Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Mitigation of Multipath Effects Based on a Robust Fractional Order Bidirectional Least Mean Square (FOBLMS) Beamforming Algorithm for GPS Receivers

  • 17 Accesses

Abstract

Consideration on positioning and location services among the public has been increasing in the recent years with their applications in most of the anticipating milieus such as automobile navigation system etc. This insists for a development of high recitation global navigation satellite system such as global positioning system (GPS). Multipath effects, interference, signal jamming etc. are the major sources of error influencing the performance of the GPS receiver. Literature presents many of the multipath mitigation techniques. Among them, adaptive processing technology based beamforming algorithms appears a viable solution for multipath mitigation. The least mean square (LMS) beamforming algorithms were sensitive to dynamic environments thus affecting the accuracy of GPS. In this paper, an adaptive beamforming algorithm called fractional order bidirectional least mean square (FOBLMS) algorithm is proposed to mitigate the multipath effects and to conceal the jammer signal in a GPS receiver. The FOBLMS is an integration of the fractional calculus and bidirectional least mean square algorithm. The effectiveness of the proposed algorithm is validated using the bit error rate and experimentation gain results over the existing beamforming algorithms. Experimental results demonstrated that the performance of the proposed beamforming algorithm is better than LMS algorithm with maximal relative antenna gain of 28.92 dB, 32.84 dB for two and four element antenna arrays at − 60° and 10°, direction of arrivals respectively. The outcome of this work would be useful for developing a robust technique for multipath mitigation in GPS receivers.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

References

  1. 1.

    Enge, P., & Misra, P. (1999). Special issue on global positioning system. Proceedings of the IEEE,87(1), 3–15.

  2. 2.

    Yang, Y., Hatch, R. R., & Sharpe, R. T. (2004). GPS multipath mitigation in measurement domain and its applications for high accuracy navigation. In Proceedings of the ION GNSS (pp. 1–6).

  3. 3.

    Xiang, F., Liao, G., Zeng, C., & Wang, W. (2013). A multipath mitigation discriminator for GPS receiver. International Journal of Electronics and Communications. https://doi.org/10.1016/j.aeue.2013.04.007.

  4. 4.

    Weill, L. R. (2002). Multipath mitigation using modernized GPS signals: How good can it get? In Proceedings of ION-GPS (pp. 493–505).

  5. 5.

    Mukhopadhyay, M., Sarkar, B. K., & Chakraborty, A. (2007). Augmentation of anti-jam GPS system using smart antenna with a simple DOA estimation algorithm. Proceedings of Progress in Electromagnetic Research,67, 231–249.

  6. 6.

    Dong, D., Wang, M., Chen, W., & Zeng, Z. (2016). Mitigation of multipath effect in GNSS short baseline positioning by the multipath hemispherical map. Journal of Geo-Informatics,90, 255–262. https://doi.org/10.1007/s00190-015-0870-9.

  7. 7.

    Garin, L., & Rousseau, J. M. (1997). Enhanced strobe correlator multipath rejection for code and carrier. In Proceedings of the tenth international technical meeting of the satellite division of the institute of navigation ION GPS-97.

  8. 8.

    Xiang, F., Liao, G., Zeng, C., & Wang, W. (2013). A multipath mitigation discriminatorfor GPS receiver. International Journal of Electronics and Communications. https://doi.org/10.1016/j.aeue.2013.04.007.

  9. 9.

    Moradi, R., Schuster, W., Feng, S., & Jokinen, A. (2014). The carrier-multipath observable: a new carrier-phase multipath mitigation technique. GPS Solution. https://doi.org/10.1007/s10291-014-0366-8.

  10. 10.

    Bétaille, D., Cross, P. A., & Euler, H. J. (2006). Assessment and improvement of the capabilities of a window correlator to model GPS multipath phase errors. IEEE Transactions on Aerospace and Electron Systems,42(2), 707–718. https://doi.org/10.1109/TAES.2006.1642583.

  11. 11.

    Bhuiyan, M., Lohan, E., & Renfors, M. (2008). Code tracking algorithms for mitigating multipath effects in fading channels for satellite-based positioning. EURASIP Journal on Advances in Signal Processing. https://doi.org/10.1155/2008/863629.

  12. 12.

    Sun, L., Chen, J., Tan, S., & Chai, Z. (2014). Research on multipath limiting antenna array with fixed phase center. GPS Solution. https://doi.org/10.1007/s10291-014-0400-x.

  13. 13.

    Sahmoudi, M., Amin, M. G. (2007). Optimal robust beamforming for interference and multipath mitigation in GNSS arrays. In Proceedings of IEEE international conference on acoustics, speech and signal processing. https://doi.org/10.1109/icassp.2007.366774.

  14. 14.

    Yapıcı, Y., & Yılmaz, A. O. (2012). An analysis of the bidirectional LMS algorithm over fast-fading channels. IEEE Transactions on Communications,60(7), 1759–1764. https://doi.org/10.1109/tcomm.2012.050812.110116.

  15. 15.

    Miller, K. S., & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. New York: Wiley.

  16. 16.

    Daneshmand, S., Broumandan, A., Nielsen, J., & Lachapelle, G. (2013). Interference and multipath mitigation utilising a two-stage beamformer for global navigation satellite systems applications. IET Radar Sonar Navigation,7(1), 55–66. https://doi.org/10.1049/iet-rsn.2012.0027.

  17. 17.

