Different equivalent approaches to the geodetic reference system

  • Athanasios Dermanis
  • Fernando SansòEmail author
Satellite Positioning for Geosciences


A new approach to the determination of least-squares solutions for the rank deficient model is presented, which, in place of the classical minimal constraints, utilizes the expression of the excess parameters as a function of a subset of unknown parameters describing the model without ambiguities. The role of the lack of reference system definition in the resulting rank deficiency is explained, first for the original non-linear model case, and is specialized next to the linearized model. The whole set of solutions is parameterized in terms of two matrices defining the linearized relation from the model describing parameters to the remaining ones. Particular values are obtained for the case of solution with minimal trace of its covariance matrix, as well for the solution for minimum norm. Finally, the connection with the existing classical approach is established, while the approach is further elaborated in terms of the full-rank decompositions of the model design matrix.


Geodetic reference system Rank deficient model Least-squares solutions New approach 


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Copyright information

© Accademia Nazionale dei Lincei 2017

Authors and Affiliations

  1. 1.Aristotle University ThessalonikiThessalonikiGreece
  2. 2.Politecnico di MilanoMilanItaly

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