Scaling of the variance covariance matrix obtained from Bernese software

  • Bahattin ErdoganEmail author
  • Ali Hasan Dogan
Original Study


Global positioning system (GPS) refers positioning, timing and navigation services for different engineering applications. GPS positioning accuracies vary depending on the several parameters such as surveying method, data processing strategy and software packages. Bernese v5.2 software package is an important tool for processing and analyzing of the GPS measurements especially for the precise applications in scientific community. Although the accuracies of the estimated coordinates are sufficient, Variance–Covariance (VCV) matrices obtained from Bernese v5.2 are very optimistic because the correlations between different observables may be ignored by choosing identical weights for each measurement type in the analysis. This situation causes wrong interpretations for statistical analyses based on these VCV matrices. Therefore, the VCV matrices obtained from software should be scaled. In this study, the VCV matrices obtained from Bernese v5.2 were investigated for GPS measurements to estimate appropriate scale factor (SF) values. Baselines whose lengths ranging from 55 to 268 km and session durations between 2 and 24 h were processed with single baseline strategy for 31 consecutive days. According to the results, SF values do not depend on baseline lengths; but they vary depending on the session durations. A logarithmic function was defined for time-dependent SF values. This function has been tested in deformation analysis at the global test step and the obtained results, when the SF values are taken into account, are more reliable than the results when the unscaled VCV matrices are implemented.


Scale factor VCV matrix Bernese v5.2 GPS RMS 



We are thankful to SOPAC, IGS and CODE for the GPS data, IGS precise orbits and global ionosphere maps. Also, Figs. 1 and 4 were plotted using the Generic Mapping Tools (GMT) (Wessel and Smith 1998).


