Objectives  The fitting sequence of the traditional grey model (GM) cannot reflect the dynamic change of the stepwise ratio of the modeling data sequence, and the accuracy of the satellite clock offset prediction results need to be improved.

  Methods  The stepwise ratio sequence of modeling data is proposed as target, and a discrete grey model(DGM) that reflects the trend of the modeling data sequence stepwise ratio is established.The specific steps of the method applied to satellite clock offset prediction are given as well. We first generate a corresponding stepwise ratio sequence for the modeling clock offset sequence. Then, the stepwise ratio sequence is used for DGM modeling and forecasting. Finally, after combining the relationship between the stepwise ratio and the modeled clock offset sequence, the forecast results are restored to obtain the corresponding clock offset prediction evalue.

  Results  The post-precision clock offset data provided by iGMAS are used for forecasting experiments, and evaluate the quadratic polynomial model (QPM) and the GM forecast results. The results show that the improved algorithm clock offset prediction accuracy is better than those of the QPM and GM. In the single-day forecast test, the average accuracy of forecast products obtained by this method.Compared to the QPM results, BeiDou navigation satellite system(BDS) satellites and global positioning system(GPS) satellites are increased by 54.71% and 46.40%, respectively, and compared to the GM results, BDS satellites and GPS satellites are increased by 82.96% and 67.81%, respectively.In the continuous multi-day forecasting experiment, BDS satellites and GPS satellites are increased by 38.15% and 37.09% compared to the QPM results, respectively, and BDS satellites and GPS satellites are increased by 57.43% and 26.30% compared with the GM results, respectively.

  Conclusions  The prediction test results verify that the proposed method can predict satellite clock offset with high accuracy and relatively stable performance, and its prediction accuracy and universality are significantly better than the commonly used QPM and GM algorithms. In addition, this method solves the problem that the GM prediction fails when the satellite clock offset stepwise ratio changes drastically, and provides a new idea for high-precision satellite clock offset prediction.