Research on Modeling and Prediction Method of BeiDou Satellite Clock Bias Based on Multi-scale Feature Fusion

The modeling and prediction of satellite clock bias directly influence the operational performance of navigation systems and the positioning accuracy for users. Clock bias series exhibit typical nonlinear characteristics, including complex periodic components and stochastic properties, which are difficult to comprehensively capture using existing prediction models. To address this challenge, this study proposes a multi-frequency scale feature fusion model for clock bias prediction to enhance prediction accuracy. The proposed method employs polynomial fitting to extract the low-frequency trend of the clock bias series and utilizes the maximal overlap discrete wavelet transform (MODWT) to decompose the residual signals into periodic components and noise at different frequency scales. By combining the multi-scale feature extraction capability of temporal convolutional networks (TCN) with the temporal modeling capability of gated recurrent units (GRU), the model effectively captures the nonlinear features of clock bias series at various frequencies, thereby improving prediction accuracy. Experiments were conducted using precision clock bias data of BeiDou-3 satellites provided by the International GNSS Service (IGS) for medium and long term clock bias predictions over 12 hour and 24 hour horizons. Comparisons were made with quadratic polynomial (QP) models, the Grey Model (GM), long short-term memory (LSTM) networks, and GRU based models. The results demonstrate that the proposed method improves the average prediction accuracy by 67.9%, 91.1%, 53.5%, and 52.1% for 12-hour predictions and by 63.4%, 90.3%, 42.5%, and 38.8% for 24-hour predictions, respectively.