toronto, 2–5 Aug 2010
30.
go back to reference D’Amico S, Ardaens J-S, De Florio S, Montenbruck O, Persson S, Noteborn R (2010) GPS-based spaceborne autonomous formation flying experiment (SAFE) on PRISMA: initial commissioning. AIAA/AAS astrodynamics specialist conference, Toronto, 2–5 Aug 2010 D’Amico S, Ardaens J-S, De Florio S, Montenbruck O, Persson S, Noteborn R (2010) GPS-based spaceborne autonomous formation flying experiment (SAFE) on PRISMA: initial commissioning. AIAA/AAS astrodynamics specialist conference, Toronto, 2–5 Aug 2010
31.
go back to reference Spangelo S, Kleshy A, Cutler J (2010) Position and time system for the RAX small satellite mission. AIAA-2010-7980, AIAA/AAS astrodynamics specialist conference, Toronto, 2–5 Aug 2010 Spangelo S, Kleshy A, Cutler J (2010) Position and time system for the RAX small satellite mission. AIAA-2010-7980, AIAA/AAS astrodynamics specialist conference, Toronto, 2–5 Aug 2010
32.
go back to reference Sust M, Carlström A, Garcia-Rodriguez A (2009) European spaceborne dual frequency GPS receiver for science and earth observation. ION-GNSS-2009, Savannah, GA, 22–25 Sept 2009 Sust M, Carlström A, Garcia-Rodriguez A (2009) European spaceborne dual frequency GPS receiver for science and earth observation. ION-GNSS-2009, Savannah, GA, 22–25 Sept 2009
33.
go back to reference 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 Solutions 12(4):289–299. doi:10.1007/s10291-008-0091-2 CrossRef 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 Solutions 12(4):289–299. doi:10.​1007/​s10291-008-0091-2 CrossRef
34.
go back to reference Zin A, Landenna S, Conti A, Marradi L, Di Raimondo MS (2006) L1/L2 Integrated GPS/WAAS/EGNOS Receiver. ENC-GNSS- 2006 - The European Navigation Conference, 8-10 May 2006, Manchester, UK. Zin A, Landenna S, Conti A, Marradi L, Di Raimondo MS (2006) L1/L2 Integrated GPS/WAAS/EGNOS Receiver. ENC-GNSS- 2006 - The European Navigation Conference, 8-10 May 2006, Manchester, UK.
35.
go back to reference Serre S, Mercier F, Garcia A, Grondin M, Boyer C, Favaro H, Gerner J-L, Issler J-L (2010) First In-orbit Results of the L2C-L1C/A GPS receiver on board the PROBA-2 microsatellite. ION-GNSS-2010, Portland, Oregon, 22–24 Sept 2010 Serre S, Mercier F, Garcia A, Grondin M, Boyer C, Favaro H, Gerner J-L, Issler J-L (2010) First In-orbit Results of the L2C-L1C/A GPS receiver on board the PROBA-2 microsatellite. ION-GNSS-2010, Portland, Oregon, 22–24 Sept 2010
36.
go back to reference Langley RB, Montenbruck O, Markgraf M, Kang CS, Kim D (2004) Qualification of a commercial dual-frequency GPS receiver for the e-POP platform onboard the Canadian CASSIOPE spacecraft. NAVITEC’2004, Noordwijk, The Netherlands, 8–10 Dec 2004 Langley RB, Montenbruck O, Markgraf M, Kang CS, Kim D (2004) Qualification of a commercial dual-frequency GPS receiver for the e-POP platform onboard the Canadian CASSIOPE spacecraft. NAVITEC’2004, Noordwijk, The Netherlands, 8–10 Dec 2004
37.
go back to reference Markgraf M, Renaudie C, Montenbruck O (2008) The NOX payload – flight validation of a low-cost dual-frequency GPS receiver for micro- and nano-satellites. Small satellites systems and services – the 4S symposium, Rhodes, Greece, 26–30 May 2008 Markgraf M, Renaudie C, Montenbruck O (2008) The NOX payload – flight validation of a low-cost dual-frequency GPS receiver for micro- and nano-satellites. Small satellites systems and services – the 4S symposium, Rhodes, Greece, 26–30 May 2008
38.
go back to reference Misra P, Enge P (2006) Global positioning system (GPS): signals, measurements and performance, 2nd edn. Ganga-Jamuna, Lincoln Misra P, Enge P (2006) Global positioning system (GPS): signals, measurements and performance, 2nd edn. Ganga-Jamuna, Lincoln
39.
