The rank deficiency in estimation theory and the definition of reference systems

  • Athanasios Dermanis
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)


The concept of reference frame is examined from the viewpoint of both geophysical and geodetic applications. The concept of parameter estimability in linear models is related to the deterministic concept of determinability in linear or nonlinear improper models without full rank. The geometry of such models is investigated in its linear and nonlinear aspects with emphasis on the common invariance characteristics of observable and estimable parameters and is applied to the choice of datum problem in geodetic networks. The time evolution of the reference frame is investigated and optimal choices are presented from different equivalent points of view. The transformation of a global geodetic network into an estimate of a geocentric Tisserand frame for the whole earth is investigated and a solution is given for the rotational part. The translation to a geocentric frame poses the problem of the estimability of the geocenter coordinates and the more general problem of estimability of coefficients of an unknown function of position, having as domain the frame-dependent coordinates.


Reference frames estimable parameters earth rotation. 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Athanasios Dermanis
    • 1
  1. 1.Department of Geodesy and SurveyingThe Aristotle University of ThessalonikiGreece

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