This paper presents a general solution for computing the multi-object
posterior for sets of trajectories from a sequence of multi-object (unlabelled)
filtering densities and a multi-object dynamic model. Importantly, the proposed
solution opens an avenue of trajectory estimation possibilities for
multi-object filters that do not explicitly estimate trajectories. In this
paper, we first derive a general multi-trajectory backward smoothing equation
based on random finite sets of trajectories. Then we show how to sample sets of
trajectories using backward simulation for Poisson multi-Bernoulli filtering
densities, and develop a tractable implementation based on ranked assignment.
The performance of the resulting multi-trajectory particle smoothers is
evaluated in a simulation study, and the results demonstrate that they have
superior performance in comparison to several state-of-the-art multi-object
filters and smoothers.Comment: Accepted for publication in IEEE Transactions on Signal Processin
