  The Bernoulli filter is a Bayes filter for joint detection and tracking of a
target in the presence of false and miss detections. This paper presents a
mathematical formulation of the Bernoulli filter in the framework of
possibility theory, where uncertainty is represented using {\em possibility}
functions, rather than {\em probability} distributions. Possibility functions
model the uncertainty in a non-additive manner, and have the capacity to deal
with partial (incomplete) problem specification. Thus, the main advantage of
the possibilistic Bernoulli filter, derived in this paper, is that it can
operate even in the absence of precise measurement and/or dynamic model
parameters. This feature of the proposed filter is demonstrated in the context
of target tracking using multi-static Doppler shifts as measurements.
