Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications |
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| Authors: | Markus Vennebusch Axel Nothnagel Hansjörg Kutterer |
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| Institution: | (1) Institute of Geodesy and Geoinformation of the University of Bonn, Nussallee 17, 53115 Bonn, Germany;(2) Present address: Institut für Erdmessung, Leibniz University Hannover, Schneiderberg 50, 30167 Hannover, Germany;(3) Geodetic Institute, Leibniz University Hannover, Nienburger Strasse 1, 30167 Hannover, Germany |
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| Abstract: | 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. |
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| Keywords: | Geometry of least-squares adjustment Singular value decomposition Cluster analysis Regression diagnostics Influential data Geodetic VLBI |
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