Robust GNSS Multipath Error Modeling Based on Deep Quantile Regression with Gaussian Overbounding

Safety-critical navigation applications require safe localization error characterization. This requirements extends toglobal navigation satellite systems (GNSS), which are essential for on-board based navigation solutions for different transportation applications. Existing integrity monitoring systems, such as satellite-based augmentation systems (SBAS) or advanced receiver autonomous integrity monitoring (ARAIM), are only capable of providing a robust signal-in-space error description for civil aviation. However, for land-based applications, the local GNSS error, in particular multipath error, due to harsh environments, remains a critical challenge. In this work, an artificial intelligence (AI)-based GNSS code multipath error overbound model for safe error distribution characterization is presented. Two main contributions are made: First, a quantile regression loss function is designed to predict conservative quantiles based on a neural network, so that they are compatible for safety purposes. Second, the quantiles are used to obtain a Gaussian overbound, which describes the underlying error with a parametric distribution that ensures error bounding conditions. The proposed algorithm is first validated with a simple simulation example. Its use and benefit for multipath error modeling is then evaluated with real GNSS data in railway application. Results suggest the capability of this algorithm to reliably characterize multipath errors in challenging scenarios. The method and algorithm can be used for robust multipath distribution characterization in combination with positioning and integrity monitoring algorithms, such as horizontal-ARAIM for railway signaling.