Least committed basic belief density induced by a multivariate Gaussian: Formulation with applications

Authors:
François Caron;Branko Ristic;Emmanuel Duflos;Philippe Vanheeghe
Affiliations:
LAGIS, Ecole Centrale de Lille, Cité Scientifique, BP48, 59651 Villeneuve d'Ascq Cedex, France;ISR Division, DSTO, P.O. Box 1500, Edinburgh SA 5111, Australia;LAGIS, Ecole Centrale de Lille, Cité Scientifique, BP48, 59651 Villeneuve d'Ascq Cedex, France;LAGIS, Ecole Centrale de Lille, Cité Scientifique, BP48, 59651 Villeneuve d'Ascq Cedex, France
Venue:
International Journal of Approximate Reasoning
Year:
2008

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Abstract

We consider here the case where our knowledge is partial and based on a betting density function which is n-dimensional Gaussian. The explicit formulation of the least committed basic belief density (bbd) of the multivariate Gaussian pdf is provided in the transferable belief model (TBM) framework. Beliefs are then assigned to hyperspheres and the bbd follows a @g^2 distribution. Two applications are also presented. The first one deals with model based classification in the joint speed-acceleration feature space. The second is devoted to joint target tracking and classification: the tracking part is performed using a Rao-Blackwellized particle filter, while the classification is carried out within the developed TBM scheme.