Neural network-compensated satellite clock bias prediction for Low Earth Orbit (LEO) satellites

Tianhao Wu, Bofeng Li, Haibo Ge

Accurate prediction of Low Earth Orbit (LEO) Satellite Clock Bias (SCB) is crucial for real-time precise applications of LEO-enhanced GNSS (LeGNSS). However, the inherent instability of oscillators aboard LEO satellites presents challenges for traditional model-driven SCB prediction methods, which struggle to capture the complex variability of LEO SCB sufficiently and thus cannot achieve high-accuracy solutions. To address this challenge, we propose a neural network-compensated SCB prediction method (NNC-SP), which builds on a periodic polynomial (PP) model for baseline prediction and applies an enhanced Informer model to compensate for unmodeled patterns. Two key innovations are introduced: (1) a Dimension-Segment-Wise (DSW) pre-embedding module that segments input data to better capture local temporal structures; and (2) a smoothed Mean Squared Error loss function that incorporates relative relationships within SCB sequences, beyond pointwise errors. The method is validated using one year of SCB data from the GRACE-FO C and D satellites. When trained with a 1-hour prediction arc, NNC-SP improves prediction accuracy by approximately 90% across all lengths. For GRAC, the RMSEs for 5-, 10-, 30-, and 60-minute predictions are 0.07, 0.12, 0.38, and 0.90 ns, respectively; for GRAD, the corresponding values are 0.14, 0.22, 0.67, and 1.52 ns. Further improvements are achieved by training for shorter arcs: for example, the RMSEs are 0.05 and 0.11 ns for GRAC and 0.08 and 0.17 ns for GRAD at 5- and 10-minute predictions, respectively. NNC-SP also demonstrates robust performance, outperforming PP in 95% of cases. These results confirm its promise for high-accuracy real-time SCB prediction in future LeGNSS applications.