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.
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References
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
3GPP TS 22.368 (2014) Service requirements for machine-type communications, V13.1.0, Dec 2014
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
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
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
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
Fisher S (2014) Observed time difference of arrival (OTDOA) positioning in 3GPP LTE. White Paper, Qualcomm Technologies
3GPP TR 37.857 (2015) Study on indoor positioning enhancements for UTRA and LTE
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
Torrieri D (1984) Statistical theory of passive location systems. IEEE Trans Aerosp Electron Syst AES–20(2):183–198
Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93:964–979
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
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
Schmidt R (1986) Multiple emitter location and signal parameter estimation. IEEE Trans Antennas Propag 34:276–280
Wiener N (1938) The homogeneous chaos. Am J Math 60(4):897–936
Soize C, Ghanem R (2004) Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM J Sci Comput 26(2):395–410
Li J, Xiu D (2009) A generalized polynomial chaos based ensemble Kalman filter with high accuracy. J Comput Phys 228(15):5454–5469
Du J, Roblin C (2016) Statistical modeling of disturbed antennas based on the polynomial chaos expansion. IEEE Antennas Wirel Propag Lett
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
Haarscher A, De Doncker Ph, Lautru D (2011) Uncertainty propagation and sensitivity analysis in ray-tracing simulations. PIER M 21:149–161
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
Marelli S, Sudret B (2015) UQLab user manual–Polynomial chaos expansions. Chair of Risk, Safety & Uncertainty Quantification, ETH Zurich
Abramowitz M, Stegun I (1964) Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Courier Corporation
Abdi H, Williams LJ (2010) Principal component analysis. Wiley Interdiscipl Rev Comput Stat 2(4):433–459
Acknowledgements
This work was supported by F.R.S-FNRS, and by Innoviris through the Copine-IoT project.
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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
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DOI: https://doi.org/10.1007/978-3-030-04870-9_7
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