Parallel Deep Quantile Estimation with Gaussian Overbounding for GNSS Multipath Modeling

Florian Roessl and Omar García Crespillo

Abstract:	Global navigation satellite systems (GNSS) is being widely introduced for safety-related applications (beyond aviation). For instance, in the context of train localization, the use of GNSS require the robust modeling of each measurement error component in order to satisfy the safety or integrity requirements. However, due to the challenging railway environment the modeling of the local multipath error remains an active area of research. There is currently no well-accepted multipath error model or approach for railway application that provides a robust and yet not overly conservative error characterization. In order to address this gap, we proposed in previous work to leverage artificial intelligence (AI) for estimating the multipath empirical error distribution using a quantile based description. The quantile-based empirical distribution is then bounded in the cumulative distribution function (CDF) sense in order to provide a parametric and robust model, which can be incorporated into a GNSS integrity monitoring systems. In this work, we explore deeper on one side the impact of different model parameters and design choices of the neural network that estimates the quantile levels on the prediction performance. On the other side, we propose and analyze different architecture possibilities considering the joint estimation of all quantiles together or in a parallel network scheme. The advantages and disadvantages of these design alternatives are analyzed and discussed based on a simplified simulation scenario as well as with real railway data. Finally, the new derived multipath models are applied to a modified H-ARAIM algorithm on the railway scenario.
Published in:	Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025) September 8 - 12, 2025 Hilton Baltimore Inner Harbor Baltimore, Maryland
Pages:	992 - 1003
Cite this article:	Roessl, Florian, Crespillo, Omar García, "Parallel Deep Quantile Estimation with Gaussian Overbounding for GNSS Multipath Modeling," Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025), Baltimore, Maryland, September 2025, pp. 992-1003. https://doi.org/10.33012/2025.20233
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