Improved Strategies for BeiDou Ultrarapid Satellites’ Clock Bias Prediction Using BDS-2 and BDS-3 Integrated Processing

GNSS ultrarapid clock biases are key inputs of rapid high-accuracy applications, especially for its prediction parts. With the fast development of the BeiDou system (BDS), the system performances are mainly represented by orbit and clock products. However, it is suggested that the BDS-predicted clock biases cannot meet the requirement of real-time or near real-time services. In this research, the BDS satellite-predicted ultrarapid clock bias products are optimized with three methods, namely, one-step strategy, intersatellite correlation, and variogram model, using the combined estimation of BDS-2 and BDS-3 satellites. Firstly, considering the traditional two-step strategy for modelling clock bias prediction, we take all terms (including trend and periodic terms) into one-step solution of model estimation based on the sparse modelling in machine learning. Secondly, because of the much more stable on-board atomic clock of BDS-3 satellites, the intersatellite correlations between BDS-2 and BDS-3 are utilized to enhance the solution of model coefficients. Thirdly, to further improve the model, the temporal correlations in model residuals are used to reconstruct the stochastic function obtained by variogram. In addition, to verify the proposed improved strategies, 12 schemes of BDS clock bias prediction experiments are designed and analyzed with different conditions. According to the results of predicted clock biases, it is indicted that (1) the stability of BDS-3 on-board clocks is more optimal compared with BDS-2, which can be used to strengthen the solution of the clock bias prediction model; (2) the one-step estimation of the clock bias model by sparse modelling can slightly increase the accuracy of prediction results; (3) both BDS-2- and BDS-3-predicted clock biases benefited each other by inserting the intersatellite correlations into the weight matrix, in which the accuracy of 18-hour period with one-step strategy can be improved by 28.6% and 27.2% for BDS-2 and BDS-3, respectively; and (4) after the introduction of the variogram model in updating the weight matrix, the clock bias prediction model is further corrected by 8.0% and 11.1% for BDS-2 and BDS-3. In summary, improved strategies for BDS ultrarapid satellites’ clock bias prediction using BDS-2 and BDS-3 integrated processing are meaningful for the current BDS ultrarapid satellites’ clock bias prediction products