Prediction of Range Error in GPS Signals during X-Class Solar Flares Occurred between January–April 2023 Using OKSM and RNN

Positioning, navigation and time are the cornerstones of satellite navigation. These aspects are frequently affected by ionospheric variations caused by solar flares (SF). In this study, we have attempted to predict the range error (RE) caused by ionospheric delay in Global Positioning System (GPS) signals during six different X-class SF that occurred in the 25th solar cycle using two different approaches, namely, a recurrent neural network (RNN) and the ordinary Kriging-based surrogate model (OKSM). The total electron content (TEC) collected from Hyderabad station along with other input parameter includes the Planetary A and K index (Ap and Kp), solar sunspot number (SSN), disturbance storm time index (Dst), and radio flux measured at 10.7 cm (F10.7) were used for prediction. The OKSM uses the previous six days of datasets to predict the RE on the seventh day, whereas the RNN model uses the previous 45 days of datasets to predict the RE on the 46th day. The performance of both models is evaluated using statistical parameters such as root mean square error (RMSE), normalized root mean square error (NRMSE), Pearson’s correlation coefficient (CC), and symmetric mean absolute percentage error (sMAPE). The results indicate that the OKSM performs well in adverse space weather conditions when compared to RNN.