含误差预报校正的GM(1,1)卫星钟差预报新方法
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摘要
为了提高卫星钟差预报精度,该文提出用AR(p)模型对GM(1,1)建模过程中的模型残差进行建模预报,以此来提高GM(1,1)模型预报卫星钟差的精度。首先,剔除卫星钟差数据中的异常值,采用拉格朗日插值法将缺失的数据补齐;然后,用GM(1,1)模型对卫星钟差进行预报,对GM(1,1)的模型残差作平稳化处理后,采用AR(p)模型对处理后的残差序列进行预报;最后,将GM(1,1)和AR(p)模型的预报结果对应相加即得到钟差的最终预报值。此外,该文采用IGS公布的事后精密卫星钟差进行预报试验,并将该文结果与卫星钟差预报中常用的二次多项式和修正指数曲线法模型预报结果进行对比分析。结果表明,该方法可以对GPS卫星钟差进行高精度的中短期预报。
In order to improve the accuracy of satellite clock bias(SCB)prediction,it was proposed to use auto-regressive(AR(p))to model the residuals of grey model(GM(1,1))in the modeling process,so as to improve the GM(1,1)poor precision.Firstly,the anomaly of the SCB data was eliminated,and the missing data was filled with the Lagrange interpolation method.Then,the GM(1,1)model was used to forecast the SCB.Finally,the prediction results of GM(1,1)and AR(p)model were added to achieve the final forecast value.In addition,the predictive test was carried out by using the precision SCB published by IGS,and the results were compared with those used in the prediction of SCB using the quadratic polynomial method(QPM)and modified exponential curve method(MECM)model.The results showed that this method could make high-precision short-term forecast of GPS SCB.
In order to improve the accuracy of satellite clock bias(SCB)prediction,it was proposed to use auto-regressive(AR(p))to model the residuals of grey model(GM(1,1))in the modeling process,so as to improve the GM(1,1)poor precision.Firstly,the anomaly of the SCB data was eliminated,and the missing data was filled with the Lagrange interpolation method.Then,the GM(1,1)model was used to forecast the SCB.Finally,the prediction results of GM(1,1)and AR(p)model were added to achieve the final forecast value.In addition,the predictive test was carried out by using the precision SCB published by IGS,and the results were compared with those used in the prediction of SCB using the quadratic polynomial method(QPM)and modified exponential curve method(MECM)model.The results showed that this method could make high-precision short-term forecast of GPS SCB.
引文
[1]郭承军,腾云龙.神经网络在卫星钟差短期预报中的应用研究[J].测绘科学,2011,36(4):198-200.(GUOChengjun,TENG Yunlong.Application of neural network in satellite clock bias short-term prediction[J].Science of Surveying and Mapping,2011,36(4):198-200.)
[2]陈正生,吕志平,张清华,等.基于时间序列分解的GPS卫星钟差预报[J].测绘科学,2011,36(3):116-118.(CHEN Zhengsheng,LYU Zhiping,ZHANG Qinghua et al.GPS satellite clock error prediction based on ARMA analysis[J].Science of Surveying and Mapping,2011,36(3):116-118.)
[3]HUANG Guanwen,YANG Yuanxi,ZHANG Qin.Estimate and predict satellite clock error using adaptively robust sequential adjustment with classified adaptive factors based on opening windows[J].Acta Geodaetica et Cartographica Sinica,2011,40(1):15-21.
[4]韩宝民.精密卫星钟差加密方法及其对星载GPS低轨卫星定轨精度影响[J].武汉大学学报(信息科学版),2006,31(12):1075-1078.(HAN Baomin.Densification methods of gps satellite clock errors and their impact on orbit determination precision of LEOs[J].Geomatics and Information Science of Wuhan University,2006,31(12):1075-1078.)
[5]黄观文,张勤,王继刚.GPS卫星钟差的估计与预报研究[J].大地测量与地球动力学,2009,29(6):108-122,125.(HUANG Guanwen,ZHANG Qin,WANGJigang.Research on estimation and prediction of GPSsatellite clock error[J].Journal of Geodesy and Geodynamics,2009,29(6):108-122,125.)
[6]刘晓刚,吴晓平,赵润,等.几种时间预报模型的钟差长期预报效果分析[J].测绘通报,2011(1):15-17,48.(LIU Xiaogang,WU Xiaoping,ZHAO Run,et al.Analysis of long-term clock bias forecast effects of several time prediction models[J].Bulletin of Surveying and Mapping,2011(1):15-17,48.)
[7]YUAN Haibo,WANG Zhengming,DONG Shaowu,et al.Dynamic grey-autoregressive model of an atomic clock[J].Metrologia,2008,45(6):1-5.