go back to reference Wu JT, Wu SC, Hajj GA, Bertiger WI, Lichten SM (1993) Effects of antenna orientation on GPS carrier phase. Manuscr Geodaet 18:91–98 Wu JT, Wu SC, Hajj GA, Bertiger WI, Lichten SM (1993) Effects of antenna orientation on GPS carrier phase. Manuscr Geodaet 18:91–98
40.
go back to reference Yunck TP (1993) Coping with the atmosphere and ionosphere in precise satellite and ground positioning. In: Valance-Jones A (ed) Environmental effects on spacecraft trajectories and positioning. AGU Monograph, Washington, DC Yunck TP (1993) Coping with the atmosphere and ionosphere in precise satellite and ground positioning. In: Valance-Jones A (ed) Environmental effects on spacecraft trajectories and positioning. AGU Monograph, Washington, DC
41.
go back to reference Lear WM (1987) GPS navigation for low-Earth orbiting vehicles. NASA 87-FM-2, Rev. 1, JSC-32031, Lyndon B. Johnson Space Center, Houston, TX Lear WM (1987) GPS navigation for low-Earth orbiting vehicles. NASA 87-FM-2, Rev. 1, JSC-32031, Lyndon B. Johnson Space Center, Houston, TX
42.
go back to reference Tancredi U, Renga A, Grassi M (2010) GPS-based relative navigation of LEO formations with varying baselines. AIAA/AAS astrodynamics specialist conference, Toronto, 2–5 Aug 2010 Tancredi U, Renga A, Grassi M (2010) GPS-based relative navigation of LEO formations with varying baselines. AIAA/AAS astrodynamics specialist conference, Toronto, 2–5 Aug 2010
43.
go back to reference Psiaki ML, Mohiuddin S (2007) Modeling, analysis, and simulation of GPS carrier phase for spacecraft relative navigation. J Guid Contr Dyn 30(6):1628–1639. doi:10.2514/1.29534 CrossRef Psiaki ML, Mohiuddin S (2007) Modeling, analysis, and simulation of GPS carrier phase for spacecraft relative navigation. J Guid Contr Dyn 30(6):1628–1639. doi:10.​2514/​1.​29534 CrossRef
44.
go back to reference Hofmann-Wellenhoff B, Lichtenegger H, Collins J (2001) GPS: theory and practice, 5th edn. Springer, New York Hofmann-Wellenhoff B, Lichtenegger H, Collins J (2001) GPS: theory and practice, 5th edn. Springer, New York
45.
go back to reference Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodesy 70(1–2):65–82. doi:10.1007/BF00863419 CrossRef Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodesy 70(1–2):65–82. doi:10.​1007/​BF00863419 CrossRef
46.
go back to reference Cox DB, Brading JDW (2000) Integration of LAMBDA ambiguity resolution with Kalman filter for relative navigation of spacecraft. Navig: J ION 47(3):205–210 Cox DB, Brading JDW (2000) Integration of LAMBDA ambiguity resolution with Kalman filter for relative navigation of spacecraft. Navig: J ION 47(3):205–210
47.
go back to reference Mohiuddin S, Psiaki ML (2005) Satellite relative navigation using carrier-phase differential GPS with integer ambiguities. AIAA guidance, navigation, and control conference, San Francisco, 15–18 Aug 2005 Mohiuddin S, Psiaki ML (2005) Satellite relative navigation using carrier-phase differential GPS with integer ambiguities. AIAA guidance, navigation, and control conference, San Francisco, 15–18 Aug 2005
49.
go back to reference Wu S-Ch, Bar-Sever Y.E (2006) Real-time sub-cm differential orbit determination of two low-Earth orbiters with GPS bias fixing. ION GNSS 2006, Fort Worth, TX, 26–29 Sep 2006 Wu S-Ch, Bar-Sever Y.E (2006) Real-time sub-cm differential orbit determination of two low-Earth orbiters with GPS bias fixing. ION GNSS 2006, Fort Worth, TX, 26–29 Sep 2006
51.
go back to reference Laurichesse D, Mercier F, Berthias JP, Broca P, Cerri L (2009) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination. Navig: J ION 56(2):135–149 Laurichesse D, Mercier F, Berthias JP, Broca P, Cerri L (2009) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination. Navig: J ION 56(2):135–149
52.
