Short-Term Clock offset Predicting Products Based on Low Sampling Estimation for Real-time Service

With the widespread application of precise point positioning (PPP), real-time clock offset products have become a focal point of global navigation satellite system (GNSS). Real-time clock offset estimation offers high accuracy but demands stable data communication and involves significant computational pressure. And the accuracy of ultra-rapid products does not meet the requirements of positioning, navigation and timing (PNT) services. To address this, a short-term clock prediction method based on low sampling rate estimation is proposed. This method provides users with a set of clock model coefficients, enabling them to obtain high sampling rate clock offset at any time. Based on the clock products with 60s intervals estimated by square root information filtering (SRIF) from 80 stations, the most suitable short-term model that the linear model with the same arc length for fitting and prediction is determined by adaptive analysis of the order of polynomial model and data arc lengths. Based on this, short-term predicted parameters for 5min, 10min, 15min, 30min and 60min are obtained. These parameters are then interpolated to 30s interval for detailed accuracy assessment and PPP validation. The results indicate that the clock offset predicting accuracies of BDS-3 are 0.029ns, 0.033ns, 0.037ns, 0.047ns, 0.071ns for 5min, 10min, 15min, 30min and 60min, while the Galileo are 0.023ns, 0.027ns, 0.032ns, 0.039ns, 0.062ns. The predicted clock offsets of Galileo are slightly better than those of BDS-3. The PPP results show that the 2D and 3D positioning accuracies for the 5min prediction are 0.058m and 0.115m, respectively, with positioning accuracy declining as the prediction arc length increases. Overall, the positioning performance of the predicted clock products within 30min are nearly consistent to the real-time estimated clock. Compared to Centre National d’Etudes Spatiales (CNES), the results of PPP performance are similar，and superior to the performance of ultra-rapid clock products. Therefore, short-term predicted products based on low sampling rate estimated clock can serve as a more stable alternative to real-time products in the PPP applications. The updating frequency of the clock offset model coefficients is determined based on the needs of PPP users. The method reduces the sampling rate for estimating clock offset while maintaining high-precision clock offset products. Additionally, it can still offer high-precision real-time clock offset prior information to the PPP users during interruptions in real-time estimation.