Prediction models of GNSS satellite clock errors: Evaluation and application in PPP

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Satellite clock error prediction plays a key role in GNSS technology for Positioning, Navigation and Timing (PNT) service. However, due to the different types and quality of the space-borne atomic clocks, it is rather difficult to predict high-accuracy satellite clock errors by using one unique prediction model. In general, the performance of existing prediction models varies with different types of satellite clocks, lengths of fitting arcs and predicting arcs. In this article, three common-used prediction models e.g. polynomial model, grey model, and Auto-Regressive Integrated Moving Average (ARIMA) model are evaluated with GNSS precise satellite clock products provided by GFZ. The prediction precision of these models is calculated with respect to precise clock products, specified by different lengths of fitting arcs and prediction arcs respectively. Then, the clock errors predicted by these models are applied to kinematic Precise Point Positioning (PPP) separately and the corresponding positioning performance is discussed. The numerical results show that polynomial model performs the best compared to other two models. For 5-min prediction, the RMS values of predicted clock for GPS, Galileo, GLONASS, and BDS are 0.14 ns, 0.016 ns, 0.21 ns and 0.089 ns respectively. For kinematic PPP with 5-min predicted clock products, polynomial model has the minimum RMS values among three models, with 0.031 m, 0.026 m, and 0.068 m for east, north, and up components, respectively. Moreover, sub-decimeter can be reached for horizontal component with 1-hour predicted clock products. ARIMA model is comparable to polynomial model when the prediction arc is 5–15 min but becomes relatively worse with the increase of the length of prediction arc. Grey model is the worst among the three models, it can meet the requirement of sub-decimeter precision in kinematic PPP only if the prediction arc is shorter than 15 min.