Improving BDS-2/3 satellite clock bias prediction using a TCN-Transformer framework with cross-attention mechanism

Satellite clock bias (SCB) prediction is essential for enhancing the accuracy and reliability of real-time precise point positioning (RT-PPP) in Global Navigation Satellite Systems (GNSS). To address the nonlinearity, non-stationarity, and short-term interruptions of SCB data under complex environments, this paper proposes an enhanced SCB prediction model combining Temporal Convolutional Networks (TCN) and Transformers. Experimental results indicate that, in a 24-h prediction task, the proposed model reduces root mean square error (RMSE) and range error (RE) by 95.6%, 86.0%, and 61.3%, and 93.7%, 86.3%, and 58.8%, respectively, compared with LSTM, Transformer, and CNN-BiGRU-Attention models, while improving computational efficiency by 48.6% over the Transformer. Moreover, although the clock bias products generated by the proposed method result in slightly higher static PPP positioning errors than the International GNSS Service (IGS) rapid clock products, the error differences are generally at the millimeter level, demonstrating the feasibility of using predicted clock bias products to replace rapid clock products in the short term. This method addresses the PPP positioning issue during short-term network service interruptions from the perspective of time series prediction and provides potential solutions for engineering applications such as landslide, earthquake, and subsidence monitoring.