Characterization and prediction of low earth orbit satellite clock offsets based on Fourier analysis network

Abstract Accurate characterization and prediction of low earth orbit (LEO) satellite clock offsets are critical for enabling LEO-based positioning, navigation, and timing applications, supporting autonomous constellation operations, and facilitating inter-satellite coordination. Compared with global navigation satellite systems satellites, LEO platforms face greater challenges in clock modeling and prediction due to limited oscillator performance and the highly dynamic near-Earth environment. This study analyzes the onboard clock offsets of the Gravity Recovery and Climate Experiment Follow-On satellites, revealing dominant periodicities after removing the linear trend. The dominant component is associated with the South Atlantic Anomaly, with a typical period of about 12 h and an amplitude exceeding 25 ns. Relativistic effects further introduce once- and twice-per-revolution terms, with a combined amplitude of approximately 1.5 ns. Correcting these components significantly improves the onboard clock frequency stability. Motivated by the significant periodic patterns discovered in the LEO satellite clock behavior, we propose a Fourier analysis network (FAN) model for clock offset prediction. The model integrates a Fourier series structure directly into the neural network architecture, enabling efficient capture and representation of periodic patterns. We benchmark the FAN model against the autoregressive integrated moving average (ARIMA) model and the long short-term memory (LSTM) network. Results demonstrate that the prediction performance of the ARIMA model is significantly inferior to that of both neural network-based models. Compared to LSTM, FAN consistently achieves better prediction accuracy across different prediction window lengths, improving short-term prediction performance (⩽30 min) by 6.7%–11.1% and long-term performance (⩾1 h) by 22.7%–34.1%.