go back to reference de Ruiter A, Lee J, Ng A, Kim Y (2008) Orbit determination and relative positioning techniques for JC2Sat-FF. In: Proceedings of the 3rd international symposium on formation flying, missions and technology, ESA/ESTEC, ESA SP-654, Noordwijk, The Netherlands, 23–25 Apr 2008 de Ruiter A, Lee J, Ng A, Kim Y (2008) Orbit determination and relative positioning techniques for JC2Sat-FF. In: Proceedings of the 3rd international symposium on formation flying, missions and technology, ESA/ESTEC, ESA SP-654, Noordwijk, The Netherlands, 23–25 Apr 2008
53.
go back to reference Psiaki ML (2010) Kalman filtering and smoothing to estimate real-valued states and integer constants. J Guid Contr Dyn 33(5):1404–1417CrossRef Psiaki ML (2010) Kalman filtering and smoothing to estimate real-valued states and integer constants. J Guid Contr Dyn 33(5):1404–1417CrossRef
54.
go back to reference Clohessy WH, Wiltshire RS (1960) Terminal guidance system for satellite rendezvous. J Aerosp Sci 270:653 Clohessy WH, Wiltshire RS (1960) Terminal guidance system for satellite rendezvous. J Aerosp Sci 270:653
55.
go back to reference Vallado DA (1997) Fundamentals of astrodynamics and applications. McGraw-Hill, New York Vallado DA (1997) Fundamentals of astrodynamics and applications. McGraw-Hill, New York
56.
go back to reference Schaub H-P (2002) Spacecraft relative orbit geometry description through orbit element differences. In: 14th US national congress of theoretical and applied mechanics, Blacksburg, 23–28 June, 2002 Schaub H-P (2002) Spacecraft relative orbit geometry description through orbit element differences. In: 14th US national congress of theoretical and applied mechanics, Blacksburg, 23–28 June, 2002
57.
go back to reference Montenbruck O, Kirschner M, D’Amico S, Bettadpur S (2006) E/I-vector separation for safe switching of the GRACE formation. Aerosp Sci Technol 10(7):628–635MATHCrossRef Montenbruck O, Kirschner M, D’Amico S, Bettadpur S (2006) E/I-vector separation for safe switching of the GRACE formation. Aerosp Sci Technol 10(7):628–635MATHCrossRef
58.
go back to reference Tschauner J, Hempel P (1965) Rendezvous zu einem in Elliptischer Bahn Umlaufenden Ziel. Astronaut Acta 11:104–109MATH Tschauner J, Hempel P (1965) Rendezvous zu einem in Elliptischer Bahn Umlaufenden Ziel. Astronaut Acta 11:104–109MATH
59.
go back to reference Yamanaka K, Ankersen F (2002) New state transition matrix for relative motion on an arbitrary elliptical orbit. J Guid Contr Dyn 25(1):60–66. doi:10.2514/2.4875 CrossRef Yamanaka K, Ankersen F (2002) New state transition matrix for relative motion on an arbitrary elliptical orbit. J Guid Contr Dyn 25(1):60–66. doi:10.​2514/​2.​4875 CrossRef
60.
go back to reference Gim D-W, Alfriend KT (2001) The state transition matrix of relative motion for the perturbed non-circular reference orbit. Paper no. 01–222, AAS/AIAA space flight mechanics meeting, Santa Barbara, Feb 2001 Gim D-W, Alfriend KT (2001) The state transition matrix of relative motion for the perturbed non-circular reference orbit. Paper no. 01–222, AAS/AIAA space flight mechanics meeting, Santa Barbara, Feb 2001
61.
go back to reference Carter T, Humi M (2002) Clohessy–Wiltshire equations modified to include quadratic drag. J Guid Contr Dyn 25(6):1058–1063CrossRef Carter T, Humi M (2002) Clohessy–Wiltshire equations modified to include quadratic drag. J Guid Contr Dyn 25(6):1058–1063CrossRef
62.
go back to reference Schweighart SA, Sedwick RJ (2002) High-fidelity linearized J2 model for satellite formation flight. J Guid Contr Dyn 25(6):1073–1080CrossRef Schweighart SA, Sedwick RJ (2002) High-fidelity linearized J2 model for satellite formation flight. J Guid Contr Dyn 25(6):1073–1080CrossRef
63.
go back to reference Hamel JF, De LaFontaine J (2007) Linearized dynamics of formation flying spacecraft on a J2-perturbed elliptical orbit. J Guid Contr Dyn 30(6):1649–1658. doi:10.2514/1.29438 CrossRef Hamel JF, De LaFontaine J (2007) Linearized dynamics of formation flying spacecraft on a J2-perturbed elliptical orbit. J Guid Contr Dyn 30(6):1649–1658. doi:10.​2514/​1.​29438 CrossRef
64.
