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

Using Zonotopes for Overestimation-Free Interval Least-Squares–Some Geodetic Applications 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

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

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2005 by Springer Science + Business Media, Inc.
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-005-3034-4
Publisher site
See Article on Publisher Site

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.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2005

References

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