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

Vorst, Thomas Van der; Eeckhaute, Mathieu Van; Benlarbi-Delaï, Aziz; Sarrazin, Julien; Quitin, François; Horlin, François; Doncker, Philippe De

doi:10.1007/978-3-030-04870-9_7

Cited by 3 publications

(5 citation statements)

References 18 publications

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“…As the presence of singularities is restrictive for the gPC algorithm, ρ is equal to the size of the smallest of both ellipses, i.e., ρ = min( ρre , ρim ). The largest and optimal value of ρ, named ρeq , is reached when both ellipses overlap ( ρre = ρim ) at a certain κ eq , which can be found by solving Equations ( 20) and (21). Figure 4 illustrates this procedure for a singularity located at p = ±1.1125.…”

Section: Tanh Mapmentioning

confidence: 99%

“…With the appropriate approach, gPC can even compete with MC when a high number of random variables are used [ 12 , 13 , 14 , 15 , 16 , 17 ]. In the context of localization, gPC has also been used—for example, in [ 18 , 19 ], where the effects of element displacements on DOA estimation were investigated; in [ 20 ], where the effects of random element gain and phase variations were studied, and in [ 21 ], where the uncertainty in multiple angle-of-arrival measurements was translated into an uncertainty in position estimation.…”

Section: Introductionmentioning

confidence: 99%

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A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

Brandt

Verhaevert

Hecke

et al. 2022

Sensors

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The effects of random array deformations on Direction-of-Arrival (DOA) estimation with root-Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) are characterized by a conformally mapped generalized Polynomial Chaos (gPC) algorithm. The studied random deformations of the array are elliptical and are described by different Beta distributions. To successfully capture the erratic deviations in DOA estimates that occur at larger deformations, specifically at the edges of the distributions, a novel conformal map is introduced, based on the hyperbolic tangent function. The application of this new map is compared to regular gPC and Monte Carlo sampling as a reference. A significant increase in convergence rate is observed. The numerical experiments show that the UCA root-MUSIC algorithm is robust to the considered array deformations, since the resulting errors on the DOA estimates are limited to only 2 to 3 degrees in most cases.

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Section: Tanh Mapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

Brandt

Verhaevert

Hecke

et al. 2022

Sensors

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show abstract

“…The interest of the Polynomial Chaos Expansion theory is to obtain statistical informations on the model response with less computational effort than by a Monte-Carlo simulation of the actual model. The estimation of the xand y-coordinates are separately expanded on the same polynomial chaos basis [4]…”

Section: B Polynomial Chaos Expansions Of the Positionmentioning

confidence: 99%

“…The set of indices A is determined by the parameters of the expansions: the number of variables and the total degree of the expansion. Detailed explanations on the PCE and the way to compute the coefficients can be found in [4]. It can be easily demonstrated that the mean and the variance of the x-coordinate are respectively given by:…”

Section: B Polynomial Chaos Expansions Of the Positionmentioning

confidence: 99%

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Anchor Selection In Angle-Of-Arrival Estimation-Based Localization Using Polynomial Chaos Expansions

Vorst

Nguyen

Monfared

et al. 2020

2020 IEEE 91st Vehicular Technology Conference (VTC2020-Spring)

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Angle-of-arrival (AoA) estimation-based localization systems are a promising technology in the context of Internetof-Things. The system considered is a densely deployed set of anchors equipped with arrays of antennas able to measure the AoA of the signal emitted by the device to be located. Naturally, the AoA measurements are prone to uncertainties due to noise, channel conditions and uncertainties on the anchors placement and orientations. In this work, a method based on Polynomial Chaos Expansions is proposed to perform anchor selection in order to enhance the precision of the positioning. An experimental setup with six anchors is implemented to evaluate the performance of the proposed method. The experimental results demonstrate that by applying our anchor selection method, the performance of the localization system improves.

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A new localization mechanism in IoT using grasshopper optimization algorithm and DVHOP algorithm

Janabi

Kurnaz

2023

Wireless Netw

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

Cited by 3 publications

References 18 publications

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

Anchor Selection In Angle-Of-Arrival Estimation-Based Localization Using Polynomial Chaos Expansions

A new localization mechanism in IoT using grasshopper optimization algorithm and DVHOP algorithm

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