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Deformation Detection According to a Bayesian Approach

  • B. Betti
  • F. Sansò
  • M. Crespi
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 122)

Abstract

Sometimes, when we deal with deformations monitoring, the estimated displacements in repeated surveys are small with respect to the measurement precisions; therefore, they are not significant according to the classical testing procedure. Nevertheless, even at a first glance, these data seem to show a correlation pattern: for instance, we can have all sinking benchmarks along a control leveling line. In these cases it seems reasonable to make the hypothesis that the displacements are due to a real slow deformation.

Therefore, our main goal was to understand how it is possible to use this correlation pattern in order to increase the power of the test. The proposed solution consists in formulating the testing procedure in the frame of the Bayesian theory, which allows to incorporate the correlation pattern into the prior distribution of the parameters.

We derived the Bayesian test statistics both for the cases with known and unknown variance of unit weight. Moreover we applied the proposed approach to an elementary through realistic example obtaining encouraging results.

Keywords

Probability Density Function Bayesian Approach Correlation Pattern Ambiguity Resolution Classical Testing Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Betti, B., Crespi, M., and Sansò, F. (1993). A geometric illustration of ambiguity resolution in GPS theory and a Bayesian approach. Manuscripta Geodaetica, 18(6):317–330.Google Scholar
  2. Koch, K.R. (1988). Parameter estimation and hypothesis testing in linear models. Springer, Berlin Heidelberg New York Tokyo.Google Scholar
  3. Koch, K.R. (1990). Bayesian Inference with Geodetic Applications. Number 31 in Lecture Notes in Earth Sciences. Springer, Berlin Heidelberg New York.Google Scholar
  4. Selby, S.M. (1973). Standard Mathematical Tables. 21th Edition. The Chemical Rubber Company, Cleveland.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • B. Betti
    • 1
  • F. Sansò
    • 1
  • M. Crespi
    • 2
  1. 1.DIIARPolitecnico di MilanoItaly
  2. 2.DITSUniv. di Roma ”La Sapienza”Italy

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