Continuous-discrete trajectory PHD and CPHD filters
Ángel F. García‐Fernández, Simon R. Maskell · 2020
This paper presents the continuous-discrete trajectory probability hypothesis density (CD-TPHD) and the continuous-discrete trajectory cardinality PHD (CD-TCPHD) filter. We consider continuous-time models for target appearance, dynamics and disappearance, which are discretised to obtain the corresponding continuous-discrete models. The CD-TPHD filter propagates a Poisson point process approximation to the posterior (multi-trajectory) density over the set of alive trajectories sampled at the time instants when the measurements have been taken. The CD-TCPHD filter proceeds analogously but propagating a density on an independent and identically distributed (IID) cluster process. An important, novel feature of these filters is that they can infer the time of appearance and the state at appearance time of the trajectories in continuous time, not being constrained to discretised time steps.