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<p>Low Earth Orbit (LEO) satellite augmentation has become a hot research topic for future Positioning, Navigation, and Timing (PNT) applications. To provide real-time LEO-augmented PNT services, high-precision real-time LEO satellite clocks are required. In practice, latencies in the clock determination could range from minutes to hours, depending on the concrete data tracking/transmission strategies and potential operational constraints. Under such circumstances, real-time LEO satellite clocks are basically predicted clocks, whereas the prediction accuracy could play a major role when the prediction time extends over a few minutes. The LEO satellite clock estimates are subject to various systematic effects, resulting in highly nonlinear behavior that is difficult to capture with a single deterministic model. To address this, Deep Learning (DL) models are applied to predict the LEO satellite clocks using real data from the Sentinel-3B satellite. Three novel approaches are proposed in this contribution:&#xa0;1) an improved Autoformer model enhanced by a pre-training and fine-tuning strategy; 2) an optimized Long Short-Term Memory (LSTM) prediction model; and 3) a Wavelet–LSTM model, where wavelet decomposition enables multi-scale analysis of the clock series to augment the LSTM's predictive capability. The results of the three models are compared with a mathematical polynomial periodic model. Experimental results indicate that while the first two DL models underperform in clock prediction, i.e., often fall short of the polynomial periodic model in accuracy, the Wavelet–LSTM model presents the best performance for all prediction times. Under evaluation mode 1 (average prediction accuracy), it attains a prediction accuracy of approximately 0.05&#xa0;ns for short-term predictions (within 10&#xa0;min) and maintains accuracy within about 0.3&#xa0;ns for long-term predictions (up to 60&#xa0;min), indicating the potential applicability of the high-precision PNT applications.</p>

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LEO satellite clock prediction using deep learning: a wavelet–LSTM method with autoformer and LSTM comparisons

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月22日

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  • Jinqian Wang,
  • Meifang Wu,
  • Kan Wang,
  • Wei Xie

摘要

Low Earth Orbit (LEO) satellite augmentation has become a hot research topic for future Positioning, Navigation, and Timing (PNT) applications. To provide real-time LEO-augmented PNT services, high-precision real-time LEO satellite clocks are required. In practice, latencies in the clock determination could range from minutes to hours, depending on the concrete data tracking/transmission strategies and potential operational constraints. Under such circumstances, real-time LEO satellite clocks are basically predicted clocks, whereas the prediction accuracy could play a major role when the prediction time extends over a few minutes. The LEO satellite clock estimates are subject to various systematic effects, resulting in highly nonlinear behavior that is difficult to capture with a single deterministic model. To address this, Deep Learning (DL) models are applied to predict the LEO satellite clocks using real data from the Sentinel-3B satellite. Three novel approaches are proposed in this contribution: 1) an improved Autoformer model enhanced by a pre-training and fine-tuning strategy; 2) an optimized Long Short-Term Memory (LSTM) prediction model; and 3) a Wavelet–LSTM model, where wavelet decomposition enables multi-scale analysis of the clock series to augment the LSTM's predictive capability. The results of the three models are compared with a mathematical polynomial periodic model. Experimental results indicate that while the first two DL models underperform in clock prediction, i.e., often fall short of the polynomial periodic model in accuracy, the Wavelet–LSTM model presents the best performance for all prediction times. Under evaluation mode 1 (average prediction accuracy), it attains a prediction accuracy of approximately 0.05 ns for short-term predictions (within 10 min) and maintains accuracy within about 0.3 ns for long-term predictions (up to 60 min), indicating the potential applicability of the high-precision PNT applications.