New algorithm for detecting AO outliers in AR model and its application in the prediction of GPS satellite clock errors

doi:10.11947/j.AGCS.2019.20180271

Abstract

Abstract: Based on the EM algorithm, an algorithm for detecting additive outlier in an autoregressive (AR) time series is proposed. The algorithm can fit the AR model and detect the additive outlier at the same time, and it can efficiently prevent the occurrence of masking and swamping.At last, the proposed algorithm is applied to process the data of GPS satellite clock error prediction. The examples verify the effectiveness of the algorithm in detecting the additive outlier and predicting the satellite clock error.

Key words: autoregressive model, EM algorithm, AO outlier, satellite clock error

CLC Number:

P228

HAN Songhui, ZHANG Guochao, ZHANG Ning, ZHU Jianqing. New algorithm for detecting AO outliers in AR model and its application in the prediction of GPS satellite clock errors[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(10): 1225-1235.

References 37

[1]	LI Xiaoyu, DONG Xurong, ZHENG Kun, et al. Research of satellite clock error prediction based on RBF neural network and ARMA model[C]//Proceedings of 2013 China Satellite Navigation Conference (CSNC). Berlin:Springer, 2013:325-334.
[2]	KIM J, KIM M. ARMA prediction of SBAS ephemeris and clock corrections for low earth orbiting satellites[J]. International Journal of Aerospace Engineering, 2015(3):268-275.
[3]	郭海荣, 杨生, 杨元喜, 等. 基于卫星双向时间频率传递进行钟差预报的方法研究[J]. 武汉大学学报(信息科学版), 2007, 32(1):43-46. GUO Hairong, YANG Sheng, YANG Yuanxi, et al. Numerical prediction methods for clock difference based on two-way satellite time and frequency transfer data[J]. Geomatics and Information Science of Wuhan University, 2007, 32(1):43-46.
[4]	王宇谱, 李博, 白文乾, 等. 导航卫星钟差预报研究综述[C]//第九届中国卫星导航学术年会论文集. 哈尔滨:中国卫星导航学术年会组委会, 2018. WANG Yupu, LI Bo, BAI Wenqian, et al. A review of navigation satellite clock bias prediction[C]//Proceedings of the China Satellite Navigation Conference (CSNC). Harbin:Organizing Committee of China Satellite Navigation Academic Annual Conference, 2018.
[5]	WINKLER G M R. Introduction to robust statistics and data filtering[J/OL].(1998-10-08)[2017-11-24]. http://www.wriley.com/ROBSTAT.htm.
[6]	王宇谱, 吕志平, 王宁, 等. 顾及卫星钟随机特性的抗差最小二乘配置钟差预报算法[J]. 测绘学报, 2016, 45(6):646-655. DOI:10.11947/j.AGCS.2016.20150569. WANG Yupu, LÜ Zhiping, WANG Ning, et al. Prediction of navigation satellite clock bias considering clock's stochastic variation behavior with robust least square collocation[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(6):646-655. DOI:10.11947/j.AGCS.2016.20150569.
[7]	RILEY W J. Frequency jump detection and analysis[C]//Proceedings of the 40th Annual PTTI Meeting. Reston, Virginia, USA:Curran Associates, Inc., 2008.
[8]	牛飞, 韩春好, 张义生, 等. 导航卫星星载原子钟异常监测分析[J]. 武汉大学学报(信息科学版), 2009, 34(5):585-588. NIU Fei, HAN Chunhao, ZHANG Yisheng, et al. Analysis and detection on atomic clock anomaly of navigation satellites[J]. Geomatics and Information Science of Wuhan University, 2009, 34(5):585-588.
[9]	HUANG Guanwen, ZHANG Qin. Real-time estimation of satellite clock offset using adaptively robust Kalman filter with classified adaptive factors[J]. GPS Solutions, 2012, 16(4):531-539.
[10]	ZHANG Guochao, GUI Qingming, HAN Songhui, et al. A Bayesian method of GNSS cycle slips detection based on ARMA model[C]//Proceedings of 2017 Forum on Cooperative Positioning and Service. Harbin:IEEE, 2017:219-222.
[11]	ABRAHAM B, BOX G E P. Bayesian analysis of some outlier problems in time series[J]. Biometrika, 1979, 66(2):229-236.
[12]	TSAY R S. Time series model specification in the presence of outliers[J]. Journal of the American Statistical Association, 1986, 81(393):132-141.
[13]	归庆明, 李涛, 衡广辉. 时间序列异常值探测的Bayes方法及其在电离层VTEC数据处理中的应用[J]. 武汉大学学报(信息科学版), 2011, 36(7):802-806. GUI Qingming, LI Tao, HENG Guanghui. Bayesian methods for time series outliers detection and applications in ionospheric VTEC data processing[J]. Geomatics and Information Science of Wuhan University, 2011, 36(7):802-806.
[14]	LOUNI H. Outlier detection in ARMA models[J]. Journal of Time Series Analysis, 2008, 29(6):1057-1065.
[15]	BENKABOU S E, BENABDESLEM K, CANITIA B. Unsupervised outlier detection for time series by entropy and dynamic time warping[J]. Knowledge and Information Systems, 2018, 54(2):463-486.
