Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Geodetic Science

Editor-in-Chief: Eshagh, Mehdi

Open Access
See all formats and pricing
More options …

The effect of correlation on uncertainty estimates – with GPS examples

P. Jansson
  • Corresponding author
  • Division of Geodesy & Geoinformatics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ C.-G. Persson
  • Lantmäteriet (Swedish Mapping, Cadastral and Land Registration Authority), SE-80182 Gävle, Sweden
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-09-07 | DOI: https://doi.org/10.2478/jogs-2013-0016


This article deals with the effect of correlation on the estimates of measurement uncertainty, with some focus on Global Positioning Satellite (GPS) time series analysis. Analytical derivations and Monte Carlo simulations form the theoretical basis, which shows that uncompensated correlation produces unrealistic uncertainty estimates. Tools for handling correlation in connection with estimation of uncertainty, construction of confidence intervals, hypothesis testing, design of measurement strategies, and development of tolerances are outlined and demonstrated. The GPS observation time series used in the article has a short to medium range correlation, and can therefore be handled with the presented tools - based on a simple Location-model and stationary stochastic processes.

Keywords : correlation; least squares estimation; measurement uncertainty; Monte Carlo simulation; time series analysis

  • Amiri-Simkooei A. R. and Tiberius C. C. J. M., 2007, Assessing receiver noise using GPS short baseline time series, GPS Solutions 11, 21-35.Web of ScienceGoogle Scholar

  • Bjerhammar A., 1973, Theory of errors and generalized matrix inverses, Elsevier Scientific Publishing Company, Amsterdam, 420 pages.Google Scholar

  • Bona P., 2000, Precision, cross correlation, and time correlation of GPS phase and code observations, GPS Solutions 4, 3-13.CrossrefGoogle Scholar

  • Borre K. and Tiberius C., 2000, Time series analysis of GPS observables, In: Proceedings of The 13th International Technical Meeting of the Satellite Division of the Institute of Navigation GPS 2000, September 19-22, 2000, Salt Lake City, Utah.Google Scholar

  • Bryson A. E. and Henrikson L. J., 1967, Estimation using sampled-data containing sequentially correlated noise, Technical report no. 533, Harvard University, USA.Google Scholar

  • El Rabbany A. E-S., 1994, The effect of physical correlations on the ambiguity resolution and accuracy estimation in GPS differential positioning, Technical report no. 170, University of New Brunnswick, Canada.Google Scholar

  • Khodabandeh A., Amiri-Simkooei A. R. and Sharifi M. A., 2012, GPS position time-series analysis based on asymptotic normality of M-estimation, J. Geod. 86, 15-33.Google Scholar

  • Miller C., O’Keefe K. and Gao Y., 2010, Operational performance of RTK positioning when accounting for the time correlated nature of GNSS phase errors, ION GNSS 2010, September 21 -24, USA.Google Scholar

  • Odolinski R., 2011, Temporal correlation for network RTK positioning, GPS Solutions 16, 147-155.Web of ScienceGoogle Scholar

  • Olynik M. C., 2002, Temporal characteristics of GPS error sources and their impact on relative positioning, UCGE reports no. 20162, University of Calgary, Canada.Google Scholar

  • Persson C-G., 1981, On the estimation of variance components in linear models - with special reference to geodetic applications, Division of Geodesy, Royal Institute of Technology, Stockholm, Sweden.Google Scholar

  • Petovello M., O’Keefe K., Lachapelle G. and Cannon M., 2009, Consideration of time-correlated errors in a Kalman filter applicable to GNSS, J. Geod. 83, 1, 51-56.Web of ScienceGoogle Scholar

  • Tienstra J. M., 1947, An extension of the technique of the methods of least squares to correlated observaions, Bulletin géodésique, vol. 6, pp. 301-335.Google Scholar

  • Vollat U., Landau H. Chen X., Doucet K. and Pagels C., 2002, Network RTK versus single base RTK - understanding the error characteristics, ION GPS 2002, 24-27 September 2002, Portland, USA.Google Scholar

  • Williams S. D. P., 2003, Offsets in global positioning system time, J. Geophys. Res., 108(B6), 2310, doi:10.1029/2002JB002156, 2003.CrossrefGoogle Scholar

About the article

Published Online: 2013-09-07

Published in Print: 2013-09-01

Citation Information: Journal of Geodetic Science, Volume 3, Issue 2, Pages 111–120, ISSN (Print) 2081-9943, DOI: https://doi.org/10.2478/jogs-2013-0016.

Export Citation

This content is open access.

Comments (0)

Please log in or register to comment.
Log in