Possibilistic Bernoulli Filter for Extended Target Tracking

An extended object in target tracking refers to the object which produces a time-varying number of noisy detections (measurements) from its scattering or feature points. The optimal sequential Bayesian state estimator for an appearing/disappearing extended object in the presence of false and missed detections is known as the Bernoulli Filter Ext (BF-X). Bayesian estimation methods rely on probabilistic models. When probabilistic models are known only partially or imprecisely, quantitative modeling of uncertainty can be carried out using possibility functions. This paper formulates the analog of the BF-X in the framework of possibility theory, where uncertainty is represented using possibility functions, rather than usual probability distributions. Possibility functions have the capacity to model with integrity the partial or imprecise probabilistic specifications and thus the proposed possibilistic BF-X is characterised by an enhanced robustness in the absence of precise measurement or dynamic models.