Radioelectronics and Communications Systems

, Volume 61, Issue 8, pp 350–360 | Cite as

Stochastic Estimation of Ephemerides of Navigation Satellites in Perturbed Orbits

  • S. V. Sokolov
  • V. V. KamenskijEmail author
  • S. M. Kovalev


The errors of navigation satellite ephemerides are one of the key factors to determine the accuracy of satellite navigation. To improve the accuracy of ephemerides calculation, modern satellites are equipped with inter-satellite measurement equipment. However, random interference is inevitably present in the data transmission path and it is necessary to minimize its effect. To perform this task, it is proposed to use the stochastic estimation of ephemerides of navigation satellites that are moving along disturbed orbits in the form of a procedure of parametric optimization based on the minimization of the additive set of two functionals. The optimization of the first functional provides the minimum of uncertainty in the estimation of ephemerides. The optimization of the second functional provides the minimum of the norm of the vector of orbital parameters variations in the current time interval. To illustrate the effectiveness of the proposed approach, a numerical simulation of the satellite constellation’s ephemerides estimation was carried out for the corresponding trajectory perturbations. The simulation results illustrate the possibility to determine the ephemerides of navigation satellites with the accuracy within units of meters based on the approach considered that uses the noisy inter-satellite measurements.


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  1. 1.
    A. I. Perov, V. N. Harisov, et al. GLONASS. Principles of Construction and Operation, 4th ed. [in Russian, ed. by A. I. Perov and V. N. Harisov] (Radiotekhnika, Moscow, 2010). URI:
  2. 2.
    A. Fateev, A. Vassilyev, S. Somov, “Attitude guidance and control of the navigation satellites at passage of singular orbit sites,” AIP Conf. Proc. 1798, No. 1, 020149 (2017). DOI: 10.1063/1.4972741.CrossRefGoogle Scholar
  3. 3.
    E. V. Akimov, D. A. Kozorez, M. N. Krasilshchikov, D. M. Kruzhkov, “Utilization of GNSS IT technologies for space communication and navigation system autonomous operation,” Vestnik Komp’iuternykh i Informatsionnykh Tekhnologii, No. 8, 9 (2017). DOI: 10.14489/vkit.2017.08.pp.009–018.Google Scholar
  4. 4.
    V. I. Kuznetsov, T. V. Danilova, “Multifunctional astronomical self-organizing system of autonomous navigation and orientation for artificial Earth satellites,” Cosmic Research 55, No. 2, 142 (2017). DOI: 10.1134/S0010952517020046.CrossRefGoogle Scholar
  5. 5.
    G. G. Stupak, S. G. Revnivykh, E. I. Ignatovich, V. V. Kurshin, V. V. Betanov, S. S. Panov, N. Z. Bondarev, V. E. Chebotarev, N. N. Balashova, A. I. Serdyukov, L. N. Sintsova, “Choice of structure of constellation of the prospective system GLONASS,” The Research of the Science City 6, No. 3–4, 4 (2013). URI: Scholar
  6. 6.
    V. D. Shargorodsky, V. E. Kosenko, M. A. Sadovnikov, A. A. Chubikin, V. I. Moklyak, “The role of laser tools to ensure the accuracy of GLONASS,” The Research of the Science City 6, No. 3–4, 17 (2013). URI: Scholar
  7. 7.
    R. Hryshchuk, A. Zavada, “Earth remote sensing satellite navigation based on optical trajectory measurements,” Recent Advances in Systems, Control and Information Technology, SCIT 2016. Advances in Intelligent Systems and Computing, Vol. 543 (Springer, Cham, 2017). DOI: 10.1007/978-3-319-48923-0_54.Google Scholar
  8. 8.
    K. V. Kislenko, V. V. Suevalov, “Technology of high-precision determination of the parameters of the relative motion of space vehicles according to the GLONASS satellite navigation equipment,” Cosmonautics and Rocket Engineering, No. 4, 158 (2017).Google Scholar
  9. 9.
    R. Tuttle, “Next-gen GPS navigation satellites must keep improving to keep u.s. ahead of attempts at jamming,” Aviation Week & Space Technology 158, No. 20, 46 (2003).Google Scholar
  10. 10.
    A. Ya. Yudanin, B. S. Mogilnitskii, A. S. Tolstikov, “Improvement in the orbital parameters of GLONASS navigation satellites based on non-interrogatory measurements of pseudodistances,” Meas. Tech. 52, No. 12, 1256 (2009). DOI: 10.1007/s11018-010-9430-0.CrossRefGoogle Scholar
  11. 11.
    O. N. Bogdanov, “Refinement of trajectory parameters for GPS and GLONASS navigation satellites using IGS position data,” Moscow University Mechanics Bulletin 64, No. 3, 61 (2009). DOI: 10.3 103/S0027133009030029.CrossRefGoogle Scholar
  12. 12.
    Y. J. Qian, W. X. Jing, C. S. Gao, “Autonomous navigation method for multi-satellites mission,” Harbin Gongye Daxue Xuebao 42, No. 5, 705 (2010).Google Scholar
  13. 13.
    N. A. Dugin, M. B. Nechaeva, A. A. Antipenko, A. F. Dement’ev, Yu. V. Tikhomirov, “Measurement of antenna parameters by signals from space satellites of the GLONASS and NAVSTAR navigation systems,” Radiophys. Quantum Electronics 54, No. 3, 159 (2011). DOI: 10.1007/s11141-011-9278-4.CrossRefGoogle Scholar
  14. 14.
    S. V. Sokolov, S. M. Kovalev, V. V. Kamensky, P. A. Kucherenko, “Stochastic filtering for inter-satellite measurements in great-circle trajectories,” J. Instrum. Engineering 59, No. 4, 275 (2016). DOI: 10.17586/0021-3454-2016-59-4-275-281.Google Scholar
  15. 15.
    S. V. Sokolov, “Synthesis of spatial trajectories of analytical models and their application to solving satellite navigation,” Appl. Physics Mathematics 1, No. 2, 3 (2013). URI: Scholar
  16. 16.
    S. V. Sokolov, “Analytical models of spatial trajectories for solving navigation problems,” J. Appl. Math. Mech. 79, No. 1, 17 (2015). DOI: 10.1016/j.jappmathmech.2015.04.013.MathSciNetCrossRefGoogle Scholar
  17. 17.
    A. A. Chernov, V. D. Yastrebov, “Method for estimating perturbations in algorithms for solving navigation problems,” Izv. RAN: Space Research 22, No. 3 (1984).Google Scholar
  18. 18.
    V. I. Tikhonov, V. N. Harisov, Statistical Analysis and Synthesis of Radio Engineering Devices and Systems [in Russian] (Radio i Svyaz’, Moscow, 1991).Google Scholar

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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Rostov State Transport UniversityRostov-on-DonRussia

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