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A new relationship between the quality criteria for geodetic networks

  • Ivandro Klein
  • Marcelo Tomio Matsuoka
  • Matheus Pereira Guzatto
  • Felipe Geremia Nievinski
  • Mauricio Roberto Veronez
  • Vinicius Francisco Rofatto
Original Article
  • 309 Downloads

Abstract

The goal of this paper is to present a new relationship between the quality criteria for geodetic networks. The quality criteria described here are fourfold: positional uncertainty of network points, considering both bias and precision (at a given confidence level); the maximum allowable number of undetected outliers; the level of reliability and its homogeneity for the observations; and the minimum power of the data snooping test procedure for multiple alternative hypotheses. The highlights consist of the use of advanced concepts, such as reliability measures for multiple outliers and the power of the test for multiple alternative hypotheses (instead of the single outlier and/or the single alternative hypothesis case); and a sequential computational procedure, wherein the quality criteria are mathematically related, instead of being treated as separate criteria. Its practical application is demonstrated numerically in the design of a real horizontal network. A satisfactory performance was achieved by means of simulations. Furthermore, Monte Carlo experiments were conducted to verify the power of the test and the positional uncertainty following the approach proposed. Results provide empirical evidence that the quality criteria present realistic outputs.

Keywords

Quality criteria Geodetic networks design Positional uncertainty Multiple outliers Power of the test Data snooping Multiple alternative hypotheses 

Notes

Acknowledgements

The authors would like to thank the National Council for Scientific and Technological Development (CNPq) for financial support (Processes 303306/2012-2, 477914/2012-8, 305599/2015-1 and 309399/2014-9). We also like to thank the reviewers for their comments and suggestions which helped in the improvement of this paper. Finally, we dedicate this work to Professor Baarda (in memoriam) for the fifty years of Baarda (1968).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Land Surveying ProgramFederal Institute of Santa Catarina (IFSC)FlorianópolisBrazil
  2. 2.Graduate Program in Geodetic Sciences Federal University of Paraná (UFPR)CuritibaBrazil
  3. 3.Laboratory of Surveying and GeodesyFederal University of Uberlândia (UFU)Monte CarmeloBrazil
  4. 4.Graduate Program in Remote Sensing Federal University of Rio Grande do Sul (UFRGS)Porto AlegreBrazil
  5. 5.Department of GeodesyGraduate Program in Remote Sensing, Federal University of Rio Grande do Sul (UFRGS)Porto AlegreBrazil
  6. 6.Advanced Visualization Laboratory (Vizlab)Graduate Program in Applied Computing, Unisinos UniversitySão LeopoldoBrazil

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