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Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris

CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

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Volume 3, Issue 2


Uncertainty modeling of random and systematic errors by means of Monte Carlo and fuzzy techniques

Hamza Alkhatib
  • Geodetic Institute, Leibniz University of Hannover, Nienburger Str. 1, 30167 Hannover, Germany. E-mail:
  • Other articles by this author:
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/ Ingo Neumann
  • Institute of Geodesy—Geodetic Lab, University FAF Munich, Werner Heisenberg Weg 39, 85579 Neubiberg, Germany
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/ Hansjörg Kutterer
  • Geodetic Institute, Leibniz University of Hannover, Nienburger Str. 1, 30167 Hannover, Germany
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Published Online: 2009-06-15 | DOI: https://doi.org/10.1515/JAG.2009.008


The standard reference in uncertainty modeling is the “Guide to the Expression of Uncertainty in Measurement (GUM)”. GUM groups the occurring uncertain quantities into “Type A” and “Type B”. Uncertainties of “Type A” are determined with the classical statistical methods, while “Type B” is subject to other uncertainties which are obtained by experience and knowledge about an instrument or a measurement process. Both types of uncertainty can have random and systematic error components. Our study focuses on a detailed comparison of probability and fuzzy-random approaches for handling and propagating the different uncertainties, especially those of “Type B”. Whereas a probabilistic approach treats all uncertainties as having a random nature, the fuzzy technique distinguishes between random and deterministic errors. In the fuzzy-random approach the random components are modeled in a stochastic framework, and the deterministic uncertainties are treated by means of a range-of-values search problem. The applied procedure is outlined showing both the theory and a numerical example for the evaluation of uncertainties in an application for terrestrial laserscanning (TLS).

Keywords.: GUM; Monte Carlo methods; fuzzy methods

About the article

Received: 2009-01-02

Accepted: 2009-03-05

Published Online: 2009-06-15

Published in Print: 2009-06-01

Citation Information: Journal of Applied Geodesy, Volume 3, Issue 2, Pages 67–79, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/JAG.2009.008.

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