Skip to main content
Log in

Low Computational Complexity in Low-Cost GNSS Receivers

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

One of the key issues in low-cost GNSS receivers is the computational complexity. One of the computational components of the GNSS receivers is the satellite positioning calculations. The main focus of this paper is to reduce the computational burden of this stage of processing. In this paper, four different models to fit the GPS and GLONASS satellites orbit are investigated. These models are compared with each other in terms of their computational load and accuracy, and the models have good accuracy and less computational load are selected. Among these four methods, the Hermite model and the Chebyshev model are superior to other methods for determining orbits of GPS and GLONASS satellites, respectively. In order to evaluate the performance of these models, two different data including ground stations data and measured data by GNSS receivers are used. The results show that these two models can improve the computational burden by about 90% compared to conventional methods like the Runge–Kutta and the Keplerian parameters that used in GNSS receivers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  1. Tabatabaei, A., Mosavi, M. R., Khavari, A., & Shahhoseini, H. S. (2016). Reliable urban canyon navigation solution in GPS and GLONASS integrated receiver using improved fuzzy weighted least-square method. Journal of Wireless Personal Communications,94(4), 3181–3196.

    Article  Google Scholar 

  2. Shojaeezand, T., Mohammad-Khani, G. R., & Azmi, P. (2017). Variance analysis of the new method of applying multiuser detection in a GPS receiver in high dynamic conditions. Journal of Wireless Personal Communications,98(3), 1–13.

    Google Scholar 

  3. Mosavi, M. R., Nabavi, H., & Nakhaei, A. (2013). Neural technologies for precise timing in electric power systems with a single-frequency GPS receiver. Journal of Wireless Personal Communications,75(2), 925–941.

    Article  Google Scholar 

  4. Moaiied, M. M., & Mosavi, M. R. (2016). Increasing accuracy of combined GPS and GLONASS positioning using fuzzy kalman filter. Iranian Journal of Electrical & Electronic Engineering,12(1), 21–28.

    Google Scholar 

  5. Gunning, K., Walter, T., & Enge, P. (2017). Characterization of GLONASS broadcast clock and ephemeris: nominal performance and fault trends for ARAIM. In The proceedings institute of navigation (pp. 170–183), January 2017, Hyatt Regency Monterey, Monterey, CA.

  6. Akim, E. L., & Tuchin, D. A. (2003). GPS errors statistical analysis for ground receiver measurements. In The proceedings of 17th international symposium on space flight dynamics, June 2003, Keldysh IAM, Moscow, Russia.

  7. Hu, H., & Fang, L. (2009). Interpolation and fitting algorithms for GPS satellite orbit. In The international remote sensing and geoscience for agricultural engineering (pp. 1–5), July 2009, Zhangjiajie, China.

  8. Gaglione, S., Angrisano, A., Pugliano, G., Robustelli, U., Santamaria, R., & Vultaggio, M. (2011). A stochastic sigma model for GLONASS satellite pseudo range. Journal of Applied Geomatics,3(4), 49–57.

    Article  Google Scholar 

  9. Góral, W., & Skorupa, B. (2012). Determination of intermediate orbit and position of GLONASS satellites based on the generalized problem of two fixed centers. Journal of Acta Geodynamica et Geomaterialia,9(3), 283–290.

    Google Scholar 

  10. Kosti, A. A., Anastassi, Z. A., & Simos, T. E. (2009). An optimized explicit Runge–Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems. Journal of Mathematical Chemistry,47(1), 315–330.

    Article  Google Scholar 

  11. Sermutlu, E. (2004). Comparison of Runge–Kutta methods of order 4 and 5 on Lorenz equation. Journal of Arts and Sciences,1(1), 61–69.

    Google Scholar 

  12. Ozawa, K. (1999). A four-stage implicit Runge–Kutta–nyström method with variable coefficients for solving periodic initial value problems. Japan Journal of Industrial and Applied Mathematics,16(1), 25–46.

    Article  MathSciNet  Google Scholar 

  13. Liu, L., & Liao, X. (1994). Numerical calculations in the orbital determination of an artificial satellite for a long arc. Journal of Celestial Mechanics and Dynamical Astronomy,59(3), 221–235.

