The variation law of satellite clock bias (SCB) can be regarded as a grey system because the spaceborne atomic clock is very sensitive and vulnerable to many factors. GM (1,1) model is the core and foundation of the grey system, which has been highly valued and successfully applied in SCB prediction since its production. However, there are still some problems to be further studied such as the lack of stability of its prediction effect in practical application. In view of this, an improved GM (1,1) model by optimizing the initial condition has been proposed in this paper so as to increase the prediction performance. The new initial condition is obtained by the weighted combination of the latest and oldest components of the original clock bias sequence. And the weight values of these two components are acquired from a method of minimizing the sum of squares of fitting errors. We adopt GPS rapid precision SCB data provided by the International GNSS Service (IGS) for 15 mins, 30 mins, 1 h, 3 h, 6 h, 12 h, and 24 h prediction experiments. The results show that the improved GM (1,1) model is effective and feasible, and its prediction accuracy and stability are significantly better than those of the traditional GM (1,1) model, ARIMA model, and QP model, even for the SCB signal with obvious fluctuation.

Due to the sensitivity of spaceborne atomic clock to many factors, the variation law of satellite clock bias (SCB) can be regarded as a grey system. The GM (1,1) model is a most classical and basic model of grey system, which has been successfully applied in SCB prediction. Moreover, many improved models have been proposed and widely used in various forecasts since GM (1,1) was generated. However, the prediction performance of these models is not obviously improved compared with the classical models in clock bias prediction. In view of this, a new GM (1,1) model has been come up with in this paper by optimising fitting model and initial condition. The new fitting model is obtained by differentiating time response function of winterisation, and the new initial condition is generated through one or more components of the original clock bias sequence. The authors employ GPS rapid and precise SCB provided by the International GNSS Service (IGS) for prediction experiments. The results show that the new GM (1,1) model is effective and feasible, and its prediction accuracy and stability are enormously better than that of the classical GM (1,1) model, especially for ultra-short-term prediction.

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