Transformer-Based Ionospheric Prediction and Explainability Analysis for Enhanced GNSS Positioning

Abstract

This study aims to investigate the impact of ionospheric models on Global Navigation Satellite System (GNSS) positioning and proposes an ionospheric prediction method based on a Transformer deep learning model. We construct a Transformer-based deep learning model that utilizes global ionospheric maps as input to achieve spatiotemporal prediction of Total Electron Content (TEC). To gain a deeper understanding of the model's prediction mechanism, we employ integrated gradients for explainability analysis. The results reveal the key ionospheric features that the model focuses on during prediction, providing guidance for further model optimization. This study demonstrates the efficacy of a Transformer-based model in predicting Vertical Total Electron Content (VTEC), achieving comparable accuracy to traditional methods while offering enhanced adaptability to spatial and temporal variations in ionospheric behavior. Furthermore, the application of advanced explainability techniques, particularly the Integrated Decision Gradient (IDG) method, provides unprecedented insights into the model's decision-making process, revealing complex feature interactions and spatial dependencies in VTEC prediction, thus bridging the gap between deep learning capabilities and explainable scientific modeling in geophysical applications. The model achieved positioning accuracies of -1.775 m, -2.5720 m, and 2.6240 m in the East, North, and Up directions respectively, with standard deviations of 0.3399 m, 0.2971 m, and 1.3876 m. For VTEC prediction, the model successfully captured the diurnal variations of the Equatorial Ionization Anomaly (EIA), with differences between predicted and CORG VTEC values typically ranging from -6 to 6 TECU across the study region. The gradient score analysis revealed that solar activity indicators (F10.7 and sunspot number) showed the strongest correlations (0.7-0.8) with VTEC variations, while geomagnetic indices exhibited more localized impacts. The IDG method effectively identified feature importance variations across different spatial locations, demonstrating the model's ability to adapt to regional ionospheric characteristics.