Multiple target tracking based on sets of trajectories

This paper proposes the set of target trajectories as the state variable for multiple target tracking. The main objective of multiple target tracking is to estimate an unknown number of target trajectories given a sequence of measurements. This quantity of interest is perfectly represented as a set of trajectories without the need of arbitrary parameters such as labels or ordering. We use finite-set statistics to pose this problem in the Bayesian framework and formulate a state space model where the random state is a random finite set that contains trajectories. All information of interest is thus contained in the multitrajectory filtering probability density function (PDF), which represents the multitrajectory PDF of the set of trajectories given the measurements. For the standard measurement and dynamic models, we describe a family of PDFs that is conjugate in the sense that the multitrajectory filtering PDF remains within that family during both the prediction and update steps.