Posterior uncertainty under a class of outer measures is asymptotically normal, yielding MAP estimators and likelihood-ratio-like tests whose limits are determined by the curvature of the possibility function.
A linear algorithm for multi-target tracking in the context of possibility theory
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abstract
We present a modelling framework for multi-target tracking based on possibility theory and illustrate its ability to account for the general lack of knowledge that the target-tracking practitioner must deal with when working with real data. We also introduce and study variants of the notions of point process and intensity function, which lead to the derivation of an analogue of the probability hypothesis density (PHD) filter. The gains provided by the considered modelling framework in terms of flexibility lead to the loss of some of the abilities that the PHD filter possesses; in particular the estimation of the number of targets by integration of the intensity function. Yet, the proposed recursion displays a number of advantages such as facilitating the introduction of observation-driven birth schemes and the modelling the absence of information on the initial number of targets in the scene. The performance of the proposed approach is demonstrated on simulated data.
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2019 1verdicts
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Elements of asymptotic theory with outer probability measures
Posterior uncertainty under a class of outer measures is asymptotically normal, yielding MAP estimators and likelihood-ratio-like tests whose limits are determined by the curvature of the possibility function.