Robust Machine Learning–Based Ionospheric Delay Grid Modeling for PPP‐RTK Under Sparse Reference Stations and Severe Geomagnetic Disturbance

Abstract

Sparse reference station networks and severe geomagnetic disturbances can significantly degrade the accuracy of regional ionospheric delay modeling at the network side, thereby reducing the positioning performance of PPP‐RTK. To address this issue, this study proposes a machine learning‐based ionospheric delay grid modeling method that finely models the ionospheric delay computation and interpolation errors embedded in the ionospheric delay residuals. To evaluate the performance of the proposed approach, 274 stations uniformly distributed across Europe were used for experiments based on observation data from 2024. Five machine learning models, including GBDT, XGBoost, RF, SVM, and LSTM, were comparatively analyzed. For a representative test station (TLL1) with an average reference station spacing of 260 km, the ionospheric delay products generated by the proposed method exhibit errors smaller than 10 cm for most epochs. Compared with the traditional inverse distance weighting (IDW) method, the five machine learning models improve the average root mean square error (RMSE) by 60.2%, 57.1%, 61.6%, 49.3%, and 50.7%, respectively. During severe geomagnetic disturbances, the probability that the modeling error remains smaller than 5 cm exceeds 85%, whereas it is only about 60% when using the IDW method. PPP‐RTK experiments further demonstrate that the proposed method enables rapid or even instantaneous convergence in sparse reference station networks. For the TLL1 station, the maximum RMSE in the U direction is reduced by more than 60%, and the average convergence time decreases by up to 75%. These results demonstrate the effectiveness and robustness of the proposed method for enhancing PPP‐RTK performance in challenging environments.