Using Zonotopes for Overestimation-Free Interval Least-Squares - Some Geodetic Applications

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Steffen Schön
  • Hansjörg Kutterer

Research Organisations

External Research Organisations

  • Graz University of Technology
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Details

Original languageEnglish
Pages (from-to)137-155
Number of pages19
JournalReliable Computing
Volume11
Issue number2
Publication statusPublished - Apr 2005

Abstract

Interval methods are very convenient to describe the uncertainty of measurements and derived parameters in engineering sciences. In this paper, the geodetic determination of points in the 2d or 3d Euclidean space by least-squares estimation is studied. Up to now, two problems limited the applicability of interval mathematics. First, due to overestimation, interval boxes are too pessimistic uncertainty measures for point positions. Second, the shape of the interval boxes depends on the orientation of the geodetic coordinate system to parametrise the configuration. It is shown that both problems can be overcome by zonotopes which describe directly the factual range of the leastsquares problem with interval-valued observations. The advantages of this concept are discussed using typical geodetic network scenarios. In addition, the possible benefit for other engineering applications is motivated.

ASJC Scopus subject areas

Cite this

Using Zonotopes for Overestimation-Free Interval Least-Squares - Some Geodetic Applications. / Schön, Steffen; Kutterer, Hansjörg.
In: Reliable Computing, Vol. 11, No. 2, 04.2005, p. 137-155.

Research output: Contribution to journal › Article › Research › peer review

Schön S, Kutterer H. Using Zonotopes for Overestimation-Free Interval Least-Squares - Some Geodetic Applications. Reliable Computing. 2005 Apr;11(2):137-155. doi: 10.1007/s11155-005-3034-4
Schön, Steffen ; Kutterer, Hansjörg. / Using Zonotopes for Overestimation-Free Interval Least-Squares - Some Geodetic Applications. In: Reliable Computing. 2005 ; Vol. 11, No. 2. pp. 137-155.
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abstract = "Interval methods are very convenient to describe the uncertainty of measurements and derived parameters in engineering sciences. In this paper, the geodetic determination of points in the 2d or 3d Euclidean space by least-squares estimation is studied. Up to now, two problems limited the applicability of interval mathematics. First, due to overestimation, interval boxes are too pessimistic uncertainty measures for point positions. Second, the shape of the interval boxes depends on the orientation of the geodetic coordinate system to parametrise the configuration. It is shown that both problems can be overcome by zonotopes which describe directly the factual range of the leastsquares problem with interval-valued observations. The advantages of this concept are discussed using typical geodetic network scenarios. In addition, the possible benefit for other engineering applications is motivated.",
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