    Article  MathSciNet  Google Scholar 

  14. Maciuk, K. (2016). Different approaches in GLONASS orbit computation from broadcast ephemeris. Journal of Geodetski Vestnik,60(3), 455–466.

    Article  Google Scholar 

  15. Goral, W., & Skorupa, B. (2015). Calculation of Position and Velocity of GLONASS Satellite Based on Analytical Theory of Motion. Journal of Planetary Geodesy,50(3), 105–114.

    Google Scholar 

  16. Neta, B., Clynch, J. R., Danielson, D. A., & Sagovac, C. P. (1996). Fast interpolation for Global Positioning System (GPS) satellite orbits. In The proceedings AIAA/AAS astrodynamics specialist conference (pp. 1–10), June 1996, San Diego, CA, USA.

  17. Feng, Y., Zheng, Y., & Bai, Z. (2004). Representing GPS orbits and corrections efficiently for precise wide area positioning. In The proceedings institute of navigation (pp. 2316–2323), September 2004, Long Beach, CA.

  18. Feng, Y., & Zheng, Y. (2005). Efficient interpolation to GPS orbits for precise wide area applications. Journal of GPS Solutions,9(4), 273–282.

    Article  Google Scholar 

  19. Schenewerk, M. (2003). A brief review of basic GPS orbit interpolation strategies. Journal of GPS Solutions,6(4), 265–267.

    Article  Google Scholar 

  20. Yousif, H., & El-Rabbany, A. (2007). Assessment of several interpolation methods for precise GPS orbit. Journal of Navigation,60(03), 443–455.

    Article  Google Scholar 

  21. Cho, D. J., & Park, S. H. (2009). A Study of GPS precise ephemeris interpolation for maritime precise positioning applications. Journal of Navigation and Port Research,33(10), 699–702.

    Article  Google Scholar 

  22. Hu, H., Yuan, C., & Fang, L. (2009). Extrapolation and fitting algorithms for GLONASS satellite orbit. In The 3rd international symposium on intelligent information technology application (pp. 282–285), November 2009, NanChang, China.

  23. Seppänen, M., Luhtala, J. A., Piché, R., Martikainen, S., & Löytty, S. A. (2012). Autonomous prediction of GPS and GLONASS satellite orbits. Journal of the Institute of Navigation,59(2), 119–134.

    Article  Google Scholar 

  24. Korvenoja, P., & Piché, R. (2000). Efficient satellite orbit approximation. In The proceedings institute of navigation (pp. 1930–1937), September 2000, Salt Palace Convention Center, Salt Lake City, UT.

  25. ICD-GLONASS. (2008). Global navigation satellite system GLONASS interface control document. Version 5.1, Moscow.

  26. Dow, J., Neilan, R., & Rizos, C. (2009). The International GNSS service in a changing landscape of global navigation satellite systems. Journal of Geodesy,83(3), 191–198.

    Article  Google Scholar 

  27. Schoenberg, I. J. (1966). On Hermite-Birkhoff interpolation. Journal of Mathematical Analysis and Applications,16(3), 538–543.

    Article  MathSciNet  Google Scholar 

  28. Acar, Y., Doğan, H., & Panayirci, E. (2016). Pilot symbol aided channel estimation for spatial modulation-OFDM systems and its performance analysis with different types of interpolations. Journal of Wireless Personal Communications,94(3), 1387–1404.

    Article  Google Scholar 

  29. Burden, R. L., Faires, J. D., & Burden, A. M. (2016). Numerical analysis. USA: Brooks Cole.

    MATH  Google Scholar 

  30. Zhan, J., Zhang, Y., Tong, H., Zhang, G., & Ou, G. (2013). Research on performance evaluation of receiver combining measurements from RDSS and RNSS for position fixing and report. In The 4th China satellite navigation conference (CSNC) (pp. 331–343), May 2013, Wuhan, China.

  31. IS-GPS. (2016). Interface control documentNavstar GPS space segment/navigation user interfaces. IS-GPS-200H.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohammad Reza Mosavi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abedi, A.A., Mosavi, M.R. & Mohammadi, K. Low Computational Complexity in Low-Cost GNSS Receivers. Wireless Pers Commun 112, 37–59 (2020). https://doi.org/10.1007/s11277-019-07014-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-019-07014-5

Keywords

Navigation