A multi-scale decomposition-fusion method for satellite clock bias prediction supporting real-time applications in data-scarce scenarios

High-precision satellite clock bias (SCB) prediction is essential for real-time remote sensing, real-time precise point positioning (RT-PPP), Earth observation, and spaceborne geodetic applications of Global Navigation Satellite Systems (GNSS). However, real-time services are frequently interrupted in data-scarce environments such as communication outages, which severely restrict the continuity and reliability of high-precision applications. To address this issue, a multi-scale decomposition-fusion modeling method is proposed for short-term SCB prediction. First, the Daubechies 6 (db6) wavelet is used to perform three-level multi-resolution decomposition and single-branch reconstruction of the SCB time series, decomposing them into one low-frequency approximation component and three high-frequency detail components. Then, component-adaptive prediction models are developed according to the characteristics of each subsequence: the metabolic grey model combined with a backpropagation (BP) neural network (MGM + BP) is applied to the approximation component; the first-order weighted local (FWL) model is used for the first detail component; the long short-term memory (LSTM) network is used for the second detail component; and the quadratic polynomial (QP) model is employed for the third detail component. Thirdly, the final SCB predictions are obtained by linearly superimposing the predicted values of all components. Experiments are conducted with GPS SCB products from the GNSS Analysis Center of Wuhan University. Results demonstrate that the proposed fusion model outperforms conventional models in both prediction accuracy and stability. The average root mean square (RMS) error for 6-h prediction is 0.20 ns, with maximum improvements in accuracy and stability reach 62.26% and 40.00%, respectively. Moreover, the proposed method exhibits strong robustness and is less sensitive to satellite clock types and the linear characteristics of clock bias series. Thus, the SCB predicted by the proposed model can fully meet the accuracy requirements of real-time remote sensing and centimeter-level RT-PPP in scenarios where real-time clock products are unavailable.