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Modelling and prediction of atmospheric drag coefficients in LEO satellite orbit determination and prediction with Bi-LSTM approach

Chen, Xiang, Tang, Chengpan, Dai, Wujiao, Hu, Xiaogong, Chen, Liucheng, Zhang, Zhongying, Zhu, Xinhui, and Li, Mingzhe, 2025. Modelling and prediction of atmospheric drag coefficients in LEO satellite orbit determination and prediction with Bi-LSTM approach. Advances in Space Research, 75(3):2874–2888, doi:10.1016/j.asr.2024.10.063.

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@ARTICLE{2025AdSpR..75.2874C,
       author = {{Chen}, Xiang and {Tang}, Chengpan and {Dai}, Wujiao and {Hu}, Xiaogong and {Chen}, Liucheng and {Zhang}, Zhongying and {Zhu}, Xinhui and {Li}, Mingzhe},
        title = "{Modelling and prediction of atmospheric drag coefficients in LEO satellite orbit determination and prediction with Bi-LSTM approach}",
      journal = {Advances in Space Research},
     keywords = {Low Earth Orbit, Orbit prediction, Atmospheric drag coefficient, Artificial neural networks, Short-arc orbit determination},
         year = 2025,
        month = feb,
       volume = {75},
       number = {3},
        pages = {2874-2888},
     abstract = "{In the precise orbit determination (POD) of Low Earth Orbit (LEO)
        satellites with onboard Global Navigation Satellite System
        (GNSS) observations, atmospheric drag coefficients (Cd) are
        estimated piece-wise to absorb atmosphere density modeling
        errors, attitude modeling errors and windward area errors when
        the satellite physical metadata is not available. This study
        focuses on modeling and prediction of atmospheric drag
        coefficient in LEO satellite orbit determination and prediction.
        Orbit determination was conducted to determine atmospheric drag
        coefficients for eight LEO satellites with the orbital altitudes
        from 500 km to 1300 km. The Bidirectional Long Short-Term Memory
        (Bi-LSTM) neural network was used to model and predict the
        atmospheric drag coefficient estimations. The average Mean
        Absolute Percentage Error (MAPE) and average relative error
        between the predicted and estimated values of Cd for the eight
        satellites, were 0.09 and 0.11, respectively, indicating a
        satisfactory prediction performance of Cd. Prediction of the Cd
        is applied in orbit prediction and 30-minute short arc orbit
        determination (SOD). The results of the orbit prediction show
        that the modeling of Cd plays a key role in improving the
        accuracy of orbit prediction. The accuracy of the orbit
        prediction method based on the Cd prediction is better than that
        of the method without Cd prediction, and the average accuracy
        improves by 67.5 \% and 73.7 \% for the eight satellites in 2019
        and 2023, respectively. The highest accuracy improvement rate is
        94.5 \% for GRACE-C satellite in 2019 and 86.6 \% for Swarm-B
        satellite in 2023. Among them, the RMS of the average 3D error
        of the 3-day orbit prediction of the Swarm-B satellite is the
        lowest in both 2019 and 2023, at 2.11 m and 8.79 m,
        respectively. The results show that the SOD method with
        constrained Cd for eight satellites has different degrees of
        accuracy improvement in most arcs relative to the method without
        constrained Cd. The average orbital accuracy with constrained Cd
        improves by 14.8 \% and 17.1 \% for the eight satellites in 2019
        and 2023, respectively, with the highest accuracy improvement of
        24.7 \% for GRACE-C satellite in 2019 and 24.2 \% for GRACE-D
        satellite in 2023. The average orbit error of GRACE-C satellite
        is reduced from 9.23 cm to 5.95 cm, and the average orbit error
        of GRACE-D satellite is reduced from 13.45 cm to 8.22 cm.}",
          doi = {10.1016/j.asr.2024.10.063},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2025AdSpR..75.2874C},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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