  1. Ananga N, Coleman R, Rizos C (1994) Variance-covariance estimation of GPS networks. Bull Géod 68(2):77–87CrossRefGoogle Scholar
  2. Cetin S, Aydin C, Dogan U (2018) Comparing GPS positioning errors derived from GAMIT/GLOBK and Bernese GNSS software packages: a case study in CORS-TR in Turkey. Surv Rev 22:1–11CrossRefGoogle Scholar
  3. Cooper MAR (1987) Control surveys in civil engineering. Nichols Pub Co, AsburyGoogle Scholar
  4. Dach R, Walser P (2017) Bernese GNSS Software Version 5.2: tutorial processing example—introductory course, terminal session. University of Bern, Astronomical Institute, BernGoogle Scholar
  5. Dach R, Lutz S, Walser P, Fridez P (2015) Bernese GNSS software version 5.2. University of Bern, Bern Open Publishing, BernGoogle Scholar
  6. Dogan U, Uludag M, Demir D (2014) Investigation of GPS positioning accuracy during the seasonal variation. Measurement 53:91–100CrossRefGoogle Scholar
  7. Eckl M, Snay R, Soler T, Cline M, Mader G (2001) Accuracy of GPS-derived relative positions as a function of interstation distance and observing-session duration. J Geodes 75(12):633–640CrossRefGoogle Scholar
  8. El-Rabbany A, Kleusberg A (2003) Effect of temporal physical correlation on accuracy estimation in GPS relative positioning. J Surv Eng 129(1):28–32CrossRefGoogle Scholar
  9. Geirsson H (2003) Continuous GPS measurements in Iceland 1999–2002. M.Sc, University of Iceland, ReykjavikGoogle Scholar
  10. Han S and Rizos C (1995a) Selection and scaling of simultaneous baselines for GPS network adjustment, or correct procedures for processing trivial baselines. Geomat Res Australas 63:51–66Google Scholar
  11. Han S and Rizos C (1995b) Standardisation of the variance-covariance matrix for GPS rapid static positioning. Geomat Res Australas 62:37–54Google Scholar
  12. Kashani I, Wielgosz P, Grejner-Brzezinska DA (2004) On the reliability of the VCV matrix: a case study based on GAMIT and Bernese Gps Software. GPS Solut 8(4):193–199CrossRefGoogle Scholar
  13. Koch K (1985) Ein statistisches auswerteverfahren für deformationsmessungen. Allg Vermess Nachr 92(3):97–108Google Scholar
  14. Koch K-R (2013) Parameter estimation and hypothesis testing in linear models. Springer, BerlinGoogle Scholar
  15. Li B (2016) Stochastic modeling of triple-frequency BeiDou signals: estimation, assessment and impact analysis. J Geodes 90(7):593–610CrossRefGoogle Scholar
  16. Li B, Shen Y, Xu P (2008) Assessment of stochastic models for GPS measurements with different types of receivers. Chin Sci Bull 53(20):3219–3225Google Scholar
  17. Li B, Shen Y, Lou L (2011) Efficient estimation of variance and covariance components: a case study for GPS stochastic model evaluation. IEEE Trans Geosci Remote 49(1):203–210CrossRefGoogle Scholar
  18. Li B, Lou L, Shen Y (2015) GNSS elevation-dependent stochastic modeling and its impacts on the statistic testing. J Surv Eng 142(2):04015012CrossRefGoogle Scholar
  19. Li B, Zhang L, Verhagen S (2017) Impacts of BeiDou stochastic model on reliability: overall test, w-test and minimal detectable bias. GPS Solut 21(3):1095–1112CrossRefGoogle Scholar
  20. Mao A, Harrison CG, Dixon TH (1999) Noise in GPS coordinate time series. J Geophys Res Solid Earth 104(B2):2797–2816CrossRefGoogle Scholar
  21. McClusky S, Balassanian S, Barka A, Demir C, Ergintav S, Georgiev I, Gurkan O, Hamburger M, Hurst K, Kahle H (2000) Global positioning system constraints on plate kinematics and dynamics in the eastern Mediterranean and Caucasus. J Geophys Res Solid Earth 105(B3):5695–5719CrossRefGoogle Scholar
  22. Nocquet J, Calais E and Nicolon P (2002) Reference frame activity: Combination of National (RGP) and Regional (REGAL) Permanent Networks Solutions with EUREF-EPN and the ITRF2000. In Proceedings of The EUREF 2002 Symposium, 398–404Google Scholar
  23. Pelzer H (1971) Geodatische netze in landes- und ingenieurvermessung II. Wittwer Verlag, StuttgartGoogle Scholar
  24. Pope AJ (1976) The statistics of residuals and the detection of outliers. NOAA Technical Report NOS 65 National Geodetic Survey, RockvilleGoogle Scholar
  25. Sanli DU, Engin C (2009) Accuracy of GPS positioning over regional scales. Surv Rev 41(312):192–200CrossRefGoogle Scholar
  26. Soler T, Michalak P, Weston N, Snay R, Foote R (2006) Accuracy of OPUS solutions for 1-to 4-h observing sessions. GPS Solutions 10(1):45–55CrossRefGoogle Scholar
  27. Soycan M, Ocalan T (2011) A regression study on relative GPS accuracy for different variables. Surv Rev 43(320):137–149CrossRefGoogle Scholar
  28. Tut I, Sanli D, Erdogan B, Hekimoğlu S (2013) Efficiency of BERNESE single baseline rapid static positioning solutions with search strategy. Surv Rev 45(331):296–304CrossRefGoogle Scholar
  29. Wang J, Satirapod C, Rizos C (2002) Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. J Geodes 76(2):95–104CrossRefGoogle Scholar
  30. Wessel P, Smith WH (1998) New, improved version of Generic Mapping Tools released. Eos Trans Am Geophys Union 79(47):579CrossRefGoogle Scholar
  31. Xu P, Liu Y, Shen Y, Fukuda Y (2007) Estimability analysis of variance and covariance components. J Geodes 81(9):593–602CrossRefGoogle Scholar
  32. Yang Y, Xu T, Song L (2005) Robust estimation of variance components with application in global positioning system network adjustment. J Surv Eng 131(4):107–112CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 2019

Authors and Affiliations

  1. 1.Civil Engineering Faculty, Department of Geomatic EngineeringYildiz Technical UniversityIstanbulTurkey

Personalised recommendations