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Analysing Time Series of GNSS Residuals by Means of AR(I)MA Processes

  • X. Luo
  • M. Mayer
  • B. Heck
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 137)

Abstract

The classical least-squares (LS) algorithm is widely applied in processing data from Global Navigation Satellite Systems (GNSS). However, some limiting factors impacting the accuracy measures of unknown parameters such as temporal correlations of observational data are neglected in most GNSS processing software products. In order to study the temporal correlation characteristics of GNSS observations, this paper introduces autoregressive (integrated) moving average (AR(I)MA) processes to analyse residual time series resulting from the LS evaluation. Based on a representative data base the influences of various factors, like baseline length, multipath effects, observation weighting, atmospheric conditions on ARIMA identification are investigated. Additionally, different temporal correlation models, for example first-order AR processes, ARMA processes, and empirically determined analytical autocorrelation functions are compared with respect to model appropriateness and efficiency.

Keywords

GNSS Stochastic model Temporal correlations Time series analysis AR(I)MA processes 

Notes

Acknowledgements

The Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) is gratefully acknowledged for supporting this research work. We also thank two anonymous reviewers for their valuable comments.

References

  1. Brockwell PJ, Davis RA (2002) Introduction to time series and forecasting, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  2. Dach R, Hugentobler U, Fridez P, Meindl M (2007) Bernese GPS Software Version 5.0. Astronomical Institute, University of Bern, BernGoogle Scholar
  3. Hannen EJ, Rissanen J (1982) Recursive estimation of mixed autoregressive moving-average order. Biometrika 69(1): 81–94CrossRefGoogle Scholar
  4. Hartung J, Elpelt B, Klösener KH (2005) Statistik: Lehr- und Handbuch der angewandten Statistik, 14th edn. Oldenbourg Wissenschaftsverlag, MunichGoogle Scholar
  5. Howind J (2005) Analyse des stochastischen Modells von GPS-Trägerphasenbeobachtungen. Deutsche Geodätische Kommission, MunichGoogle Scholar
  6. Hurvich CM, Tsai CL (1989) Regression and time series model selection in small samples. Biometrika 76(2): 297–307CrossRefGoogle Scholar
  7. Klees R, Ditmar P, Broersen P (2003) How to handle colored observation noise in large least-squares problems. J Geodesy 76(11–12):629–640CrossRefGoogle Scholar
  8. Li J, Miyashita K, Kato T, Miyazaki S (2000) GPS time series modeling by autoregressive moving average method: application to the crustal deformation in central Japan. Earth Planets Space 52(3):155–162Google Scholar
  9. Luo X, Mayer M, Heck B (2008) Improving the stochastic model of GNSS observations by means of SNR-based weighting. In: Sideris MG (ed) Observing our changing Earth. Proceedings of the 2007 IAG general assembly, 02–13 July 2007, Perugia, Italy, IAG Symposia, vol 133, pp 725–734Google Scholar
  10. Niell AE (1996) Global mapping functions for the atmosphere delay at radio wavelengths. J Geophys Res 101(B2):3227–3246Google Scholar
  11. Ragheb AE, Clarke PJ, Edwards SJ (2007) GPS sidereal filtering: coordinate- and carrier-phase-level strategies. J Geodesy 81(5):325–335CrossRefGoogle Scholar
  12. Said SE, Dickey DA (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71(3):599–607CrossRefGoogle Scholar
  13. Schön S, Brunner FK (2008) A proposal for modelling physical correlations of GPS phase observations. J Geodesy 82(10):601–612CrossRefGoogle Scholar
  14. Teusch A (2006) Einführung in die Spektral- und Zeitreihenanalyse mit Beispielen aus der Geodäsie. Deutsche Geodätische Kommission, MunichGoogle Scholar
  15. Tiberius C, Jonkman N, Kenselaar F (1999) The stochastics of GPS observables. GPS World 10(2):49–54Google Scholar
  16. Tiberius C, Kenselaar, F (2003) Variance component estimation and precise GPS positioning: case study. J Surv Eng 129(1):11–18CrossRefGoogle Scholar
  17. Wang J, Satirapod C, Rizos C (2002) Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. J Geodesy 76(2):95–104CrossRefGoogle Scholar
  18. Wheelon AD (2001) Electromagnetic scintillation: I. Geometrical optics. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Geodetic Institute, Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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