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, 23:25 | Cite as

Comparing satellite orbit determination by batch processing and extended Kalman filtering using inter-satellite link measurements of the next-generation BeiDou satellites

  • Xia RenEmail author
  • Yuanxi Yang
  • Jun Zhu
  • Tianhe Xu
Original Article
  • 223 Downloads

Abstract

The next-generation BeiDou satellites are equipped with inter-satellite link (ISL) payloads to realize the ability of autonomous navigation (Auto-Nav). We focus on the application of batch processing and extended Kalman filtering (EKF) algorithm on Auto-Nav of BeiDou satellite system (BDS). The mathematical model of dual one-way measurements and principle of batch mode and EKF are introduced. Using real ISL measurements, Auto-Nav experiments are conducted with batch processing and EKF, respectively. For the sub-constellation, the EKF with a priori equipment delay constraints is proposed. The result shows that (1) with three ISLs and only one anchor station, the ISL measurements are sparsely distributed and the coverage of the whole arc is about 31%. The observations and dynamic models per epoch contribute more to satellite position and velocity parameters than to equipment delay parameters. (2) For batch processing, the overlap precision of precise orbit determination (POD) with ISLs and ground-satellite links (GSLs) is about 0.1 m in the radial direction and is better than 1 m three-dimensionally. The variation of the estimated equipment delays is within \(\pm \,0.6\) ns. The observation residuals of ISLs behave such as a normal distribution, while the residual of GSLs show periodical variation due to uncorrected troposphere delay. (3) For the EKF, the ISL-only orbit determination is sensitive to the accuracy of the initial state. Compared with batch result, the precision of ISL-only orbit determination using EKF is better than 2 m given accurate initial states. The filtering does not show constellation drift or rotation within 8 days. However, with approximate initial states which position accuracy is 100 m, the precision of POD decreases to dozens of meters. (4) For the EKF, the accuracy of POD improves to 1.5 m in three dimensions with the support of an anchor station. The period for equipment delay parameters to converge is about 24 h. However, the convergence rate of equipment delay parameters is much slower than that of satellite state parameters. The possible reason is the unbalanced contribution of observation and dynamic model information on the estimated parameters. Thus, it is better to constrain the equipment delay parameters with a priori information while filtering.

Keywords

Inter-satellite link Autonomous navigation Batch processing Extended Kalman filtering 

Notes

Acknowledgements

The study was funded by the National Key Research and Development Program of China (2016YFBOS01700, 2016YFB0501701), National Natural Science Foundation of China (41374019, 11503096, 41574013), and China Postdoctoral Science Foundation (2015M572691).

References

  1. Ananda MP, Bemstein H, Cunningham KE, Feess WA, Stroud EG (1990) Global positioning system (GPS) autonomous navigation. In: Position location and navigation symposium.  https://doi.org/10.1109/PLANS.1990.66220
  2. Chen JP, Hu XG, Tang CP, Zhou SS, Guo R, Pan JY, Li R, Zhu LF (2016) Orbit determination and time synchronization for new-generation BeiDou satellites: preliminary results (in Chinese). Sci Sin Phys Mech Astron 46(11):119502CrossRefGoogle Scholar
  3. Gill E (1999) Precise GNSS-2 satellite orbit determination based on inter-satellite-links. In: 14th international symposium on space flight mechanics, February 8–12, Iguassu, BrazilGoogle Scholar
  4. Menn MD, Bemstein H (1994) Ephemeris observability issues in the global positioning system (GPS) autonomous navigation (AUTONAV). In: IEEE position location and navigation symposium.  https://doi.org/10.1109/PLANS.1994.303376
  5. Montenbruck O, Gill E (2001) Satellite orbit models, methods, and application. Springer, New YorkGoogle Scholar
  6. Rajan J (2002) Highlights of GPS II-R autonomous navigation. In: Proceedings of ION AM 2002, institute of navigation, Albuquerque, New Mexico, USA, June 24–26, pp 354–363Google Scholar
  7. Rajan J, Brodie P, Rawicz H (2003) Modernizing GPS autonomous navigation with anchor capability. In: Proceedings of ION GPS 2003, Institute of Navigation, Portland, Oregon, USA, September 9–12, pp 1534–1542Google Scholar
  8. Ren X, Yang YX, Zhu J, Xu TH (2017) Orbit determination of the next-generation BeiDou satellites with intersatellite link measurements and a priori orbit constraints. Adv Space Res 60(10):2155–2165CrossRefGoogle Scholar
  9. Ruan RG, Feng LP, Jia XL (2014) Equipment delay estimation for GNSS satellite combined orbit determination with satellite-ground link and inter-satellite link observations. Acta Geod Cartogr Sin 43(2):137–142Google Scholar
  10. Tang CP et al (2016) Improvement of orbit determination accuracy for BeiDou navigation satellite system with two-way satellite time frequency transfer. Adv Space Res 58(7):1390–1400CrossRefGoogle Scholar
  11. Tang CP, Hu XG, Zhou SS, Yang JP, Guo R, Hu GM, Zhu LF, Li XJ, Wu S, Wang Y (2017) Centralized autonomous orbit determination of Beidou navigation satellites with inter-satellite link measurements: preliminary results (in Chinese). Sci Sin Phys Mech Astron 47(2):029501CrossRefGoogle Scholar
  12. Wolf R (2000) Onboard autonomous integrity monitoring using intersatellite links. Dissertation for the doctor degree. University of München, GermanyGoogle Scholar
  13. Yang Y (1989) The respective roles and contributions of various observations in integrated geodesy. Acta Geod Cartogr Sin 18(3):232–238Google Scholar
  14. Yang Y (2006) Adaptive navigation and kinematic positioning. Surveying and Mapping Press, BeijingGoogle Scholar
  15. Yang Y, Zhang X, Xu J (2011) Adaptively constrained Kalman filtering for navigation applications. Surv Rev 43(322):370–381CrossRefGoogle Scholar
  16. Yang D, Yang J, Li G, Zhou Y, Tang CP (2017) Globalization highlight: orbit determination using BeiDou inter-satellite ranging measurements. GPS Solut 21(3):1395–1404CrossRefGoogle Scholar
  17. Yi H, Xu B, Gao YT, Wang JS (2011) Long-term semi-autonomous orbit determination supported by a few ground stations for navigation constellation. Sci Sin Phys Mech Astron 54(7):1342–1353CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Geo-Information EngineeringXi’anChina
  2. 2.Xi’an Research Institute of Surveying and MappingXi’anChina
  3. 3.Information Engineering UniversityZhengzhouChina
  4. 4.State Key Laboratory of Astronautic DynamicsXi’anChina
  5. 5.Xi’an Satellite Control CenterXi’anChina
  6. 6.Institute of Space ScienceShandong UniversityWeihaiChina

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