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

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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.