Journal of Systems Science and Complexity

, Volume 31, Issue 5, pp 1206–1226 | Cite as

Observability Analysis and Navigation Algorithm for Distributed Satellites System Using Relative Range Measurements

  • Qiya Su
  • Yi HuangEmail author


The problem of navigation for the distributed satellites system using relative range measurements is investigated. Firstly, observability for every participating satellites is analyzed based on the nonlinear Keplerian model containing J2 perturbation and the nonlinear measurements. It is proven that the minimum number of tracking satellites to assure the observability of the distributed satellites system is three. Additionally, the analysis shows that the J2 perturbation and the nonlinearity make little contribution to improve the observability for the navigation. Then, a quasi-consistent extended Kalman filter based navigation algorithm is proposed, which is quasi-consistent and can provide an online evaluation of the navigation precision. The simulation illustrates the feasibility and effectiveness of the proposed navigation algorithm for the distributed satellites system.


Distributed satellites system (DSS) navigation observability quasi-consistent extended Kalman filter (QCEKF) relative range 


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  1. [1]
    Schetter T, Campbell M, and Surka D, Multiple agent-based autonomy for satellite constellations, Artificial Intelligence, 2003, 145: 147–180.CrossRefGoogle Scholar
  2. [2]
    Norma M and Heinz N I, Agent-based artificial immune system model for the detection of faults in a distributed satellite system, Proceedings of the First AESS European Conference on Satellite Telecommunications (ESTEL), Rome, 2012, 1–6.Google Scholar
  3. [3]
    Tapley B D, Ries J C, Davis G W, et al., Precision orbit determination for TOPEX/POSEIDON, Journal of Geophysical Research, Dec. 1994, 99(C12): 24383–24404.Google Scholar
  4. [4]
    Kang W, Ross I M, Pham K, et al., Autonomous observability of networked multisatellite systems, Journal of Gudance, Control, and Dynamics, 2009, 32(3): 869–877.CrossRefGoogle Scholar
  5. [5]
    Markley F L, Autonomous navigation using landmark and intersatellite data, AIAA/AAS Astrodynamics Conference, Seattle, WA, 1984.CrossRefGoogle Scholar
  6. [6]
    Psiaki M L, Autonomous low-Earth-orbit determination from magnetometer and sun sensor data, Journal of Guidance, Control, and Dynamics, 1999, 22(2): 296–302.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Long A C, Leung D, Folta D, et al., Autonomous navigation of high-Earth satellites using celestial objects and Doppler measurements, AIAA/AAS Astrodynamics Specialist Conference, Denver, CO, 2000.CrossRefGoogle Scholar
  8. [8]
    Liu Y and Liu L, Orbit determination using satellite-to-satellite tracking data, Chinese Journal of Astronomy and Astrophysics, 2001, 1(3): 281–286.CrossRefGoogle Scholar
  9. [9]
    Grechkoseev A K, Study of observability of motion of an orbital group of navigation space system using intersatellite range measurements I, Journal of Computer and Systems Sciences International, 2011, 50(2): 293–308.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Grechkoseev A K, Study of observability of motion of an orbital group of navigation space system using intersatellite range measurements II, Journal of Computer and Systems Sciences International, 2011, 50(3): 472–482.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Huxel P J and Bishop R H, Navigation algorithms and observability analysis for formation flying missions, Journal of Guidance, Control and Dynamics, 2009, 32(4): 1218–1231.CrossRefGoogle Scholar
  12. [12]
    Hill K and Born G H, Autonomous interplanetary orbit determination using satellite-to-satellite tracking, Journal of Guidance, Control and Dynamics, 2007, 30(3): 679–686.CrossRefGoogle Scholar
  13. [13]
    Hill K and Born G H, Autonomous orbit determination from lunar halo orbits using crosslink range, Journal of Spacecraft and Rockets, 2008, 45(3): 548–553.CrossRefGoogle Scholar
  14. [14]
    Psiaki M L, Autonomous orbit determination for two spacecraft from relative position measurements, Journal of Guidance, Control, and Dynamics, 1999, 22(2): 305–312.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Yim J R, Crassidis J L, and Junkins J L, Autonomous orbit navigation of two spacecraft system using relative line of sight vector measurements, Proceedings of the AAS Space Flight Mechanics Meeting, Maui, Hawaii, USA, Feb. 2004.Google Scholar
  16. [16]
    Shorshi G and Bar-Itzhack I Y, Satellite autonomous navigation and orbit determination using magnetometers, Proceedings of the 31st Conference on Decision and Control, Tucson, Arizona, 1992, 542–548.Google Scholar
  17. [17]
    Wiegand M, Autonomous satellite navigation via Kalman filter of magnetometer data, Acta Astronautica, 1996, 38(4–8): 395–403.CrossRefGoogle Scholar
  18. [18]
    Bar-Shalom Y, Li X R, and Kirubarajan T, Estimation with Application to Tracking and Navigation, John Wiley & Sons Inc., New York, 2001.CrossRefGoogle Scholar
  19. [19]
    Jiang Y G, Xue W C, Huang Y, et al., The consistent extended Kalman filter, Proceedings of the 33rd Chinese Control Conference, Nanjing, China, July, 2014.Google Scholar
  20. [20]
    Sabol C, Burns R, and McLaughlin C A, Satellite formation flying design and evolution, Journal of Spacecraft and Rockets, 2001, 38(2): 270–278.CrossRefGoogle Scholar
  21. [21]
    Clohessy W and Wiltshire R, Terminal guidance systems for satellite rendezvous, Journal of the Aerospace Sciences, 1960, 27: 653–674.CrossRefzbMATHGoogle Scholar
  22. [22]
    Roy A E, Orbital Motion, 4th Edition, Institute of Physics Publishing, Bristol, 2005.zbMATHGoogle Scholar
  23. [23]
    Isidori A, Nonlinear Control Systems, 3rd Edition, Springer-Verlag World Publishing Corp, London, 1995.CrossRefzbMATHGoogle Scholar
  24. [24]
    Eckart C and Young G, A principal axis transformation for non-hermitian matrices, Bulletin of the American Mathematical Society, 1939, 45: 118–121.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    Dochain D, Tali-Mammar N, and Babary J P, On modeling, monitoring and control of fixed bed bioreactors, Computers & Chemical Engineering, 1997, 21(11): 1255–1266.Google Scholar
  26. [26]
    Klema V C and Laub A J, The singular value decomposition: Its computation and some applications, IEEE Transaction Automatic Control, 1980, 25(2): 164–176.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Simon D, Optimal State Estimation — Kalman, H∞, and Nonlinear Approaches, John Wiley & Sons Inc., New Jersey, 2006.CrossRefGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Beijing Institute of Remote Sensing EquipmentBeijingChina
  2. 2.Key Laboratory of Systems and Control, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  3. 3.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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