go back to reference Montenbruck O, Gill E (2000) Satellite orbits – models, methods and applications. Springer Verlag, HeidelbergMATH Montenbruck O, Gill E (2000) Satellite orbits – models, methods and applications. Springer Verlag, HeidelbergMATH
65.
go back to reference Dach R, Hugentobler U, Fridez P, Meindl M (2007) Bernese GPS software version 5.0 – user manual. University of Bern, Jan 2007 Dach R, Hugentobler U, Fridez P, Meindl M (2007) Bernese GPS software version 5.0 – user manual. University of Bern, Jan 2007
66.
go back to reference Rowlands D, Marshall JA, McCarthy J et al (1995) GEODYN system description II, vol 1–5. Hughes STX, Greenbelt Rowlands D, Marshall JA, McCarthy J et al (1995) GEODYN system description II, vol 1–5. Hughes STX, Greenbelt
68.
go back to reference Springer T (2009), NAPEOS Mathematical Models and Algorithms. DOPS-SYS-TN-0100-OPS-GN, Issue 1.0, Nov. 2009, ESA/ESOC, Darmstadt Springer T (2009), NAPEOS Mathematical Models and Algorithms. DOPS-SYS-TN-0100-OPS-GN, Issue 1.0, Nov. 2009, ESA/ESOC, Darmstadt
69.
go back to reference Goldstein DB, Born GH, Axelrad P (2001) Real-time, autonomous precise orbit determination using GPS. Navig: J ION 48(3):155–168 Goldstein DB, Born GH, Axelrad P (2001) Real-time, autonomous precise orbit determination using GPS. Navig: J ION 48(3):155–168
71.
go back to reference Vallado DA, Finkleman D (2008) A critical assessment of satellite drag and atmospheric density modeling. AIAA-2008-6442, AIAA/AAS astrodynamics specialist conference, Honolulu, Hawaii, 18–21 Aug 2008 Vallado DA, Finkleman D (2008) A critical assessment of satellite drag and atmospheric density modeling. AIAA-2008-6442, AIAA/AAS astrodynamics specialist conference, Honolulu, Hawaii, 18–21 Aug 2008
72.
go back to reference Wu SC, Yunck TP, Thornton CL (1991) Reduced-dynamic technique for precise orbit determination of low Earth satellites. J Guid Contr Dyn 14(1):24–30CrossRef Wu SC, Yunck TP, Thornton CL (1991) Reduced-dynamic technique for precise orbit determination of low Earth satellites. J Guid Contr Dyn 14(1):24–30CrossRef
74.
go back to reference Montenbruck O, Hauschild A, Zangerl F, Zsalcsik W, Ramos-Bosch P, Klein U (2009) Onboard real-time navigation for the sentinel-3 mission. ION-GNSS-2009, Savannah, USA, 22–25 Sept 2009 Montenbruck O, Hauschild A, Zangerl F, Zsalcsik W, Ramos-Bosch P, Klein U (2009) Onboard real-time navigation for the sentinel-3 mission. ION-GNSS-2009, Savannah, USA, 22–25 Sept 2009
75.
go back to reference Montenbruck O, Wermuth M, Kahle R (2010) GPS based relative navigation for the TanDEM-X mission – first flight results. ION-GNSS-2010 conference, Portland, Oregon, 21–24 Sept 2010 Montenbruck O, Wermuth M, Kahle R (2010) GPS based relative navigation for the TanDEM-X mission – first flight results. ION-GNSS-2010 conference, Portland, Oregon, 21–24 Sept 2010
76.
go back to reference D’Amico S, Gill E, Garcia-Fernandez M, Montenbruck O (2006) GPS-based real-time navigation for the PRISMA formation flying mission. 3rd ESA workshop on satellite navigation user equipment technologies, NAVITEC’2006, Noordwijk, 11–13 Dec 2006 D’Amico S, Gill E, Garcia-Fernandez M, Montenbruck O (2006) GPS-based real-time navigation for the PRISMA formation flying mission. 3rd ESA workshop on satellite navigation user equipment technologies, NAVITEC’2006, Noordwijk, 11–13 Dec 2006
77.
go back to reference D’Amico S, Ardaens J-S, Montenbruck O (2009) Navigation of formation flying spacecraft using GPS: the PRISMA technology demonstration. ION-GNSS-2009, Savannah, USA, 22–25 Sept 2009 D’Amico S, Ardaens J-S, Montenbruck O (2009) Navigation of formation flying spacecraft using GPS: the PRISMA technology demonstration. ION-GNSS-2009, Savannah, USA, 22–25 Sept 2009
79.
