LSTM-Based Interpolation of Single-Differential Ionospheric Delays for PPP-RTK Positioning

The accurate and rapid estimation of ionospheric delays is essential for PPP-RTK positioning. While traditional spatial interpolation methods like Kriging rely solely on geographic correlations, they often fail to capture rapid temporal variations in the ionosphere. To overcome this limitation, this paper proposes a long short-term memory (LSTM)-based interpolation method for interpolating ionospheric delays between satellites. The method leverages both spatial and short-term temporal correlations to generate accurate ionospheric corrections at user locations. The model uses a sliding window approach, taking the most recent 10 min of historical data as input to predict ionospheric delays at the current epoch. Experimental validation using data from a reference network in Australia—with average and maximum baseline lengths of 280 km and 650 km, respectively—demonstrates that the proposed LSTM method achieves a centimeter-level interpolation accuracy, with RMS errors between 0.06 m and 0.07 m under both quiet and geomagnetic storm conditions, significantly outperforming the Kriging method (0.27–0.44 m). In PPP-RTK, the LSTM model achieved a 3D positioning accuracy of 8.99 cm RMS during quiet periods, representing improvements of 51.9% and 28.8% over the No Constraint and Kriging methods, respectively. Under geomagnetic storm conditions, it maintained a 3D RMS of 24.54 cm—over 44% more accurate than other methods—and reduced the average time-to-first-fix (TTFF) to just 7.0 min, a 39.1% improvement. This study provides a novel approach for ionospheric spatial interpolation, demonstrating a particular robustness even during geomagnetic storms.