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.

In order to analyze the influence of different data amounts on the accuracy and stability of BDS satellite clock bias prediction model, BDS satellites of different systems were randomly selected in this paper, and post-event precision satellite clock bias data released by Wuhan University was used. The prediction accuracy and stability of quadratic polynomial model, grey prediction model and autoregressive moving average model are compared and analyzed in detail by using different modelling schemes. The experimental results show that the prediction accuracy and stability of quadratic polynomial model are the highest, followed by the autoregressive moving average model and the grey prediction model, and the quadratic polynomial model and the autoregressive moving average model are more sensitive to the amount of data involved in modelling. In addition, the autoregressive moving average model has the highest prediction accuracy and stability for BDS-2 system satellite clock bias, and the grey prediction model has the highest prediction accuracy and stability for BDS-3 system satellite clock bias.

The satellite clock bias (SCB) with high sampling rate is needed in precise point positioning, and the sampling interval of SCB provided by the analysis center is relatively large, so SCB with large interval must be interpolated and encrypted by interpolation methods. Three interpolation methods are used to interpolate SCB from 5-minute sampling intervals to 30-second sampling intervals, and the interpolated results are compared and analyzed with the published SCB for 30-second sampling intervals. The results show that the accuracy of linear interpolation method is the highest, followed by cubic spline interpolation method and then Lagrange interpolation method. In addition, the interpolation accuracy of the three interpolation methods is the highest for GPS IIF and IIIA satellites launched in recent years, followed by IIR-M satellites launched in the middle of the period, and then IIR satellites launched in the early period.

In order to improve the accuracy and stability of satellite clock bias prediction, a combined satellite clock bias prediction method based on the entropy weight method is proposed. Firstly, the method adopts a quadratic polynomial model and a gray model to make a single prediction of satellite clock bias and generate two sets of prediction results. Then, by calculating the entropy of error information of the two sets of prediction results, it determines the weights of each model and realizes the optimal fusion of the models. Finally, the entropy weight combination method is used to obtain a higher precision prediction result. Four different types of BeiDou-3 satellites were randomly selected for the prediction test by using the precision satellite clock bias products released by the GNSS Analysis Center of Wuhan University. The results show that the method can provide high-precision short- and medium-term predictions of BeiDou-3 satellite clock bias, and its 6-h average prediction accuracy and stability are 0.22ns and 0.46ns, respectively, which are 72.15% and 48.84% higher than the average prediction accuracy of quadratic polynomial and gray models, and the stability is 70.00% and 20 .69% higher, respectively.