[16]	李涛, 衡广辉, 归庆明. AR序列异常值探测的Bayes方法在卫星钟差预报中的应用[J]. 全球定位系统, 2010, 35(4):15-20, 30. LI Tao, HENG Guanghui, GUI Qingming. The application of Bayesian method in autoregressive model outliers detecting of satellite clock error prediction[J]. CNSS World of China, 2010, 35(4):15-20, 30.
[17]	牛飞, 韩春好, 张义生, 等. 基于星间链路支持的导航卫星自主完好性监测设计仿真[J]. 测绘学报, 2011, 40(S1):73-79. NIU Fei, HAN Chunhao, ZHANG Yisheng, et al. Design and simulation for satellite autonomous integrity monitoring based on inter-satellite-links[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(S1):73-79.
[18]	黄观文. GNSS星载原子钟质量评价及精密钟差算法研究[D]. 西安:长安大学, 2012. HUANG Guanwen. Research on algorithms of precise clock offset and quality evaluation of GNSS satellite clock[D]. Xi'an:Chang'an University, 2012.
[19]	ZHANG Qianqian, GUI Qingming. Bayesian methods for outliers detection in GNSS time series[J]. Journal of Geodesy, 2013, 87(7):609-627.
[20]	DEMPSTER A P, LAIRD N M, RUBIN D B. Maximum likelihood from incomplete data via the EM algorithm[J]. Journal of the Royal Statistical Society. Series B (Methodological), 1977, 39(1):1-38.
[21]	BENNIS S, BERRADA F, KANG N. Improving single-variable and multivariable techniques for estimating missing hydrological data[J]. Journal of Hydrology, 1997, 191(1-4):87-105.
[22]	SEN P K. Robust nonparametrics in mixed-MANOCOVA models[J]. Journal of Statistical Planning and Inference, 1999, 75(2):433-451.
[23]	CHUNG P J, BÖHME J F. DOA estimation using fast EM and SAGE algorithms[J]. Signal Processing, 2002, 82(11):1753-1762.
[24]	BOOTH J G, CAFFO B S. Unequal sampling for Monte Carlo EM algorithms[J]. Computational Statistics & Data Analysis, 2002, 39(3):261-270.
[25]	骆剑承, 王钦敏, 马江洪, 等. 遥感图像最大似然分类方法的EM改进算法[J]. 测绘学报, 2002, 31(3):234-239. LUO Jiancheng, WANG Qinmin, MA Jianghong, et al. The EM-based maximum likelihood classifier for remotely sensed data[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(3):234-239.
[26]	杨健辉. 侧压下混凝土静态受拉与受拉疲劳性能研究[D]. 大连:大连理工大学, 2003. YANG Jianhui. Study on static and fatigue behaviors in tension for concrete under lateral pressures[D]. Dalian:Dalian University of Technology, 2003.
[27]	王红军, 田铮, 韩四儿. 混合自回归滑动平均模型——MARMA[J]. 系统工程理论与实践, 2006, 26(11):108-115. WANG Hongjun, TIAN Zheng, HAN Si'er. Mixture autoregressive moving average model[J]. Systems Engineering:Theory & Practice, 2006, 26(11):108-115.
[28]	SAMÉ A, CHAMROUKHI F, GOVAERT G, et al. Model-based clustering and segmentation of time series with changes in regime[J]. Advances in Data Analysis and Classification, 2011, 5(4):301-321.
[29]	WANG Zidong, EATOCK J, MCCLEAN S, et al. Modeling throughput of emergency departments via time series:an expectation maximization algorithm[J]. ACM Transactions on Management Information Systems, 2013, 4(4):16.
[30]	马传宁, 蔡伟, 关沧海, 等. EM算法的时序模型在沉降数据处理中的应用[J]. 测绘科学, 2017, 42(12):178-184. MA Chuanning, CAI Wei, GUAN Canghai, et al. Application of time series model of EM algorithm in settlement data processing[J]. Science of Surveying and Mapping, 2017, 42(12):178-184.
[31]	KHOO W C, ONG S H, BISWAS A. Modeling time series of counts with a new class of INAR(1) model[J]. Statistical Papers, 2017, 58(2):393-416.
[32]	陈轲, 归庆明, 柳丽, 等. Gauss-Markov模型的t型抗差估计[J]. 测绘学报, 2008, 37(3):280-284, 292. CHEN Ke, GUI Qingming, LIU Li, et al. Robust t-type estimation in Gauss-Markov model[J]. Acta Geodaetica et Cartographica Sinica, 2008, 37(3):280-284, 292.
[33]	孙同贺, 高磊. 线性EIV模型的t型估计[J]. 大地测量与地球动力学, 2016, 36(3):261-264. SUN Tonghe, GAO Lei. t-type estimation in the linear errors-in-variables model[J]. Journal of Geodesy and Geodynamics, 2016, 36(3):261-264.
[34]	YAN Ming. Image and signal processing with non-Gaussian noise:EM-type algorithms and adaptive outlier pursuit[D]. Los Angeles:University of California, 2012.
[35]	KOCH K R. Expectation maximization algorithm and its minimal detectable outliers[J]. Studia Geophysica et Geodaetica, 2017, 61(1):1-18.
[36]	高惠璇. 统计计算[M]. 北京:北京大学出版社, 1995:392-393. GAO Huixuan. Statistical computation[M]. Beijing:Peking University Press, 1995:392-393.
[37]	CHEN C, LIU L M. Joint estimation of model parameters and outlier effects in time series[J]. Journal of the American Statistical Association, 1993, 88(421):284-297.