This paper presents a novel and mathematicallyrigorous Bayes’ recursion for tracking a target that generatesmultiple measurements with state dependent sensor field ofview and clutter. Our Bayesian formulation is mathematicallywell-founded due to our use of a consistent likelihood functionderived from random finite set theory. It is established that undercertain assumptions, the proposed Bayes’ recursion reduces tothe cardinalized probability hypothesis density (CPHD) recursionfor a single target. A particle implementation of the proposedrecursion is given. Under linear Gaussian and constant sensor fieldof view assumptions, an exact closed-form solution to the proposedrecursion is derived, and efficient implementations are given.Extensions of the closed-form recursion to accommodate mildnonlinearities are also given using linearization and unscentedtransforms.