go back to reference Shampine LF, Gordon MK (1975) Computer solution of ordinary differential equations. Freeman and Comp., San FranciscoMATH Shampine LF, Gordon MK (1975) Computer solution of ordinary differential equations. Freeman and Comp., San FranciscoMATH
80.
go back to reference Wermuth M, Montenbruck O, van Helleputte T (2010) GPS High precision Orbit determination software tools (GHOST). 4th international conference on astrodynamics tools and techniques, Madrid, 3–6 May 2010 Wermuth M, Montenbruck O, van Helleputte T (2010) GPS High precision Orbit determination software tools (GHOST). 4th international conference on astrodynamics tools and techniques, Madrid, 3–6 May 2010
81.
go back to reference Hairer E, Nørsett SP, Wanner G (1987) Solving ordinary differential equations I. Springer, Berlin-Heidelberg/New YorkMATH Hairer E, Nørsett SP, Wanner G (1987) Solving ordinary differential equations I. Springer, Berlin-Heidelberg/New YorkMATH
82.
go back to reference Gill E, Montenbruck O, Kayal H (2001) The BIRD Satellite Mission as a milestone towards GPS-based autonomous navigation. Navig: J ION 48(2):69–75 Gill E, Montenbruck O, Kayal H (2001) The BIRD Satellite Mission as a milestone towards GPS-based autonomous navigation. Navig: J ION 48(2):69–75
83.
go back to reference Montenbruck O, Markgraf M, Santandrea S, Naudet J, Gantois K, Vuilleumier P (2008) Autonomous and precise navigation of the PROBA-2 spacecraft. AIAA 2008–7086, AIAA astrodynamics specialist conference, Honolulu, Hawaii, 18–21 Aug 2008 Montenbruck O, Markgraf M, Santandrea S, Naudet J, Gantois K, Vuilleumier P (2008) Autonomous and precise navigation of the PROBA-2 spacecraft. AIAA 2008–7086, AIAA astrodynamics specialist conference, Honolulu, Hawaii, 18–21 Aug 2008
84.
go back to reference Kroes R (2006) Precise relative positioning of formation flying spacecraft using GPS. Ph.D. thesis, TU Delft Kroes R (2006) Precise relative positioning of formation flying spacecraft using GPS. Ph.D. thesis, TU Delft
86.
go back to reference Brown RG, Hwang PYC (1992) Introduction to random signals and applied Kalman filtering, 2nd edn. Wiley, New YorkMATH Brown RG, Hwang PYC (1992) Introduction to random signals and applied Kalman filtering, 2nd edn. Wiley, New YorkMATH
88.
go back to reference Ilyas M, Lim J, Lee JG, Park CG (2008) Federated unscented Kalman filter design for multiple satellites formation flying in LEO. International conference on control, automation and systems, Seoul, Korea, 14–17 Oct 2008 Ilyas M, Lim J, Lee JG, Park CG (2008) Federated unscented Kalman filter design for multiple satellites formation flying in LEO. International conference on control, automation and systems, Seoul, Korea, 14–17 Oct 2008
89.
go back to reference Pardal PCPM, Kuga HK, Vilhena de Moraes R (2011) Robustness assessment between sigma point and extended Kalman filter for orbit determination. In: 22nd international symposium on spaceflight dynamics, Sao Jose dos Campos, Brazil, 28 Feb–4 Mar 2011 Pardal PCPM, Kuga HK, Vilhena de Moraes R (2011) Robustness assessment between sigma point and extended Kalman filter for orbit determination. In: 22nd international symposium on spaceflight dynamics, Sao Jose dos Campos, Brazil, 28 Feb–4 Mar 2011
90.
go back to reference Bierman GJ (1977) Factorization methods for discrete sequential estimation. Academic, New YorkMATH Bierman GJ (1977) Factorization methods for discrete sequential estimation. Academic, New YorkMATH
91.
go back to reference Busse FD, How JP, Simpson J (2002) Demonstration of adaptive extended Kalman filter for low earth orbit formation estimation using CDGPS. In: Proceedings of ION-GPS-2002, Portland, OR, 24–27 Sept 2002 Busse FD, How JP, Simpson J (2002) Demonstration of adaptive extended Kalman filter for low earth orbit formation estimation using CDGPS. In: Proceedings of ION-GPS-2002, Portland, OR, 24–27 Sept 2002
92.
