An enhanced prediction model for BDS ultra-rapid clock offset that combines singular spectrum analysis, robust estimation and gray model

Predicting the accuracy of clock offsets is critical for real-time precise point positioning. By considering the influence of gross error, periodic error, and uncertainty error on model fitting, we propose an enhanced prediction model for the BeiDou navigation satellite system ultra-rapid clock offset that combines robust estimation, singular spectrum analysis (SSA) and the gray model. First, SSA is used to decompose the clock offset sequence into two parts: a certain part and an uncertain part. Second, the robust quadratic polynomial (RQP) model with additional period terms is adopted to model the certain part. Third, the fitted residual from the second step and the uncertain part from the first step are combined and modeled by the robust gray model (RGM). Finally, the parts predicted by the RQP model with additional period terms and the RGM are added together with the initial corrected deviation to get the final prediction value. The proposed enhanced model is verified using ultra-rapid clock bias products from the International Global Navigation Satellite System Monitoring and Assessment Service (iGMAS) by taking the final clock bias products from iGMAS as a reference. The results show that the proposed model can improve prediction accuracy by 6.7%, 19.5%, 31.7%, and 42.2% over the iGMAS ultra-rapid prediction products at 3, 6, 12, and 24 h prediction spans, respectively, when using clock bias products of 2-day arcs for modeling. (paper)