Enhanced BDS-3/GNSS satellite clock offset prediction: A sliding-window optimized cascaded LSTM+MLP architecture

The performance of real-time satellite clock offset products directly impacts the service quality of high-precision positioning, navigation, and timing (PNT). To address existing issues in current clock offset prediction models, including insufficient synergy between feature extraction and nonlinear mapping, inadequate multi-scale information fusion, and noise amplification, this research proposes an enhanced BDS-3/GNSS satellite clock offset prediction method through a sliding-window optimized cascaded LSTM + MLP architecture. First, the LSTM network is used to capture the time-series characteristics of satellite clock frequencies, and we then introduce a parallel MLP to extract local nonlinear features. Second, a feature fusion layer subsequently enables adaptive weighted integration of multi-scale information. Third, a sliding window strategy is applied for local polynomial fitting of predicted data, with clock offsets finally calculated through epoch-wise integration. Experimental results demonstrate that: (1) the sliding-window polynomial model improves stability and accuracy by 17.8% and 24.8% on average compared to traditional strategies; (2) the LSTM + MLP model exhibits significantly better performance than LSTM, QP, and ARIMA in clock offsets prediction. Its stability and accuracy for 6 h, 12 h, and 24 h prediction improved by up to 44.2%/45.8%, 55.1%/50.6%, and 79.9%/77.0%, respectively. Validation using clock offset simulating a real-time service scenario demonstrates that the model prediction performance is highly consistent with that on CODE products, indicating that it is not only applicable to final products but also to real-time scenarios; (3) the model enhances PPP accuracy at monitoring stations by 9.4%, 7.8%, and 6.5% in E, N, and U directions, respectively, while effectively improving convergence speed, with the most notable improvement observed in the N direction.