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

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.

[1]  Didier Dubois,et al.  The principle of minimum specificity as a basis for evidential reasoning , 1986, IPMU.

[2]  Philippe Smets,et al.  The Transferable Belief Model , 1991, Artif. Intell..

[3]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[4]  N. D. Freitas.  Rao-Blackwellised particle filtering for fault diagnosis , 2002 .

[5]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[6]  Branko Ristic,et al.  Kalman filter and joint tracking and classification based on belief functions in the TBM framework , 2007, Inf. Fusion.

[7]  Jun S. Liu,et al.  Mixture Kalman filters , 2000 .

[8]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[9]  P. Smets,et al.  Target classification approach based on the belief function theory , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[10]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[11]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[12]  Philippe Smets,et al.  Belief functions on real numbers , 2005, Int. J. Approx. Reason..

[13]  N. de Freitas.  Rao-Blackwellised particle filtering for fault diagnosis , 2002, Proceedings, IEEE Aerospace Conference.

[14]  G. Nason,et al.  A statistical multiscale approach to image segmentation and fusion , 2005, 2005 7th International Conference on Information Fusion.

[15]  Arnaud Doucet,et al.  Particle filters for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[16]  Dsto PO Box,et al.  Belief function theory on the continuous space with an application to model based classification , 2006 .

[17]  P. Vanheeghe,et al.  Multisensor data fusion in the frame of the TBM on reals. Application to land vehicle positioning , 2005, 2005 7th International Conference on Information Fusion.

[18]  Philippe Smets,et al.  Target identification based on the transferable belief model interpretation of dempster-shafer model , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[19]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[20]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[21]  Philippe Smets,et al.  Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem , 1993, Int. J. Approx. Reason..

[22]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[23]  Branko Ristic,et al.  On target classification using kinematic data , 2004, Inf. Fusion.

[24]  Didier Dubois,et al.  New Semantics for Quantitative Possibility Theory , 2001, ECSQARU.