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An ellipsoidal calculus based on propagation and fusion

AuthorsRos, Lluís ; Sabater, Assumpta; Thomas, Federico
KeywordsEllipsoidal bounds
Ellipsoidal calculus
Set-membership uncertainty description
Issue Date2002
PublisherInstitute of Electrical and Electronics Engineers
CitationIEEE Transactions on Systems, Man and Cybernetics: Part B 32(4): 430-442 (2002)
AbstractPresents an ellipsoidal calculus based solely on two basic operations: propagation and fusion. Propagation refers to the problem of obtaining an ellipsoid that must satisfy an affine relation with another ellipsoid, and fusion to that of computing the ellipsoid that tightly bounds the intersection of two given ellipsoids. These two operations supersede the Minkowski sum and difference, affine transformation and intersection tight bounding of ellipsoids on which other ellipsoidal calculi are based. Actually, a Minkowski operation can be seen as a fusion followed by a propagation and an affine transformation as a particular case of propagation. Moreover, the presented formulation is numerically stable in the sense that it is immune to degeneracies of the involved ellipsoids and/or affine relations. Examples arising when manipulating uncertain geometric information in the context of the spatial interpretation of line drawings are extensively used as a testbed for the presented calculus.
Publisher version (URL)http://dx.doi.org/10.1109/TSMCB.2002.1018763
Appears in Collections:(IRII) Artículos
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