Bernoulli Filter for Extended Target Tracking in the Framework of Possibility Theory

Extended objects give rise to a varying number of noisy measurements from its reflection (scattering or feature) points. Due to imperfect detection, only some of the feature points are detected in each scan of input data, while false alarms can also be present. The optimal sequential Bayesian state estimator in the framework of random set theory is the Bernoulli filter for an extended target (BF-X). In this article, we formulate and derive the analog of the BF-X in the framework of possibility theory, where uncertainty is represented using possibility functions, rather than probability distributions. Possibility functions have the capacity to model partial (imprecise) probabilistic specifications, and thus, the main advantage of the proposed possibilistic BF-X is enhanced robustness in the absence of precise measurements or dynamic models.