Grey modelling and real-time forecasting for the approximate non-homogeneous white exponential law BDS clock bias sequences.

Precise forecasting of satellite clock bias is crucial for ensuring service quality and enhancing the efficiency of real-time precise point positioning (PPP).The grey model with many benefits is an excellent choice for predicting real-time clock bias. However, the absolute prediction error of a small number of satellites is very high in actual forecasting process. In order to address this issue, a non-homogeneous white exponential law grey model has been constructed specifically for predicting clock bias sequences with non-homogeneous class ratio approximating constants. Considering that any model is difficult to apply to different kinds of satellite clocks and clock bias signals, an adaptive selection strategy for forecast model is proposed to ensure more excellent prediction accuracy. Afterwards, a prediction scenario based on the observed products of the BeiDou satellite navigation system (BDS) is created to demonstrate the effectiveness of the approach described in this article. The outcomes of the method are then compared with those of a single grey model and the ultra-rapid predicted products. The outcomes demonstrate that this strategy's prediction accuracy is less than 1 ns/day and that its prediction uncertainty is much decreased, which may improve data selection for real-time applications like real-time kinematics (RTK) and PPP.