引用本文: 梅长松, 黄海军, 蒋可, 夏磊, 潘雄. 级比离散灰色模型在卫星钟差预报中的应用[J]. 武汉大学学报 ( 信息科学版), 2021, 46(8): 1154-1160.
MEI Changsong, HUANG Haijun, JIANG Ke, XIA Lei, PAN Xiong. Application of Discrete Grey Model Based on Stepwise Ratio Sequence in the Satellite Clock Offset Prediction[J]. Geomatics and Information Science of Wuhan University, 2021, 46(8): 1154-1160.
 Citation: MEI Changsong, HUANG Haijun, JIANG Ke, XIA Lei, PAN Xiong. Application of Discrete Grey Model Based on Stepwise Ratio Sequence in the Satellite Clock Offset Prediction[J]. Geomatics and Information Science of Wuhan University, 2021, 46(8): 1154-1160.

## Application of Discrete Grey Model Based on Stepwise Ratio Sequence in the Satellite Clock Offset Prediction

• 摘要: 针对传统灰色模型(grey model, GM)的拟合序列不能反映出建模数据序列级比动态变化这一问题，提出以建模序列的级比序列为对象，建立了能够反映出建模序列级比变化趋势的离散灰色模型(discrect grey model, DGM)，给出了该方法应用于卫星钟差预报的具体步骤。首先，对建模钟差序列生成对应的级比序列；然后，用DGM对级比序列建模并进行预报；最后，结合级比与钟差序列之间的关系，将级比预报结果还原得到相应的钟差预报值。采用iGMAS机构提供的事后精密钟差数据分别进行了单天和连续多天的预报试验，并与二次多项式模型(quadratic polynomial model, QPM)及GM预报结果进行对比分析。结果表明，在单天预报试验中，与QPM相比，所提方法得到的预报产品平均精度在北斗卫星导航系统(BeiDou navigation satellite system, BDS)卫星和全球定位系统(global positioning system, GPS)卫星中分别提升了54.71%、46.40%；与GM相比，所提方法得到的预报产品平均精度在BDS卫星和GPS卫星中分别提升了82.96%、67.81%。在连续多天预报试验中，与QPM相比，该方法得到的预报产品多天平均精度在BDS卫星和GPS卫星中分别提升了38.15%、37.09%；与GM相比，该方法得到的预报产品多天平均精度在BDS卫星和GPS卫星分别提升了57.43%、26.30%。

Abstract:
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.

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