TY - JOUR

T1 - Using Zonotopes for Overestimation-Free Interval Least-Squares - Some Geodetic Applications

AU - Schön, Steffen

AU - Kutterer, Hansjörg

N1 - Funding information: This paper shows results and new ideas developed during the research project KU 1250/1-2 at the German Geodetic Research Institute (DGFI, Munich). This project was sponsored by the Deutsche Forschungsgemeinschaft (DFG) which is gratefully acknowledged by the authors. The authors warmly thank the DGFI director Hon.-Prof. Hermann Drewes for his support as well as the whole DGFI team for their help and fruitful discussions during the authors’ stay in Munich. The constructive comments of the reviewers are gratefully acknowledged; they helped to clarify some topics and to improve the presentation.

PY - 2005/4

Y1 - 2005/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=18244397421&partnerID=8YFLogxK

U2 - 10.1007/s11155-005-3034-4

DO - 10.1007/s11155-005-3034-4

M3 - Article

AN - SCOPUS:18244397421

VL - 11

SP - 137

EP - 155

JO - Reliable Computing

JF - Reliable Computing

SN - 1385-3139

IS - 2

ER -