go back to reference Leung S, Montenbruck O (2005) Real-time navigation of formation-flying spacecraft using global positioning system measurements. J Guid Contr Dyn 28(2):226–235CrossRef Leung S, Montenbruck O (2005) Real-time navigation of formation-flying spacecraft using global positioning system measurements. J Guid Contr Dyn 28(2):226–235CrossRef
93.
go back to reference Roth N, Urbanek J, Johnston-Lemke B, Bradbury L, Armitage S, Leonard M, Ligori M, Grant C, Damaren C, Zee R (2011) System-level overview of CanX-4 and CanX-5 formation flying satellites. 4th international conference on spacecraft formation flying missions and technologies, St-Hubert, Quebec, 18–20 May 2011 Roth N, Urbanek J, Johnston-Lemke B, Bradbury L, Armitage S, Leonard M, Ligori M, Grant C, Damaren C, Zee R (2011) System-level overview of CanX-4 and CanX-5 formation flying satellites. 4th international conference on spacecraft formation flying missions and technologies, St-Hubert, Quebec, 18–20 May 2011
94.
go back to reference Ebinuma T, Bishop RH, Lightsey G (2001) Spacecraft rendezvous using GPS relative navigation. In: AAS 01–152, 11th annual AAS/AIAA space flight mechanics meeting, Santa Barbara, CA Ebinuma T, Bishop RH, Lightsey G (2001) Spacecraft rendezvous using GPS relative navigation. In: AAS 01–152, 11th annual AAS/AIAA space flight mechanics meeting, Santa Barbara, CA
95.
go back to reference Park YW, Brazzel JP Jr, Carpenter JR, Hinkel HD, Newman JH (1996) Flight test results from real-time relative global positioning system flight experiment on STS-69, vol 104824, NASA technical memorandum. National Aeronautics and Space Administration, Washington, DC Park YW, Brazzel JP Jr, Carpenter JR, Hinkel HD, Newman JH (1996) Flight test results from real-time relative global positioning system flight experiment on STS-69, vol 104824, NASA technical memorandum. National Aeronautics and Space Administration, Washington, DC
96.
go back to reference Moreau G, Marcille H(1997) RGPS postflight analysis of ARP-K flight demonstration. 12th international symposium on spaceflight dynamics, Darmstadt, Germany, ESA SP-403, 2–6 June 1997, pp 97–102 Moreau G, Marcille H(1997) RGPS postflight analysis of ARP-K flight demonstration. 12th international symposium on spaceflight dynamics, Darmstadt, Germany, ESA SP-403, 2–6 June 1997, pp 97–102
97.
go back to reference Highsmith D, Axelrad P (1999) Relative state estimation using GPS flight data from co-orbiting spacecraft. ION-GPS-1999, Nashville TN, 14–17 Sept 1999 Highsmith D, Axelrad P (1999) Relative state estimation using GPS flight data from co-orbiting spacecraft. ION-GPS-1999, Nashville TN, 14–17 Sept 1999
98.
go back to reference Moreau G, Marcille H (1998) On-board precise relative orbit determination. 2nd European symposium on global navigation satellite systems, Toulouse, France, 20–23 Oct 1998 Moreau G, Marcille H (1998) On-board precise relative orbit determination. 2nd European symposium on global navigation satellite systems, Toulouse, France, 20–23 Oct 1998
99.
go back to reference Cavrois B, Personne G, Stramdmoe S, Reynuad S, Narmada Zink M (2008) Two different implemented relative position/velocity estimations using GPS sensors on-board-ATV. 7th ESA conference on guidance, navigation and control systems, Tralee, Ireland, 2–5 June 2008 Cavrois B, Personne G, Stramdmoe S, Reynuad S, Narmada Zink M (2008) Two different implemented relative position/velocity estimations using GPS sensors on-board-ATV. 7th ESA conference on guidance, navigation and control systems, Tralee, Ireland, 2–5 June 2008
100.
go back to reference Kawano I, Mokuno M, Kasai T, Suzuki T (1999) First autonomous rendezvous using relative GPS navigation by ETS-VII. ION-GPS-1999, Nashville TN, 14–17 Sept 1999 Kawano I, Mokuno M, Kasai T, Suzuki T (1999) First autonomous rendezvous using relative GPS navigation by ETS-VII. ION-GPS-1999, Nashville TN, 14–17 Sept 1999
101.
