  This paper presents the probability hypothesis density (PHD) filter for sets
of trajectories: the trajectory probability density (TPHD) filter. The TPHD
filter is capable of estimating trajectories in a principled way without
requiring to evaluate all measurement-to-target association hypotheses. The
TPHD filter is based on recursively obtaining the best Poisson approximation to
the multitrajectory filtering density in the sense of minimising the
Kullback-Leibler divergence. We also propose a Gaussian mixture implementation
of the TPHD recursion. Finally, we include simulation results to show the
performance of the proposed algorithm.
