BiLSTM-driven error compensation for high-precision orbit prediction with two-line elements

With the exponential increase in the number of objects in low Earth orbit (LEO), collision risks have risen correspondingly, making high-precision orbit prediction a core requirement for ensuring satellite safety and space environment management. Two-Line Elements (TLEs) are the only publicly available orbital data source and are widely used in conjunction with the Simplified General Perturbations 4 (SGP4) model for LEO object orbit prediction. However, LEO objects are significantly affected by complex time-varying perturbations such as atmospheric drag, causing model prediction errors to grow rapidly over time—short-term errors can reach hundreds to thousands of meters, while medium- and long-term prediction errors may exceed 10 km. Although traditional dynamical models can achieve relatively high accuracy through numerical integration, they incur substantial computational costs and suffer from limited atmospheric density modeling accuracy (only about 5%–15%). Analytical methods, while computationally efficient, struggle to handle complex perturbations. In recent years, bidirectional long short-term memory (BiLSTM) networks have demonstrated strong capabilities in time-series prediction; nevertheless, an effective approach for systematically modeling and compensating for TLE-based prediction errors using solely publicly available TLE data has remained lacking.

In a recent study published in Space: Science & Technology, the team led by Li Bin from the School of Geodesy and Geomatics, Wuhan University, proposed a BiLSTM-based orbit prediction error compensation method. The study generates three sets of predicted orbit files from TLEs at different epochs, constructs error sample sequences by comparing orbital differences during overlapping time intervals, and designs a BiLSTM network architecture to capture forward and backward temporal dependencies in the error sequences, using prediction errors over 20 consecutive time steps as inputs and the error at the next step as the label. Experimental results on 340 LEO targets demonstrate that the proposed method achieves an effective compensation rate of 94%, with an average error reduction of 82%. The 8-day prediction error is reduced from 44.0 km using the traditional dynamical model to below 3.0 km, with a root-mean-square error reduction of 64%. The model exhibits sensitivity to observation sampling frequency and TLE update interval, with 5-minute sampling and a 3-day update interval identified as the optimal configuration. During periods of intense solar activity, the method still maintains an 88% three-dimensional error reduction rate with 99% of targets effectively compensated, confirming its robustness under complex space environmental conditions. This research provides an efficient and reliable data-driven solution for improving the orbit prediction accuracy of LEO space objects using only publicly available TLE data.

First, this paper focuses on the demand and data foundation for improving orbit prediction accuracy of low Earth orbit (LEO) objects, and proposes an error compensation framework based on bidirectional long short-term memory (BiLSTM) networks. With the exponential increase in the number of objects in LEO, high-precision orbit prediction has become a core requirement for ensuring satellite safety and space environment management. Two-Line Elements (TLEs) are the only publicly available orbital data source; however, LEO objects are significantly affected by complex time-varying perturbations such as atmospheric drag, causing prediction errors of the Simplified General Perturbations 4 (SGP4) model to grow rapidly over time. As illustrated in Fig. 1, the study generates three sets of predicted orbit files from TLEs at different epochs, and constructs error sample sequences by comparing orbital differences during overlapping time intervals, thereby providing the data foundation for subsequent network training. Statistical results on 340 LEO targets show that the raw prediction errors exhibit a wide distribution, with a maximum of 187 km, a mean of 21 km, and a standard deviation of 27 km. This non-uniformity offers substantial room for data-driven methods to exploit.

Second, this paper elaborates on the construction of error sequences and the training and compensation mechanism of the bidirectional long short-term memory (BiLSTM) network. As illustrated in Fig. 2, the entire workflow is divided into three parts: generation of observation data files, network modeling, and error compensation. The error sequences are constructed using a sliding window approach: the prediction errors over k consecutive time steps are used as inputs, with the error at the next step serving as the label, and each target is modeled independently. The network adopts a bidirectional architecture, processing the input sequences through two independent forward and backward LSTM layers, respectively. The hidden states from both directions are concatenated and then passed through a fully connected layer to output the predicted error, thereby capturing both forward and backward temporal dependencies in the error sequences. Through hyperparameter optimization, a single-layer network with a batch size of 64, tanh activation function, and a window size of 20 is identified as the optimal configuration. In the prediction stage, the prediction errors of the current step and the preceding 19 steps are fed into the trained model; the output predicted error is then added to the SGP4 forecast value to achieve error compensation.

Finally, this paper validates the effectiveness of the bidirectional long short-term memory (BiLSTM) network through extensive experiments. As shown in Fig. 3, taking the target NORAD ID: 1682 as an example, the raw errors in all three spatial directions grow with time during the three-day prediction window, and the errors are significantly reduced after compensation. Statistical results on 340 LEO targets demonstrate that the model achieves an average error reduction rate of 82%, with effectively compensated targets accounting for more than 94%. Fig. 4 presents the compensation effects in three spatial directions for each target, showing that the error reduction rates of most targets are stable and significant. In additional tests conducted during periods of intense solar activity, the model still maintains an 88% three-dimensional error reduction rate, with 358 targets effectively compensated, confirming its robustness. Fig. 5 presents a comparison between the BiLSTM network and the traditional dynamical model. The traditional model—incorporating the 60×60 EGM2008 gravity field, DE406 ephemeris, MSISE atmospheric model, and Cowell numerical integration—exhibits an 8-day prediction error exceeding 44.0 km, whereas the BiLSTM-compensated error consistently remains below 3.0 km, with a root-mean-square error of only 2.2 km, representing a 64% reduction compared with the traditional model. Analysis of influencing factors indicates that a 5-minute sampling frequency and a 3-day TLE update interval constitute the optimal configuration. This research provides an efficient data-driven solution for improving the orbit prediction accuracy of LEO space objects using only publicly available TLE data.