A neural network model for satellite clock bias prediction via spatiotemporal feature integration

With the rapid development of low-orbit satellite constellations, the low-earth orbit enhanced global navigation satellite system (LeGNSS) has become a research hotspot, particularly in the field of precise point positioning. The addition of low-orbit satellites can significantly reduce convergence time and improve positioning accuracy. Satellite clock bias is a primary source of error affecting positioning accuracy, necessitating high-precision correction. To meet the needs of real-time, high-precision users, it is essential to predict the bias of various types of satellite clocks relative to the time reference over a given period, thereby enabling real-time correction of satellite clock bias. In this study, we utilize long-short-term memory networks (LSTM) and one-dimensional convolutional networks (1DCNN) to extract temporal and spatial features of clock bias data, respectively. By integrating these with an attention mechanism, we design a dual-channel clock bias prediction neural network model. We analyzed the clock characteristics of the BeiDou-3 satellite’s onboard rubidium (Rb) clocks, passive hydrogen (PH) clocks, and the GRACE satellite’s onboard ultra-stable oscillators (USOs). Based on these analyses, we conducted prediction experiments using the proposed neural network model. Our method employs different sequence models to extract temporal and spatial features from the clock bias sequences and fuses them for processing, significantly enhancing prediction accuracy. Analysis results indicate that the stability of the USOs used by LEO satellites is 1–2 orders of magnitude worse than that of GNSS satellites. Additionally, the periodic component strength of LEO satellites is 1–2 orders of magnitude higher, exhibiting more pronounced nonlinear characteristics. The proposed neural network model demonstrates markedly improved accuracy in predicting clock bias compared to conventional prediction models, such as linear polynomials (LP), quadratic polynomials (QP), grey models (GM), Kalman filters, LSTM, LSTM-Attention, and CNN-LSTM. Specifically, the average predicted RMSE values of the PH clocks and Rb clocks at the 2-h, 12-h, and 24-h prediction horizons are (0.135 ns, 0.241 ns, 0.468 ns) and (0.157 ns, 0.452 ns, 0.702 ns), respectively. For the USOs, the average predicted RMSE values at the 1-h, 3-h, and 6-h horizons are (1.095 ns, 3.221 ns, 5.745 ns). The overall predictive performance outperforms several baseline algorithms, and the longer the prediction horizon, the more pronounced the performance advantage.