Model Selection Method Based on ARIMA Model in Outliers Detection of Satellite Clock Offset
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摘要: 由于各种不确定因素的干扰，人们获取的卫星钟差数据中经常会出现异常扰动，降低了卫星钟性能分析的可靠性，破坏了钟差建模和预报的有效性，影响了导航定位结果的精准度。对此，以求和自回归移动平均模型为基础，建立了钟差时间序列异常值探测模型；基于Bayes统计原理，将异常值的定位和定值问题转化为模型选择问题；通过模型后验概率的近似计算，构建了模型选择的度量标准，避免了复杂的迭代计算问题。通过全球定位系统和北斗导航卫星系统不同卫星钟差数据的仿真试验，验证了所提出的方法对于卫星钟差序列中异常影响的定位和定值的正确性和有效性。
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关键词:
- 卫星钟差 /
- 异常值 /
- Bayes原理 /
- 求和自回归移动平均模型
Abstract: Due to the interference of various uncertain factors, the abnormal disturbances often occur in the satellite clock offset data, which reduces the reliability of the performance analysis of the satellite clock, destroys the validity of the modeling and prediction of clock offset, and affects the accuracy of the navigation positioning results. As to this problem, on the basis of the autoregressive integrated move average (ARIMA) model, this paper establishes an outlier detection model of clock offset time series. Based on the principle of Bayes statistics, the problems of outliers detection and the outliers magnitudes estimation are transformed into a model selection problem. Through the approximate calculation of the posterior probability of the model, the measurement standard of the model selection is derived so the complex iterative computation is avoided. Simulation Test examples of GPS and BeiDou illustrate that the proposed method can detect the outliers effectively and estimate the magnitudes of outliers accurately in the clock offset sequence; furthermore, it can obtain higher prediction precision when the method is applied in the medium and long term prediction of the satellite clock offset. -
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图 1 不同卫星3种方法的预报误差
Figure 1. Prediction Errors of Three Methods with Different Satellites
表 1 不同异常值数量的异常扰动定位与定值结果
Table 1 Locations and Magnitudes of Abnormal Disturbances with Different Numbers of Outliers
异常扰动项 i =0 i =1 i =2 i =3 τi 31 121 187 (31, 121) (31, 187) (121, 187) (31, 121, 187) wti/μs 2.745 2 -1.548 3 10.421 9 2.960 9，-2.973 4 2.840 6，6.054 2 -3.430 1，5.841 7 2.974 5，-2.826 3，6.040 1 MDO -1.337 7 -2.761 0 -2.756 5 -1.844 5 -2.535 3 -1.149 6 -1.143 3 22.052 1 
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表 2 3种方法的预报精度/ns
Table 2 Prediction Precisions of Three Methods/ns
预报方法 RMSEP Mean MAB 基于AR模型的Bayes方法 0.94 90.2 294 抗差二次多项式法 1.34 103.8 477 模型选择法 0.50 75.8 185
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