Target tracking based on estimation of sets of trajectories

In this paper we propose the set of target trajectories as a state variable for target tracking. We argue that target tracking is fundamentally about computing the posterior distribution of the target trajectories, which all existing filtering solutions fail to produce. The new state variable enables us to solve the tracking problem in a principled and straightforward manner, without involving non-physical parameters such as an ordering or labels. We develop all the theoretical tools needed to use the set of trajectories as the state variable in a filtering framework; we adapt standard motion and measurement to random finite sets of trajectories and we also discuss general filtering recursions as well as the involved integrals. Another important component is that we present the exact filtering recursions using a conjugate family of distributions, which ensures that all future predicted and updated filtering distributions belong to the same family of distributions. The paper includes a small numerical example where we illustrate the properties of the proposed approach to trajectory estimation.