Journal of Geodesy

, Volume 83, Issue 9, pp 877–891 | Cite as

Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications

  • Markus VennebuschEmail author
  • Axel Nothnagel
  • Hansjörg Kutterer
Original Article


It is well known that high-leverage observations significantly affect the estimation of parameters. In geodetic literature, mainly redundancy numbers are used for the detection of single high-leverage observations or of single redundant observations. In this paper a further objective method for the detection of groups of important and less important (and thus redundant) observations is developed. In addition, the parameters which are predominantly affected by these groups of observations are identified. This method thus complements other diagnostics tools, such as, e.g., multiple row diagnostics methods as described in statistical literature (see, e.g., Belsley et al. in Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York, 1980). The method proposed in this paper is based on geometric aspects of adjustment theory and uses the singular value decomposition of the design matrix of an adjustment problem together with cluster analysis methods for regression diagnostics. It can be applied to any geodetic adjustment problem and can be used for the detection of (groups of) observations that significantly affect the estimated parameters or that are of negligible impact. One of the advantages of the proposed method is the improvement of the reliability of observation plans and thus the reduction of the impact of individual observations (and outliers) on the estimated parameters. This is of particular importance for the very long baseline interferometry technique which serves as an application example of the regression diagnostics tool.


Geometry of least-squares adjustment Singular value decomposition Cluster analysis Regression diagnostics Influential data Geodetic VLBI 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Markus Vennebusch
    • 1
    • 2
    Email author
  • Axel Nothnagel
    • 1
  • Hansjörg Kutterer
    • 3
  1. 1.Institute of Geodesy and Geoinformation of the University of BonnBonnGermany
  2. 2.Institut für Erdmessung, Leibniz University HannoverHannoverGermany
  3. 3.Geodetic Institute, Leibniz University HannoverHannoverGermany

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