Abstract
High-precision satellite clock bias (SCB) prediction is essential for GNSS applications, including real-time precise point positioning (RT-PPP), Earth observation, planetary exploration, and spaceborne geodetic missions. However, during communication outages or when real-time SCB products are unavailable, RT-PPP may fail due to missing clock corrections. This underscores the necessity of reliable short-term SCB prediction in data-denied environments. To address this challenge, a hybrid model that integrates wavelet transform, a particle swarm optimization-enhanced gray model, and a first-order weighted local method is proposed for short-term SCB prediction. First, the novel model employs the db1 wavelet to perform three-level multi-resolution decomposition and single-branch reconstruction on preprocessed SCB, yielding one trend term and three detailed terms. Second, the particle swarm optimization algorithm is adopted to globally optimize the parameters of the traditional gray model to avoid falling into local optima, and the optimization-enhanced gray model is applied to predict the trend term. For the three detailed terms, the embedding dimension and time delay are calculated, and they are constructed in phase space to establish a first-order weighted local model for prediction. Third, the final SCB prediction is obtained by summing the predicted results of the trend term and the three detailed terms correspondingly. The BDS-3 SCB products from the GNSS Analysis Center of Wuhan University (WHU) are selected for experiments. Results indicate that the proposed model surpasses conventional linear polynomial (LP), quadratic polynomial (QP), gray model (GM), and Legendre (Leg.) polynomial models. The average precision and stability improvements reach (80.00, 79.16, 82.14, and 72.22) % and (36.36, 41.67, 41.67, and 61.11) % for 30 min prediction, (79.31, 78.57, 80.65, and 76.92) % and (44.44, 44.44, 47.37, and 74.36) % for 60 min prediction, and the average precision of the predicted SCB products is better than 0.20 ns and 0.21 ns for 30 min and 60 min, respectively. Furthermore, the proposed model exhibits strong robustness and is less affected by changes in clock types and the amount of modeling data. Therefore, in practical applications, the short-term SCB products predicted by the novel model are fully capable of satisfying the requirements of centimeter-level RT-PPP for clock bias precision.
