High-accuracy and dependable prediction of the bias of space-borne atomic clocks is extremely crucial for the normal operation of the satellites in the case of interrupted communication. Currently, the clock bias prediction for the Chinese BeiDou Navigation Satellite System (BDS) remains still a huge challenge. To develop a high-precision approach for forecasting satellite clock bias (SCB) in allusion to analyze the shortcomings of the exponential smoothing (ES) model, a modified ES model is proposed hereof, especially for BDS-2 satellites. Firstly, the basic ES models and their prediction mechanism are introduced. As the smoothing coefficient is difficult to determine, this leads to increasing fitting errors and poor forecast results. This issue is addressed by introducing a dynamic “thick near thin far (TNTF)” principle based on the sliding windows (SW) to optimize the best smoothing coefficient. Furthermore, to enhance the short-term forecasted accuracy of the ES model, the gray model (GM) is adopted to learn the fitting residuals of the ES model and combine the forecasted results of the ES model with the predicted results of the GM model from error learning (ES + GM). Compared with the single ES models, the experimental results show that the short-term forecast based on the ES + GM models is improved remarkably, especially for the combination of the three ES model and GM model (ES3 + GM). To further improve the medium-term prediction accuracy of the ES model, the new algorithms in ES with GM error learning based on the SW (ES + GM + SW) are presented. Through examples analysis, compared with the single ES2 (ES3) model, results indicate that (1) the average forecast precision of the new algorithms ES2 + GM + SW (ES3 + GM + SW) can be dramatically enhanced by 49.10% (56.40%) from 5.56 ns (6.77 ns) to 2.83 ns (2.95 ns); (2) the average forecast stability of the new algorithms ES2 + GM + SW (ES3 + GM + SW) is also observably boosted by 53.40% (49.60%) from 8.99 ns (16.13 ns) to 4.19 ns (8.13 ns). These new coupling forecast models proposed in this contribution are more effective in clock bias prediction both forecast accuracy and forecast stability.
Grey Model Based Traffic Analysis on Car-hailing Platforms
