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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Brockwell PJ, Davis RA (2002) Introduction to time series and forecasting, 2nd edn. Springer, New York
Dach R, Hugentobler U, Fridez P, Meindl M (2007) Bernese GPS Software Version 5.0. Astronomical Institute, University of Bern, Bern
Hannen EJ, Rissanen J (1982) Recursive estimation of mixed autoregressive moving-average order. Biometrika 69(1): 81–94
Hartung J, Elpelt B, Klösener KH (2005) Statistik: Lehr- und Handbuch der angewandten Statistik, 14th edn. Oldenbourg Wissenschaftsverlag, Munich
Howind J (2005) Analyse des stochastischen Modells von GPS-Trägerphasenbeobachtungen. Deutsche Geodätische Kommission, Munich
Hurvich CM, Tsai CL (1989) Regression and time series model selection in small samples. Biometrika 76(2): 297–307
Klees R, Ditmar P, Broersen P (2003) How to handle colored observation noise in large least-squares problems. J Geodesy 76(11–12):629–640
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):155–162
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 725–734
Niell AE (1996) Global mapping functions for the atmosphere delay at radio wavelengths. J Geophys Res 101(B2):3227–3246
Ragheb AE, Clarke PJ, Edwards SJ (2007) GPS sidereal filtering: coordinate- and carrier-phase-level strategies. J Geodesy 81(5):325–335
Said SE, Dickey DA (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71(3):599–607
Schön S, Brunner FK (2008) A proposal for modelling physical correlations of GPS phase observations. J Geodesy 82(10):601–612
Teusch A (2006) Einführung in die Spektral- und Zeitreihenanalyse mit Beispielen aus der Geodäsie. Deutsche Geodätische Kommission, Munich
Tiberius C, Jonkman N, Kenselaar F (1999) The stochastics of GPS observables. GPS World 10(2):49–54
Tiberius C, Kenselaar, F (2003) Variance component estimation and precise GPS positioning: case study. J Surv Eng 129(1):11–18
Wang J, Satirapod C, Rizos C (2002) Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. J Geodesy 76(2):95–104
Wheelon AD (2001) Electromagnetic scintillation: I. Geometrical optics. Cambridge University Press, Cambridge
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Luo, X., Mayer, M., Heck, B. (2012). Analysing Time Series of GNSS Residuals by Means of AR(I)MA Processes. In: Sneeuw, N., Novák, P., Crespi, M., Sansò, F. (eds) VII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22078-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-22078-4_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22077-7
Online ISBN: 978-3-642-22078-4
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)