go back to reference Kawano I, Mokuno M, Miyano T, Suzuki T (2000) Analysis and evaluation of GPS relative navigation using carrier phase for RVD experiment satellite of ETS-VII. ION-GPS-2000, Salt Lake City, Utah, 19–22 Sept 2000 Kawano I, Mokuno M, Miyano T, Suzuki T (2000) Analysis and evaluation of GPS relative navigation using carrier phase for RVD experiment satellite of ETS-VII. ION-GPS-2000, Salt Lake City, Utah, 19–22 Sept 2000
102.
go back to reference Krieger G, Moreira A, Fiedler H, Hajnsek I, Werner M, Younis M, Zink M (2007) TanDEM-X: a satellite formation for high resolution SAR interferometry. IEEE Trans Geosci Rem Sens 45(11):3317–3341. doi:10.1109/TGRS.2007.900693 CrossRef Krieger G, Moreira A, Fiedler H, Hajnsek I, Werner M, Younis M, Zink M (2007) TanDEM-X: a satellite formation for high resolution SAR interferometry. IEEE Trans Geosci Rem Sens 45(11):3317–3341. doi:10.​1109/​TGRS.​2007.​900693 CrossRef
103.
go back to reference Wermuth M, Montenbruck O, Wendleder A (2011) Relative navigation for the TanDEM-X mission and evaluation with DEM calibration results. 22nd international symposium on spaceflight dynamics, Sao Jose dos Campos, Brazil, 28 Feb–4 Mar 2011 Wermuth M, Montenbruck O, Wendleder A (2011) Relative navigation for the TanDEM-X mission and evaluation with DEM calibration results. 22nd international symposium on spaceflight dynamics, Sao Jose dos Campos, Brazil, 28 Feb–4 Mar 2011
104.
go back to reference 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):L09607CrossRef 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):L09607CrossRef
105.
go back to reference Bertiger W, Bar-Sever Y, Desai S, Dunn C, Haines B, Kruizinga G, Kuang D, Nandi S, Romans L, Watkins M, Wu S, Bettadpur S (2002) GRACE: millimeters and microns in orbit. In: Proceedings of ION-GPS-2002, Portland, Oregon, pp 2022–2029, 24–27 Sept 2002 Bertiger W, Bar-Sever Y, Desai S, Dunn C, Haines B, Kruizinga G, Kuang D, Nandi S, Romans L, Watkins M, Wu S, Bettadpur S (2002) GRACE: millimeters and microns in orbit. In: Proceedings of ION-GPS-2002, Portland, Oregon, pp 2022–2029, 24–27 Sept 2002
106.
go back to reference Svehla D, Rothacher M (2004) Formation flying of LEO satellites using GPS. EOS Trans. AGU, 85(47), Fall Meeting Supplement Abstract SF53A-0735. American Geosciences Union 2004, San Francisco, 13–17 Dec 2004 Svehla D, Rothacher M (2004) Formation flying of LEO satellites using GPS. EOS Trans. AGU, 85(47), Fall Meeting Supplement Abstract SF53A-0735. American Geosciences Union 2004, San Francisco, 13–17 Dec 2004
107.
go back to reference Wickert J, Arras Ch, Beyerle G, Heise S, Jakowski N, Rothacher M, Schmidt Th, Stosius R (2009) Scientifc use of GPS signals in space. 7th IAA symposium on small satellite for earth observation, Berlin, 4–8 May 2009 Wickert J, Arras Ch, Beyerle G, Heise S, Jakowski N, Rothacher M, Schmidt Th, Stosius R (2009) Scientifc use of GPS signals in space. 7th IAA symposium on small satellite for earth observation, Berlin, 4–8 May 2009
108.
go back to reference Montenbruck O, Wermuth M, Kahle R (2010) GPS based relative navigation for the TanDEM-X mission – first flight results. ION-GNSS-2010 conference, Portland, Oregon, 21–24 Sep 2010 Montenbruck O, Wermuth M, Kahle R (2010) GPS based relative navigation for the TanDEM-X mission – first flight results. ION-GNSS-2010 conference, Portland, Oregon, 21–24 Sep 2010
109.
go back to reference Jäggi A, Montenbruck O, König R, Wermuth M, Moon Y, Bock H, Bodenmann D(2012)Inter-agency comparison of TerraSAR-X and TanDEM-X baseline solutions; Advances in Space Research 50(2):260–271. doi:10.1016/j.asr.2012.03.027 Jäggi A, Montenbruck O, König R, Wermuth M, Moon Y, Bock H, Bodenmann D(2012)Inter-agency comparison of TerraSAR-X and TanDEM-X baseline solutions; Advances in Space Research 50(2):260–271. doi:10.​1016/​j.​asr.​2012.​03.​027
110.
