  The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture
(MBM) are two multi-target distributions for which closed-form filtering
recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a
multi-Bernoulli birth process. This paper considers a recently developed
formulation of the multi-target tracking problem using a random finite set of
trajectories, through which the track continuity is explicitly established. A
multi-scan trajectory PMBM filter and a multi-scan trajectory MBM filter, with
the ability to correct past data association decisions to improve current
decisions, are presented. In addition, a multi-scan trajectory
$\text{MBM}_{01}$ filter, in which the existence probabilities of all Bernoulli
components are either 0 or 1, is presented. This paper proposes an efficient
implementation that performs track-oriented $N$-scan pruning to limit
computational complexity, and uses dual decomposition to solve the involved
multi-frame assignment problem. The performance of the presented multi-target
trackers, applied with an efficient fixed-lag smoothing method, are evaluated
in a simulation study.
