Transformer-Based Joint Compensation Method for RealTime Orbit and Clock Errors of LEO Satellites

Objectives: Real-time kinematic precise orbit determination (POD) of low Earth orbit (LEO) satellites is attractive for onboard applications owing to its low computational burden and independence from dynamic models. Its accuracy, however, is limited by the quality of Global Navigation Satellite System (GNSS) broadcast ephemerides and real-time precise products. Existing machine-learning-based error compensation methods address three-dimensional orbit errors while overlooking clock errors. A joint real-time compensation method is developed for both orbit and clock errors to improve LEO kinematic POD accuracy under different GNSS product conditions. Methods: A Transformer neural network with multi-head self-attention is developed to model real-time orbit and clock errors. A sliding window of state features extracted from the kinematic POD process feeds an encoder-only architecture that jointly predicts three-axis orbit and clock errors. The dataset covers the full year of 2022 from Sentinel-3A, Sentinel-3B, and Sentinel- 6A. Solutions are evaluated under broadcast ephemerides and Centre National d'Études Spatiales (CNES) real-time products, with external precise scientific orbit and clock products as reference. Results: Under broadcast ephemerides, the one-dimensional root mean square (1D RMS) orbit errors of the three LEO satellites decrease by 30.7% to 46.7% compared with conventional kinematic real-time POD results. The mean clock errors are reduced from -16.5 ns – -11.6 ns to - 0.1 ns – 0.4 ns, with the standard deviation decreasing by 38.5% to 43.5%. The RMS of signal-inspace ranging errors (SISRE) decreases from 353.0 cm – 493.1 cm to 48.0 cm – 100.6 cm, i.e., from the meter level to the decimeter level. Under CNES real-time precise ephemerides, the real-time orbit and clock errors of different LEO satellites are still reduced by 22.6% to 40.5% and 84.8% to 94.4%, respectively, verifying the effectiveness of the proposed method in improving the accuracy of LEO real-time orbit and clock products. Conclusions: In summary, the proposed Transformerbased joint compensation method significantly improves the real-time orbit and clock accuracy of LEO kinematic POD under both broadcast ephemerides and real-time precise products, across different satellite platforms and GNSS configurations.