Trajectory PHD and CPHD filters
Journal article, 2019

This paper presents the probability hypothesis density filter (PHD) and the cardinality PHD (CPHD) filter for sets of trajectories, which are referred to as the trajectory PHD (TPHD) and trajectory CPHD (TCPHD) filters. Contrary to the PHD/CPHD filters, the TPHD/TCPHD filters are able to produce trajectory estimates from first principles. The TPHD filter is derived by recursively obtaining the best Poisson multitrajectory density approximation to the posterior density over the alive trajectories by minimising the Kullback-Leibler divergence. The TCPHD is derived in the same way but propagating an independent identically distributed (IID) cluster multitrajectory density approximation. We also propose the Gaussian mixture implementations of the TPHD and TCPHD recursions, the Gaussian mixture TPHD (GMTPHD) and the Gaussian mixture TCPHD (GMTCPHD), and the L-scan computationally efficient implementations, which only update the density of the trajectory states of the last L time steps.

random finite sets

PHD

CPHD

Multitarget tracking

sets of trajectories

Author

Angel Garcia

University of Liverpool

Lennart Svensson

Chalmers, Electrical Engineering, Signalbehandling och medicinsk teknik, Signal Processing

IEEE Transactions on Signal Processing

1053-587X (ISSN)

Vol. 67 22 5702-5714 8846723

Subject Categories

Probability Theory and Statistics

Control Engineering

Signal Processing

DOI

10.1109/TSP.2019.2943234

More information

Latest update

11/6/2019