Title: Identification of multi-object dynamical systems: consistency and Fisher information,
Abstract: Learning the model parameters of a multi-object dynamical system from partial
and perturbed observations is a challenging task. Despite recent numerical
advancements in learning these parameters, theoretical guarantees are extremely
scarce. In this article, we study the identifiability of these parameters and
the consistency of the corresponding maximum likelihood estimate (MLE) under
assumptions on the different components of the underlying multi-object system.
In order to understand the impact of the various sources of observation noise
on the ability to learn the model parameters, we study the asymptotic variance
of the MLE through the associated Fisher information matrix. For example, we
show that specific aspects of the multi-target tracking (MTT) problem such as
detection failures and unknown data association lead to a loss of information
which is quantified in special cases of interest.