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

verfasst von
Steffen Schön, Hansjörg Kutterer
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.

Organisationseinheit(en)
Geodätisches Institut
Externe Organisation(en)
Technische Universität Graz
Typ
Artikel
Journal
Reliable Computing
Band
11
Seiten
137-155
Anzahl der Seiten
19
ISSN
1385-3139
Publikationsdatum
04.2005
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Software, Computational Mathematics, Angewandte Mathematik
Elektronische Version(en)
https://doi.org/10.1007/s11155-005-3034-4 (Zugang: Geschlossen)
 

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