Satellite clock bias (SCB) is a critical error source affecting the positioning and timing accuracy of Global Navigation Satellite Systems (GNSSs). The conventional back propagation neural network (BP) model, when applied to SCB prediction, is prone to local optima and exhibits rapid error divergence. To address these limitations, this study proposes and investigates two enhanced BP models: one optimized by the genetic algorithm (GA) and another by the mind evolutionary algorithm (MEA). A comprehensive comparative analysis is conducted against the standard BP model. Experiments utilize precise clock products from the International GNSS Service (IGS), with data from six representative satellites featuring different atomic clock types (IIR, IIR-M, IIF rubidium, and cesium clocks). The models are trained on 24 h of historical data and evaluated by forecasting clock biases for 2, 6, 12, and 24 h ahead. Prediction accuracy is assessed using root mean square error (RMS), range, and mean error. The results demonstrate that optimization algorithms significantly improve the BP neural network’s performance. The genetic algorithm optimized back propagation neural network (GABP) model demonstrates comprehensive superiority, achieving the highest accuracy across all forecast horizons and satellite types. For instance, in 24 h predictions, the average RMS error of the GABP model (6.516 ns) is merely 10.9% of the standard BP model’s error. Notably, for the cesium clock on satellite G24, the GABP model’s 24 h RMS (1.600 ns) is approximately 23 times lower than that of the mind evolutionary algorithm optimized back propagation neural network (MEABP) model. The GABP model also shows strong adaptability, maintaining high precision for both rubidium and cesium clocks and exhibiting gradual error growth with extended forecast duration, indicating excellent generalization and resistance to overfitting. To further evaluate generalization across different seasons and time periods, additional experiments were conducted using data from February–March, June, and October 2021 on six different satellites. The results consistently show that GABP outperforms MEABP and BP across all tested conditions. While the MEABP model outperforms the standard BP, it shows limitations in long-term forecasts, particularly for cesium clocks, due to tendencies for premature convergence and sensitivity to data noise. In conclusion, the GABP model, leveraging the robust global optimization capability of the genetic algorithm is validated as a highly effective and reliable solution for high-accuracy short- and long-term satellite clock bias prediction.
Bai et al. (Thu,) studied this question.