Application of Polynomial Chaos Expansions for Uncertainty Estimation in Angle-of-Arrival Based Localization
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.
KeywordsPolynomial chaos expansions Localization Angle-of-Arrival
This work was supported by F.R.S-FNRS, and by Innoviris through the Copine-IoT project.
- 2.3GPP TS 22.368 (2014) Service requirements for machine-type communications, V13.1.0, Dec 2014Google 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 37Google Scholar
- 7.Fisher S (2014) Observed time difference of arrival (OTDOA) positioning in 3GPP LTE. White Paper, Qualcomm TechnologiesGoogle Scholar
- 8.3GPP TR 37.857 (2015) Study on indoor positioning enhancements for UTRA and LTEGoogle 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 1522–1526Google 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 IoTGoogle Scholar
- 18.Du J, Roblin C (2016) Statistical modeling of disturbed antennas based on the polynomial chaos expansion. IEEE Antennas Wirel Propag LettGoogle 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 820–822Google Scholar
- 22.Marelli S, Sudret B (2015) UQLab user manual–Polynomial chaos expansions. Chair of Risk, Safety & Uncertainty Quantification, ETH ZurichGoogle Scholar
- 23.Abramowitz M, Stegun I (1964) Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Courier CorporationGoogle Scholar