Abstract
The precise satellite clock bias prediction is critical in improving the positioning, navigation and timing (PNT) service capabilities of the global navigation satellite system (GNSS). Due to the influence of satellite signal path and the observation environment, the satellite clock bias data usually contain outliers that heavily affect the accuracy of satellite clock bias prediction. Based on the time series ARMA model and Bayes statistical theory, we propose a method to precisely predict satellite clock bias and detect outliers in the historical sequence of satellite clock bias. At first, considering the effects of an additive outlier (AO) and innovative outlier (IO), a labeling model for robustly fitting the time series ARMA model and detecting AOs and IOs simultaneously is constructed based on the labeling method of classification variables. Second, the Bayes method for robustly fitting time series ARMA model is proposed based on the Bayes statistical theory. Furthermore, it develops an algorithm to precisely predict satellite clock bias using the Bayes method for robustly fitting the time series ARMA model mentioned above. Finally, in order to illustrate the performance of the method for precisely predicting satellite clock bias that we presented, three examples are designed based on the real GPS data come from the IGS official website, and the prediction results of the method are compared with that of original ARMA model (oARMA), quadratic polynomial model (QP) and gray model (GM). It is found that the method can precisely predict the satellite clock bias as well as accurately detect the outliers in the historical sequence.
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Data availability
The experimental data in the manuscript are all public data and can be downloaded from the IGS Web site (ftp://igs.gnsswhu.cn/pub/gps/products).
References
Bell WR (2012) Economic time series: modeling and seasonality. Chapman & Hall, Boca Raton
Berger JO (2010) Statistical decision theory and Bayesian analysis. Springer, New York
Chen L, Geng C, Zhou Q (2016) Estimation model and accuracy analysis of BeiDou/GPS real-time precise satellite clock error integrated resolving. Acta Geod Cartogr Sin 45(9):1028–1034
Chopin N, Singh SS (2015) On particle Gibbs sampling. Bernoulli 21(3):1855–1883
Cryer JD, Chan KS (2008) Time series analysis: with applications in R. Springer, Berlin
Fox AJ (1972) Outliers in time series. J Roy Stat Soc 34(3):350–363
Han S, Kwon J, Jekeli C (2001) Accurate absolute GPS positioning through satellite clock error estimation. J Geodesy 75(1):33–43
Huang G, Cui B, Zhang Q, Fu W, Li P (2018) An improved predicted model for BDS ultra-rapid satellite clock offsets. Remote Sens. https://doi.org/10.3390/rs10010060
Huang G, Zhang Q (2012) Real-time estimation of satellite clock offset using adaptively robust Kalman filter with classified adaptive factors. GPS Solutions 16(1):531–539
Huang G, Zhang Q, Xu G (2014) Real-time clock offset prediction with an improved model. GPS Solutions 18(1):95–104
Han S, Zhang G, Zhang N, Zhu J (2019) New algorithm for detecting AO outliers in AR model and its application in the prediction of GPS satellite clock errors. Acta Geod Cartogr Sin 48(10):1225–1235
Kim J, Kim M (2015) ARMA prediction of SBAS ephemeris and clock corrections for low earth orbiting satellites. Int J Aerosp Eng. https://doi.org/10.1155/2015/165178
Leonhard H, Daniel SB (2014) Applied statistical inference: likelihood and Bayes. Springer, Berlin
Li H, Liao X, Li B, Yang L (2018) Modeling of the GPS satellite clock error and its performance evaluation in precise point positioning. Adv Space Res 62(4):845–854
Lu J, Shi L, Chen F (2012) Outlier detection in time series models using local influence method. Commun Stat Theory Methods 41(12):2202–2220
Ma C, Zhu J, Han S (2020) Model selection method based on ARIMA model in outliers detection of satellite clock offset. Geomat Inf Sci Wuhan Univ 45(2):167–172
Norma L, Stephen BV, Garritt LP, Joanne RW (2013) Bayes statistical analyses for particle sieving studies. Technometrics 55(2):224–231
Rodrigues GS, Nott DJ, Sisson SA (2020) Likelihood-free approximate Gibbs sampling. Stat Comput 30(4):1057–1073
Shi J, Xu C, Li Y, Gao Y (2015) Impacts of real-time satellite clock errors on GPS precise point positioning-based troposphere zenith delay estimation. J Geodesy 89(8):747–756
Silva ME, Pereira I, McCabe B (2019) Bayesian outlier detection in non-Gaussian autoregressive time series. J Time Ser Anal 40(5):631–648
Wang D, Guo R, Xiao S, Xin J, Tang T, Yuan Y (2019) Atomic clock performance and combined clock error prediction for the new generation of BeiDou navigation satellites. Adv Space Res 63(9):2889–2898
Wang D, Guo R, Xie J, Hu X, Yuan Y (2018a) Combined clock error prediction model and accuracy evaluation of BeiDou new generation navigation satellite. Acta Geod Cartogr Sin 47(S0):61–70
Wang S, Yang F, Gao W, Yan L, Ge Y (2018b) A new stochastic model considering satellite clock interpolation errors in precise point positioning. Adv Space Res 61(5):1332–1341
Wang X, Chai H, Wang C (2020) A high-precision short-term prediction method with stable performance for satellite clock bias. GPS Solutions. https://doi.org/10.1007/s10291-020-01019-5
Wang Y, Lu Z, Qu Y, Li L, Wang N (2017) Improving prediction performance of GPS satellite clock bias based on wavelet neural network. GPS Solutions 21(2):523–534
Yu Y, Huang M, Duan T, Wang C, Hu R (2020a) Enhancing satellite clock bias prediction accuracy in the case of jumps with an improved grey model. Math Probl Eng. https://doi.org/10.1155/2020/8186568
Yu Y, Huang M, Wang C, Hu R, Duan T (2020b) A new BDS-2 satellite clock bias prediction algorithm with an improved exponential smoothing method. Appl Sci Basel. https://doi.org/10.3390/app10217456
Zhang Q, Gui Q (2013) Bayesian methods for outliers detection in GNSS time series. J Geodesy 87(7):609–627
Acknowledgements
This research was supported jointly by The National Natural Science Foundation of China (41774038, 41474009), Information Engineering University Double Important Construction Project: Research on the outlier of BDS satellite clock error based on time series model.
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Zhang, G., Han, S., Ye, J. et al. A method for precisely predicting satellite clock bias based on robust fitting of ARMA models. GPS Solut 26, 3 (2022). https://doi.org/10.1007/s10291-021-01182-3
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DOI: https://doi.org/10.1007/s10291-021-01182-3