Wavelet Transform and Time Embedding-Based Deep Learning for Orbit Correction of Lunar Navigation Satellites

Accurate orbit prediction of lunar satellites is the foundation for providing precise positioning services to user terminals. However, due to limited ground tracking capability and simplifications in the orbital dynamics model, the prediction accuracy of lunar satellite orbits declines significantly over time when ground support is unavailable. Recently, orbit error prediction methods based on deep learning have shown the significant ability. However, exisiting deep learning models are mainly applied to Earth-orbiting satellites, and they typically extract orbital error features only in time domain or frequency domain. This results in information loss during the extraction process and limited ability to extract features from complex time signals. In this paper, we propose a novel model called DWC-Mixer for orbit correction of lunar navigation satellite, which combines frequency domain decomposition based on wavelet transform with time embedding of third body perturbation. The DWC-Mixer can effectively capture the perturbation effects not considered in the dynamical model. Extracting multi frequency and multi period variations from the orbit error sequence of the dynamic model using wavelet decomposition, ultimately achieving accurate correction of the Lunar orbit satellite trajectory prediction. First, one-dimensional convolution decomposes the lunar satellite orbit error data into several scales to obtain scale specific error variations. Next, wavelet transform and max-pooling break each scale into time and frequency domain components, extracting finer features. A time-embedding step is then applied to highlight the periodic patterns within the lunar orbit error sequence. Finally, a macro-detail fusion block recombines the refined features and feeds them into an Multi-Layer Perceptron(MLP) for training, yielding accurate orbit error predictions. We evaluate the performance on a simulated dataset. By employing the DWC-Mixer model to correct theJ2dynamic model, the ELFO orbit prediction error is reduced by 34.62% compared to other baseline network models. For PCO and LLO orbits, the errors decrease by 24.74% and 7.04%, respectively. This approach offers robust technical support for the development of lunar navigation constellations.