A Grey Model Based on First Differences in the Application of Satellite Clock Bias Prediction

Abstract

In consideration of the characteristics of satellite clock bias (SCB), a grey GM(1,1) model based on the first difference method is proposed. The first differences between the SCB values of two adjacent epoches are firstly derived to obtain the corresponding first difference sequence. Then, a grey model is made based on the sequence to predict the first difference values for the time following. Finally, the predicted first difference sequence is recovered to be the corresponding predicted SCB. The clock bias data provided by the IGS (International GNSS Service) are used as the experimental data, and the cases with different lengths of modeling data and different prediction step lengths are compared and analyzed. The result shows that the prediction accuracy of this method is higher than that of traditional grey GM(1,1) model, especially for the PRN01 satellite clock, whose forecast effect is the best. With the first difference method, the model prediction accuracy and stability can be effectively improved and enhanced. This method is feasible and reliable for the relatively long term SCB prediction.