An improved model for BDS satellite ultra-rapid clock offset prediction based on BDS-2 and BDS-3 combined estimation

Ultra-rapid clock products provide the main parameters for real-time or near real-time precise point positioning services. However, it has been found that BeiDou ultra-rapid clock offsets do not meet the requirements for high-accuracy applications because of their low accuracy, especially regarding the prediction parts. This study proposes an improved model for BDS satellite ultra-rapid clock offset prediction based on BDS-2 and BDS-3 combined estimation. First, the preprocessing of the clock offset based on frequency data and a denoising method that employed a Tikhonov regularization algorithm was introduced to refine the observed series for predictive modeling. Second, given the coexistence of BDS-2 and BDS-3 satellites and the advantages of the BDS-3 onboard atomic clock, inter-satellite correlations between different satellites were used to adjust the stochastic function in estimating the coefficients for the prediction model. Third, to further improve the accuracy of the prediction model, the residuals of the clock offsets were analyzed by partial least squares regression, in which the main components related to the clock offsets were modeled by a back-propagation neural network. Six experimental schemes were introduced to verify the improved model. Experiments were divided into two groups to compare the preprocessing strategy and prediction model. The experimental results indicated: (1) both the BDS-2 and BDS-3 predicted clock offsets were mutually beneficial in the improved model; (2) because of the lower quality of the observed clock offset from BDS-3, preprocessing was used to improve the prediction accuracy by 1.0-15.2% for BDS-2, and reaching 23.2-31.9% for BDS-3; (3) the accuracy of the clock offsets were improved by 30.7-47.3% for BDS-2, and by 49.9-59.3% for BDS-3 within an 18-h period. The proposed improved model was found to have a significant effect on optimizing the ultra-rapid clock products of the International GNSS Monitoring and Assessment Service and GNSS analysis centers.