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

authored by

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.

Organisation(s)

Geodetic Institute

External Organisation(s)

Graz University of Technology

Type

Article

Journal

Reliable Computing

Volume

11

Pages

137-155

No. of pages

19

ISSN

1385-3139

Publication date

04.2005

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Software, Computational Mathematics, Applied Mathematics

Electronic version(s)

https://doi.org/10.1007/s11155-005-3034-4 (Access: Closed)