[8]郭承军,腾云龙.基于小波分析和神经网络的卫星钟差预报性能分析[J].天文学报,2010,51(4):396-403.(GUO Chengjun,TENG Yunlong.Performance analysis of satellite clock bias based on wavelet analysis and neural network[J].Acta Astronomica Sinica,2010,51(4):396-403.)
[9]朱祥维,肖华,雍少为,等.卫星钟差预报的Kalman算法及其性能分析[J].宇航学报,2008,29(3):966-970,1052.(ZHU Xiangwei,XIAO Hua,YONG Shaowei,et al.Kalman algorithm for satellite clock bias prediction and its performance analysis[J].Journal of Astronautics,2008,29(3):966-970,1052.)
[10]王继刚,胡永辉,何在民,等.组合模型预报导航卫星钟差[J].大地测量与地球动力学,2012,32(1):84-88.(WANG Jigang,HU Yonghui,HE Zaimin,et al.Combination models for navigation satellite clock prediction[J].Journal of Geodesy and Geodynamics,2012,32(1):84-88.)
[11]徐君毅,戴伟.一种新的长期卫星钟差预报方法[J].大地测量与地球动力学,2009,29(6):97-100.(XUJunyi,DAI Wei.A new method for long-term prediction of satellite clock error[J].Journal of Geodesy and Geodynamics,2009,29(6):97-100.)
[12]郑作亚,党亚民,卢秀山,等.附有周期项的预报模型及其在GPS卫星钟差预报中的应用研究[J].天文学报,2010,51(1):95-102.(ZHENG Zuoya,DANG Yamin,LUXiushan,et al.Prediction model of periodic item and its application to the prediction of GPS satellite clock bias[J].Acta Astronomica Sinica,2010,51(1):95-102.)
[13]帅平,曲广吉.导航星座自主导航的时间同步技术[J].宇航学报,2005,26(6):768-772.(SHUAI Ping,QUGuangji.Time synchronization techniques of the autonomous navigation of navigation constellation[J].Journal of Astronautics,2005,26(6):768-772.)
[14]崔先强,焦文海.灰色系统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),2005,30(5):447-450.(CUI Xianqiang,JIAO Wenhai.Grey system model for the satellite clock error predicting[J].Geomatics and Information Science of Wuhan University,2005,30(5):447-450.)
[15]路晓峰,杨志强,贾小林,等.灰色系统理论的优化方法及其在卫星钟差预报中的应用[J].武汉大学学报(信息科学版),2008,33(5):492-495.(LU Xiaofeng,YANG Zhiqiang,JIA Xiaolin,et al.Parameter optimization method of gray system theory for the satellite clock error predicating[J].Geomatics and Information Science of Wuhan University,2008,33(5):492-495.)
[16]徐君毅,曾安敏.ARIMA(0,2,q)模型在卫星钟差预报中的应用[J].大地测量与地球动力学,2009,29(5):116-120.(XU Junyi,ZENG Anmin.Application of ARIMA(0,2,q)model to prediction of satellite clock error[J].Journal of Geodesy and Geodynamics,2009,29(5):116-120.)
[17]路晓峰.导航卫星钟差评估与预报研究[D].西安:长安大学,2007.(LU Xiaofeng.Study on the evaluation of navigation satellite clock bias and the satellite cloek bias predieating[D].Xi’an:Chang’an University,2007.)
[18]张清华,隋立芬,牟忠凯.基于小波与ARMA模型的卫星钟差预报方法[J].大地测量与地球动力学,2010,30(6):100-104.(ZHANG Qinghua,SUI Lifen,MOUZhongkai.A GPS precise clock errors prediction model based on wavelet and ARMA[J].Journal of Geodesy and Geodynamics,2010,30(6):100-104.)
[2]陈正生,吕志平,张清华,等.基于时间序列分解的GPS卫星钟差预报[J].测绘科学,2011,36(3):116-118.(CHEN Zhengsheng,LYU Zhiping,ZHANG Qinghua et al.GPS satellite clock error prediction based on ARMA analysis[J].Science of Surveying and Mapping,2011,36(3):116-118.)
[3]HUANG Guanwen,YANG Yuanxi,ZHANG Qin.Estimate and predict satellite clock error using adaptively robust sequential adjustment with classified adaptive factors based on opening windows[J].Acta Geodaetica et Cartographica Sinica,2011,40(1):15-21.
[4]韩宝民.精密卫星钟差加密方法及其对星载GPS低轨卫星定轨精度影响[J].武汉大学学报(信息科学版),2006,31(12):1075-1078.(HAN Baomin.Densification methods of gps satellite clock errors and their impact on orbit determination precision of LEOs[J].Geomatics and Information Science of Wuhan University,2006,31(12):1075-1078.)