go back to reference Ardaens JS, D’Amico S, Montenbruck O (2011) Final commissioning of the PRISMA GPS navigation system. 22nd international symposium on spaceflight dynamics, Sao Jose dos Campos, Brazil, 28 Feb–4 Mar 2011 Ardaens JS, D’Amico S, Montenbruck O (2011) Final commissioning of the PRISMA GPS navigation system. 22nd international symposium on spaceflight dynamics, Sao Jose dos Campos, Brazil, 28 Feb–4 Mar 2011
111.
go back to reference Montenbruck O, Delpech M, Ardaens J-S, Delong N, D’Amico S, Harr J (2008) Cross-validation of GPS and FFRF-based relative navigation for the PRISMA mission. 4th ESA workshop on satellite navigation user equipment technologies. NAVITEC’2008, ESA/ESTEC, Noordwijk, ESA WPP-297, 10–12 Dec 2008 Montenbruck O, Delpech M, Ardaens J-S, Delong N, D’Amico S, Harr J (2008) Cross-validation of GPS and FFRF-based relative navigation for the PRISMA mission. 4th ESA workshop on satellite navigation user equipment technologies. NAVITEC’2008, ESA/ESTEC, Noordwijk, ESA WPP-297, 10–12 Dec 2008
112.
go back to reference Grelier T, Guidotti P-Y, Delpech M, Harr J, Thevenet J-B, Leyre X (2010) Formation flying radio frequency instrument: first flight results from the PRISMA mission. NAVITEC’2010, Noordwijk, The Netherlands, 8–10 Dec 2010 Grelier T, Guidotti P-Y, Delpech M, Harr J, Thevenet J-B, Leyre X (2010) Formation flying radio frequency instrument: first flight results from the PRISMA mission. NAVITEC’2010, Noordwijk, The Netherlands, 8–10 Dec 2010
113.
go back to reference D’Amico S, De Florio S, Ardaens J-S, Yamamoto T (2008) Offline and hardware-in-the-loop validation of the GPS-based real-time navigation system for the PRISMA formation flying mission. 3rd international symposium on formation flying, missions and technology, ESA/ESTEC, Noordwijk, 23–25 Apr 2008 D’Amico S, De Florio S, Ardaens J-S, Yamamoto T (2008) Offline and hardware-in-the-loop validation of the GPS-based real-time navigation system for the PRISMA formation flying mission. 3rd international symposium on formation flying, missions and technology, ESA/ESTEC, Noordwijk, 23–25 Apr 2008
114.
go back to reference D’Amico S, Ardaens J-S, Larsson R (2011) In-flight demonstration of formation control based on relative orbital elements. 4th international conference on spacecraft formation flying missions and technologies, St-Hubert, Quebec, 18–20 May 2011 D’Amico S, Ardaens J-S, Larsson R (2011) In-flight demonstration of formation control based on relative orbital elements. 4th international conference on spacecraft formation flying missions and technologies, St-Hubert, Quebec, 18–20 May 2011
115.
go back to reference Larsson R, Noteborn R, Bodin P, D’Amico S, Karlsson T, Carlsson A (2011) Autonomous formation flying in LEO – seven months of routine formation flying with frequent reconfigurations. 4th international conference on spacecraft formation flying missions and technologies, St-Hubert, Quebec, 18–20 May 2011 Larsson R, Noteborn R, Bodin P, D’Amico S, Karlsson T, Carlsson A (2011) Autonomous formation flying in LEO – seven months of routine formation flying with frequent reconfigurations. 4th international conference on spacecraft formation flying missions and technologies, St-Hubert, Quebec, 18–20 May 2011
116.
go back to reference Larsson R, D’Amico S, Noteborn R, Bodin P (2011) GPS navigation based proximity operations by the PRISMA satellites – flight results. 4th international conference on spacecraft formation flying missions and technologies, St-Hubert, Quebec, 18–20 May 2011 Larsson R, D’Amico S, Noteborn R, Bodin P (2011) GPS navigation based proximity operations by the PRISMA satellites – flight results. 4th international conference on spacecraft formation flying missions and technologies, St-Hubert, Quebec, 18–20 May 2011
Metadata
Title
GPS Based Relative Navigation
Authors
Oliver Montenbruck
Simone D’Amico
Copyright Year
2013
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-4541-8_5

Premium Partner