Skip to main content

Application of Polynomial Chaos Expansions for Uncertainty Estimation in Angle-of-Arrival Based Localization

  • Chapter
  • First Online:
Uncertainty Modeling for Engineering Applications

Abstract

For numerous applications of the Internet-of-Things, localization is an essential element. However, due to technological constraints on these devices, standards methods of positioning, such as Global Navigation Satellite System or Time-of-Arrival methods, are not applicable. Therefore, Angle-of-Arrival (AoA) based localization is considered, using a densely deployed set of anchors equipped with arrays of antennas able to measure the Angle-of-Arrival of the signal emitted by the device to be located. The original method presented in this work consists in applying Polynomial Chaos Expansions to this problem in order to obtain statistical information on the position estimate of the device. To that end, it is assumed that the probability density functions of the AoA measurements are known at the anchors. Simulation results show that this method is able to closely approximate the confidence region of the device position.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Lin X, Bergman J, Gunnarsson F, Liberg O, Razavi S, Razaghi H, Rydn H, Sui Y (2017) Positioning for the internet of things: a 3GPP perspective. IEEE Commun Mag 55(12):179–185

    Article  Google Scholar 

  2. 3GPP TS 22.368 (2014) Service requirements for machine-type communications, V13.1.0, Dec 2014

    Google Scholar 

  3. Rico-Alvarino A, Vajapeyam M, Xu H, Wang X, Blankenship Y, Bergman J, Tirronen T, Yavuz E (2016) An overview of 3GPP enhancements on machine to machine communications. IEEE Commun Mag 54(6):14–21

    Article  Google Scholar 

  4. Wang Y-P, Lin X, Adhikary A, Grovlen A et al (2017) A primer on 3GPP narrowband internet of things. IEEE Commun Mag 55(3):117–123

    Article  Google Scholar 

  5. Gomez C, Oller J, Paradellis J (2012) Overview and evaluation of bluetooth low energy: an emerging low-power wireless technology. Sensors 12(9):11734–11753

    Article  Google Scholar 

  6. Liu H, Darabi H, Banerjee P, Liu J (2007) Survey of wireless indoor positioning technique and systems. IEEE Trans Syst Man Cybern Part C 37

    Google Scholar 

  7. Fisher S (2014) Observed time difference of arrival (OTDOA) positioning in 3GPP LTE. White Paper, Qualcomm Technologies

    Google Scholar 

  8. 3GPP TR 37.857 (2015) Study on indoor positioning enhancements for UTRA and LTE

    Google Scholar 

  9. Pages-Zamora A, Vidal J, Brooks D (2002) Closed-form solution for positioning based on angle of arrival measurements. In: The 13th IEEE international symposium on personal, indoor and mobile radio communications, vol 4, pp 1522–1526

    Google Scholar 

  10. Torrieri D (1984) Statistical theory of passive location systems. IEEE Trans Aerosp Electron Syst AES–20(2):183–198

    Article  Google Scholar 

  11. Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93:964–979

    Article  Google Scholar 

  12. Van der Vorst T, Van Eeckhaute M, Benlarbi-Delaï A, Sarrazin J, Quitin F, Horlin F, De Doncker P (2017) Angle-of-arrival based localization using polynomial chaos expansions. In: Proceedings of the workshop on dependable wireless communications and localization for the IoT

    Google Scholar 

  13. Godara C (1997) Application of antenna arrays to mobile communications Part II: Beam-forming and direction-of-arrival considerations. Proc IEEE 85(8):1195–1245

    Article  Google Scholar 

  14. Schmidt R (1986) Multiple emitter location and signal parameter estimation. IEEE Trans Antennas Propag 34:276–280

    Article  Google Scholar 

  15. Wiener N (1938) The homogeneous chaos. Am J Math 60(4):897–936

    Article  MathSciNet  Google Scholar 

  16. Soize C, Ghanem R (2004) Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM J Sci Comput 26(2):395–410

    Article  MathSciNet  Google Scholar 

  17. Li J, Xiu D (2009) A generalized polynomial chaos based ensemble Kalman filter with high accuracy. J Comput Phys 228(15):5454–5469

    Article  MathSciNet  Google Scholar 

  18. Du J, Roblin C (2016) Statistical modeling of disturbed antennas based on the polynomial chaos expansion. IEEE Antennas Wirel Propag Lett

    Google Scholar 

  19. Rossi M, Dierck A, Rogier H, Vande Ginste D (2014) A stochastic framework for the variability analysis of textile antennas. IEEE Trans Antennas Propag 62(12):6510–6514

    Article  MathSciNet  Google Scholar 

  20. Haarscher A, De Doncker Ph, Lautru D (2011) Uncertainty propagation and sensitivity analysis in ray-tracing simulations. PIER M 21:149–161

    Article  Google Scholar 

  21. Van der Vorst T, Van Eeckhaute M, Benlarbi-Delaï A, Sarrazin J, Horlin F, De Doncker P (2017) Propagation of uncertainty in the MUSIC algorithm using polynomial chaos expansions. In: Proceedings of the 11th European conference on antennas and propagation, pp 820–822

    Google Scholar 

  22. Marelli S, Sudret B (2015) UQLab user manual–Polynomial chaos expansions. Chair of Risk, Safety & Uncertainty Quantification, ETH Zurich

    Google Scholar 

  23. Abramowitz M, Stegun I (1964) Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Courier Corporation

    Google Scholar 

  24. Abdi H, Williams LJ (2010) Principal component analysis. Wiley Interdiscipl Rev Comput Stat 2(4):433–459

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by F.R.S-FNRS, and by Innoviris through the Copine-IoT project.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas Van der Vorst .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Van der Vorst, T. et al. (2019). Application of Polynomial Chaos Expansions for Uncertainty Estimation in Angle-of-Arrival Based Localization. In: Canavero, F. (eds) Uncertainty Modeling for Engineering Applications. PoliTO Springer Series. Springer, Cham. https://doi.org/10.1007/978-3-030-04870-9_7

Download citation

Publish with us

Policies and ethics