Journal of Geodesy

, Volume 91, Issue 6, pp 627–652 | Cite as

Rank defect analysis and the realization of proper singularity in normal equations of geodetic networks

Original Article
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Abstract

The singularity of input normal equations (NEQ) is a crucial element for their optimal handling in the context of terrestrial reference frame (TRF) estimation under the minimal-constraint framework. However, this element is often missing in the recovered NEQ from SINEX files after the usual deconstraining based on the stated information for the stored solutions. The same setback also occurs with the original NEQ that are formed by the least-squares processing of space geodetic data due to the datum information which is carried by various modeling choices and/or software-dependent procedures. In the absence of this datum-related singularity, it is not possible to obtain genuine minimally constrained solutions because of the interference between the input NEQ’s content and the external datum conditions, a fact that may alter the geometrical information of the original measurements and can cause unwanted distortions in the estimated solution. The main goal of this paper is the formulation of a filtering scheme to enforce the proper (or desired) singularity in the input NEQ with regard to datum parameters that will be handled by the minimal-constraint setting in TRF estimation problems. The importance of this task is extensively discussed and justified with the help of several numerical examples in different GNSS networks.

Keywords

NEQ Rank defect Minimal constraints TRF estimation Frame distortion Position time series 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Geodesy and SurveyingAristotle University of ThessalonikiThessalonikiGreece
  2. 2.GNSS Research GroupRoyal Observatory of BelgiumBrusselsBelgium

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