    Swathi, N., & Sasibhushana Rao, G. (2016). An adaptive filter approach for GPS multipath error estimation and mitigation. Electromagnetics and Telecommunications. https://doi.org/10.1007/978-81-322-2728-1_50.

  18. 18.

    Suryasarman, P. M., & Springer, A. (2015). A comparative analysis of adaptive digital pre-distortion algorithms for multiple antenna transmitters. IEEE Transactions on Circuits and System,62(5), 1412–1420. https://doi.org/10.1109/tcsi.2015.2403034.

  19. 19.

    Gui, G., Liu, N., Li, X., & Adachi, F. (2015). Low-complexity large-scale multiple-input multiple-output channel estimation using affine combination of sparse least mean square filters. IET Communication,9(17), 2168–2175. https://doi.org/10.1049/iet-com.2014.0979.

  20. 20.

    Mandal, A., & Mishra, R. (2015). Design of complex non-linear adaptive equalizer in mitigating severe intersymbol interferences. Journal of Signal Processing System. https://doi.org/10.1007/s11265-015-1047-8.

  21. 21.

    Ahmad, Z., Tahir, M., & Ali, I. (2013). Analysis of beamforming algorithms for antijams. In Proceedings of international seminar/workshop on direct and inverse problems of electromagnetic and acoustic wave theory, DIPED-2013 proceedings (pp. 89–96).

  22. 22.

    Hongwei, Z., Baowang, L., & Juan, F. (2011). Adaptive beamforming algorithm for interference suppression in GNSS receivers. International Journal of Computer Science & Information Technology (IJCSIT),3(5), 17–28. https://doi.org/10.5121/ijcsit.2011.3502.

  23. 23.

    Widrow, B., & Stearns, S. (1985). Adaptive signal processing. Upper Saddle River: Prentice Hall.

  24. 24.

    Komninakis, C., Fragouli, C., Sayed, A., & Wesel, R. (2002). Multi-input multi-output fading channel tracking and equalization using Kalman estimation. IEEE Transactions on Signal Processing,50(5), 1065–1076. https://doi.org/10.1109/78.995063.

  25. 25.

    Kamatham, Y., Kinnara, B., & Kartan, M. K. (2015). Mitigation of GPS multipath using affine combination of two LMS adaptive filters. IEEE. https://doi.org/10.1109/spices.2015.7091375.

  26. 26.

    Solteiro Pires, E. J., Tenreiro Machado, J. A., de Moura Oliveira, P. B., Boaventura Cunha, J., & Mendes, L. (2010). Particle swarm optimization with fractional-order velocity. Nonlinear Dynamics,61(1–2), 295–301. https://doi.org/10.1007/s11071-009-9649-y.

  27. 27.

    Das, D. P., & Panda, G. (2004). Active mitigation of non-linear noise processes using a novel filtered-s LMS algorithm. IEEE Transactions on Speech and Audio Processing. https://doi.org/10.1109/tsa.2003.822741.

  28. 28.

    Myrick, W. L., Zoltowski, M. D., & Goldstein, J. S. (1999). Anti-jam space-time preprocessor for GPS based on multistage nested Wiener filter. Proceedings of IEEE Conference on Military Communications. https://doi.org/10.1109/milcom.1999.822769.

  29. 29.

    Zhu, Z., Gao, X., & Cao, L. (2016). Analysis on the adaptive filter based on LMS algorithm. International Journal for Light and Electron Optics. https://doi.org/10.1016/j.ijleo.2016.02.005.

  30. 30.

    Bhuiyan, M. Z. H., Zhang, J., Lohan, E. S., Wang, W., & Sand, S. (2012). Analysis of multipath mitigation techniques with land mobile satellite channel model. Radio Engineering,21(4), 1067–1077.

  31. 31.

    Aruba, R., Sinha, G. R., & Rizwan, S. M. (2016). SNR and BER analysis for multiple antenna system using. Journal of Electronics and Communication Engineering,11(4), 51–56.

  32. 32.

    Lesouple, J., Robert, T., Sahmoudi, M., Tourneret, J.-Y., & Vigneau, W. (2019). Multipath mitigation for GNSS positioning in an urban environment using sparse estimation. IEEE Transactions on Intelligent Transportation Systems,20(4), 1316–1328.

  33. 33.

    Su, M., Zheng, J., Yang, Y., & Wu, Q. (2018). A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy. GPS Solutions,22, 40.

  34. 34.

    Sudhakar, R., & Letitia, S. (2015). An adaptive fast block motion estimation algorithm based on cross octagonal diamond search pattern. International Journal of Applied Engineering Research,10, 11892–11898.

  35. 35.

    Sudhakar, R., & Letitia, S. (2016). An modified un-even hexagonal block search algorithm for fast motion estimation in video coding. International Journal of Research in Emerging Science and Technology,3(5), 56–61.

Download references

Author information

Correspondence to A. L. Siridhara.

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

Verify currency and authenticity via CrossMark

Cite this article

Siridhara, A.L., Ratnam, D.V. Mitigation of Multipath Effects Based on a Robust Fractional Order Bidirectional Least Mean Square (FOBLMS) Beamforming Algorithm for GPS Receivers. Wireless Pers Commun (2020). https://doi.org/10.1007/s11277-020-07071-1

Download citation

Keywords

  • GPS
  • Multipath mitigation
  • Beam forming
  • Bidirectional least mean square algorithm (BLMS)
  • Direction of arrival