  A novel solution to the smoothing problem for multi-object dynamical systems
is proposed and evaluated. The systems of interest contain an unknown and
varying number of dynamical objects that are partially observed under noisy and
corrupted observations. An alternative representation of uncertainty is
considered in order to account for the lack of information about the different
aspects of this type of complex system. The corresponding statistical model can
be formulated as a hierarchical model consisting of conditionally-independent
hidden Markov models. This particular structure is leveraged to propose an
efficient method in the context of Markov chain Monte Carlo (MCMC) by relying
on an approximate solution to the corresponding filtering problem, in a similar
fashion to particle MCMC. This approach is shown to outperform existing
algorithms in a range of scenarios.
