改进的灰色GM(1,1)在北斗卫星钟差短期预报中的应用

Application of improved grey model in the prediction of Bei Dou satellite clock error

根据星载原子钟钟差的特点以及传统的灰色GM(1,1)自身存在的缺陷,提出一种改进的灰色GM(1,1)钟差短期预报模型。首先采用灰色GM(1,1)对钟差序列进行预报,再采用马尔科夫对随机性波动较大的灰色残差序列进行修正,充分结合二者的优势,克服了自身的缺陷。采用5min采样率的北斗钟差数据进行算例分析,并通过不同预报步长与传统的灰色GM(1,1)对比分析,结果表明,该方法的预报精度较传统的灰色模型有了较大提高,该方法应用于钟差短期时间预报是可行的,可靠性较强。

By considering the characteristics of the clock error of the spaceborne atomic clock and the defects of the traditional grey model GM （1 , 1 ） , an improved grey model is presented for short-term prediction of clock errors. The clock error sequence is predicted by the GM （ 1 , 1 ） , then the random residual error of the grey model is corrected by Markov chain. With the use of 5 min sampling rate of BDS clock error data, the improved method is examined with different prediction step lengths and compared with the traditional grey model. Results show that the prediction accuracy of the improved method has increased greatly, the method is feasible and reliability in the application of the short-term clock error prediction.