Low Earth Orbit Satellite Clock Offset Prediction Based on the Ensemble of LSTM Models

Objectives: Accurate prediction of low Earth orbit (LEO) satellite clock offset is crucial for high-performance LEO-augmented navigation services. Affected by temperature variations, space radiation, component aging, etc., the frequency of the satellite clock undergoes nonlinear drift over time, complicating the clock offset prediction. Traditional clock offset prediction methods, such as spectral analysis, primarily model the linear and periodic components of clock offset sequences, which restricts prediction performance. In contrast, machine learning (ML) methods exhibit remarkable capability in modeling nonlinear and complex systems. As a promising ML-based time series prediction method, the Long Short-Term Memory (LSTM) network is therefore adopted for LEO satellite clock offset prediction in this study. Furthermore, an ensemble of multiple LSTM models is applied to enhance prediction stability. Methods: LSTM neural network model is employed for clock offset prediction. To facilitate the LSTM method in capturing the nonlinear variation patterns in the clock offset sequence, we first apply first-order differencing to the original clock offset sequence. After further removing the linear and quadratic trend terms from the differenced sequence, the remaining residual sequence is then input for model training. To enhance the stability of the predictions from a single LSTM model, we propose an ensemble method that integrates multiple LSTM models. The weight assigned to each constituent model is determined by its performance on the validation set. Results: Clock offset data from the GRACE-C satellite, covering the period from January to October 2023, are used for experiment. The results demonstrate that the performance of LSTM models is highly sensitive to a series of factors, such as training sample partitioning, parameter initialization, and the random optimization process during training. Even with identical training configurations, model performance may still vary across different training runs, and the model that performs best on the validation set does not necessarily achieve the optimal performance on the test set. The deficiency is mitigated through the model ensemble approach, which reduces the maximum, the 95th percentile, and the root mean square of the clock offset prediction errors. Compared to the spectral analysis method, the clock offset prediction accuracy using the ensemble approach is improved by 51.9% on average, with the maximum reaching 73.9%. Compared to the single-SLTM-based method, the ensemble approach achieves an average accuracy improvement of 5.9%, with the maximum reaching 15.0%. Conclusions: The results confirm the effectiveness of ensemble models in improving the stability and accuracy of LEO satellite clock offset prediction. In addition, the model ensemble strategy warrants further exploration in future research (e.g., employing different ML models for ensemble), as they may lead to additional improvements in clock offset prediction.