# LTE: Lightweight Transformer Encoder for Orbit Prediction
## 5 Conclusions  
As the space environment becomes increasingly complex due to the rapid rise in the number of satellites, the risk of collisions is also growing. Consequently, the need for accurate satellite orbit prediction has never been more critical. Therefore, a new approach was needed, one that differs from traditional methods that rely on predicting satellite orbits based on simulated data or physical models. Additionally, to efficiently process large volumes of data, a methodology that considers both execution time and the number of parameters used was required.  
In this paper, we proposed the LTE model for satellite orbit prediction by modifying the Transformer structure. Our model was tailored to the characteristics of orbital data by eliminating PE, which could distort input data and unnecessarily increase complexity, as well as LN, which could hinder model training through over-normalization. Additionally, we collected a TLE set from the K3, K3A, and K5 satellites operated by the KARI, which comprised approximately 4.8 million data points collected every minute from January 2016 to December 2018. Leveraging data from an operational satellite, rather than simulations, highlighted the practical utility and effectiveness of our model.  
We demonstrated the superiority of the LTE model by comparing its performance against a total of 14 prediction models. The LTE model reduced the MSE compared to the best-performing model other than the LTE. The reduction was 50.61% for K3, 42.40% for K3A, and 30.00% for K5. Additionally, on the K3 dataset, our model was 36.86% faster than the second-fastest model and used 2.33% fewer parameters than the model with the second-lowest parameter count. This showed that the LTE model not only improved prediction performance but also had a reduced execution time and parameter usage. Also, we conducted an efficiency analysis on the presence or absence of PE and LN. By varying the number of attention heads, we experimented with all combinations of PE and LN for the LTE model and evaluated the resulting prediction performances. The results indicated that PE and LN were not well suited to orbital data with repetitive and periodic patterns, thereby enhancing the explanatory power of our model.  
The LTE model also offers substantial benefits for satellite operations. Ground stations need to process large volumes of satellite data generated every second across multiple satellites. Thus, a prediction model that is both efficient and lightweight, while still achieving a high performance, is essential. Our study demonstrates the LTE model's feasibility and practical value in addressing these operational demands effectively. In conclusion, we hope that the LTE model can make a meaningful contribution to improving satellite orbit prediction, helping to mitigate the risk of collisions between satellites and space debris and thereby enhancing the safety and sustainability of the space environment.  
**Author Contributions:** Conceptualization, S.J.; methodology, S.J.; formal analysis, S.J.; investigation, S.J.; resources, S.J.; data curation, S.J.; writing--original draft preparation, Y.S.; writing--review and editing, Y.S.; project administration, Y.S.; supervision, Y.S.; funding acquisition, Y.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the Research Fund of The Catholic University of Korea in 2023, and a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-00213456).  
**Institutional Review Board Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in this article. Further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.