[5]黄观文,张勤,王继刚.GPS卫星钟差的估计与预报研究[J].大地测量与地球动力学,2009,29(6):108-122,125.(HUANG Guanwen,ZHANG Qin,WANGJigang.Research on estimation and prediction of GPSsatellite clock error[J].Journal of Geodesy and Geodynamics,2009,29(6):108-122,125.)
[6]刘晓刚,吴晓平,赵润,等.几种时间预报模型的钟差长期预报效果分析[J].测绘通报,2011(1):15-17,48.(LIU Xiaogang,WU Xiaoping,ZHAO Run,et al.Analysis of long-term clock bias forecast effects of several time prediction models[J].Bulletin of Surveying and Mapping,2011(1):15-17,48.)
[7]YUAN Haibo,WANG Zhengming,DONG Shaowu,et al.Dynamic grey-autoregressive model of an atomic clock[J].Metrologia,2008,45(6):1-5.
[8]郭承军,腾云龙.基于小波分析和神经网络的卫星钟差预报性能分析[J].天文学报,2010,51(4):396-403.(GUO Chengjun,TENG Yunlong.Performance analysis of satellite clock bias based on wavelet analysis and neural network[J].Acta Astronomica Sinica,2010,51(4):396-403.)
[9]朱祥维,肖华,雍少为,等.卫星钟差预报的Kalman算法及其性能分析[J].宇航学报,2008,29(3):966-970,1052.(ZHU Xiangwei,XIAO Hua,YONG Shaowei,et al.Kalman algorithm for satellite clock bias prediction and its performance analysis[J].Journal of Astronautics,2008,29(3):966-970,1052.)
[10]王继刚,胡永辉,何在民,等.组合模型预报导航卫星钟差[J].大地测量与地球动力学,2012,32(1):84-88.(WANG Jigang,HU Yonghui,HE Zaimin,et al.Combination models for navigation satellite clock prediction[J].Journal of Geodesy and Geodynamics,2012,32(1):84-88.)
[11]徐君毅,戴伟.一种新的长期卫星钟差预报方法[J].大地测量与地球动力学,2009,29(6):97-100.(XUJunyi,DAI Wei.A new method for long-term prediction of satellite clock error[J].Journal of Geodesy and Geodynamics,2009,29(6):97-100.)
[12]郑作亚,党亚民,卢秀山,等.附有周期项的预报模型及其在GPS卫星钟差预报中的应用研究[J].天文学报,2010,51(1):95-102.(ZHENG Zuoya,DANG Yamin,LUXiushan,et al.Prediction model of periodic item and its application to the prediction of GPS satellite clock bias[J].Acta Astronomica Sinica,2010,51(1):95-102.)
[13]帅平,曲广吉.导航星座自主导航的时间同步技术[J].宇航学报,2005,26(6):768-772.(SHUAI Ping,QUGuangji.Time synchronization techniques of the autonomous navigation of navigation constellation[J].Journal of Astronautics,2005,26(6):768-772.)
[14]崔先强,焦文海.灰色系统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),2005,30(5):447-450.(CUI Xianqiang,JIAO Wenhai.Grey system model for the satellite clock error predicting[J].Geomatics and Information Science of Wuhan University,2005,30(5):447-450.)
[15]路晓峰,杨志强,贾小林,等.灰色系统理论的优化方法及其在卫星钟差预报中的应用[J].武汉大学学报(信息科学版),2008,33(5):492-495.(LU Xiaofeng,YANG Zhiqiang,JIA Xiaolin,et al.Parameter optimization method of gray system theory for the satellite clock error predicating[J].Geomatics and Information Science of Wuhan University,2008,33(5):492-495.)
[16]徐君毅,曾安敏.ARIMA(0,2,q)模型在卫星钟差预报中的应用[J].大地测量与地球动力学,2009,29(5):116-120.(XU Junyi,ZENG Anmin.Application of ARIMA(0,2,q)model to prediction of satellite clock error[J].Journal of Geodesy and Geodynamics,2009,29(5):116-120.)
[17]路晓峰.导航卫星钟差评估与预报研究[D].西安:长安大学,2007.(LU Xiaofeng.Study on the evaluation of navigation satellite clock bias and the satellite cloek bias predieating[D].Xi’an:Chang’an University,2007.)
[18]张清华,隋立芬,牟忠凯.基于小波与ARMA模型的卫星钟差预报方法[J].大地测量与地球动力学,2010,30(6):100-104.(ZHANG Qinghua,SUI Lifen,MOUZhongkai.A GPS precise clock errors prediction model based on wavelet and ARMA[J].Journal of Geodesy and Geodynamics,2010,30(6):100-104.)