Enhanced Global Ionospheric Mapping Using Deep Ensemble Neural Networks With Uncertainty Quantification

Abstract

Global ionospheric mapping is essential for ionospheric research. However, conventional approaches often struggle to accurately capture small-scale ionospheric variations. This study proposes a deep ensemble method based on neural networks (NNs) that generates high-accuracy global vertical total electron content (VTEC) maps along with corresponding uncertainty estimates. To develop the machine learning model, we first determined the VTEC time series based on the carrier-to-code leveling method using multi-GNSS observations from global IGS stations. These VTEC time series were then used to train daily NNs, which subsequently generated global ionospheric maps (GIMs) for improved usability and accessibility. During our experiment covering the year 2023, the NNs achieved an average mean absolute error of 1.76 TEC Units (TECU) at 52 global test stations. Compared to IGS combined GIMs and two other representative GIMs from IGS analysis centers, the VTEC time series extracted from NN-GIMs showed better consistency with Jason-3 VTEC, achieving an average root mean squared error of 4.09 TECU after removing daily biases. Furthermore, NN-GIMs achieved the best baseline length repeatability in K-band Very Long Baseline Interferometry analysis. In single-frequency precise point positioning (SF-PPP) tests, NN-GIMs improved positioning accuracy by 11%, 9%, and 24% in the east, north, and up components compared to IGS combined GIMs. Additionally, the deep ensemble-based uncertainty quantification proved beneficial for weighting GNSS observations in SF-PPP, enhancing the positioning accuracy in low-latitude regions by approximately 14% compared to the elevation-based weighting scheme.