Spatiotemporal Constraints for Sets of Trajectories with Applications to PMBM Densities
Paper in proceedings, 2020

In this paper we introduce spatiotemporal constraints for trajectories, i.e., restrictions that the trajectory must be in some part of the state space (spatial constraint) at some point in time (temporal constraint). Spatiotemporal contraints on trajectories can be used to answer a range of important questions, including, e.g., “where did the person that were in area A at time t, go afterwards?”. We discuss how multiple constraints can be combined into sets of constraints, and we then apply sets of constraints to set of trajectories densities, specifically Poisson Multi-Bernoulli Mixture (PMBM) densities. For Poisson target birth, the exact posterior density is PMBM for both point targets and extended targets. In the paper we show that if the unconstrained set of trajectories density is PMBM, then the constrained density is also PMBM. Examples of constrained trajectory densities motivate and illustrate the key results.

multiple target tracking

sets of trajectories

random finite sets

time constraints

state space constraints

trajectory

point target

spatiotemporal constraints

extended target

Author

Karl Granström

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Signal Processing

Lennart Svensson

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Signal Processing

Yuxuan Xia

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Signal Processing

Angel Garcia

University of Liverpool

Jason L. Williams

Commonwealth Scientific and Industrial Research Organisation (CSIRO)

FUSION 2020 - 23nd International Conference on Information Fusion

00002020 (eISSN)

2020 IEEE 23rd International Conference on Information Fusion (FUSION)
Rustenburg, South Africa,

Deep multi-object tracking for ground truth trajectory estimation

VINNOVA, 2018-07-01 -- 2022-06-30.

Areas of Advance

Information and Communication Technology

Transport

Subject Categories

Robotics

Probability Theory and Statistics

Computer Science

DOI

10.23919/FUSION45008.2020.9190553

More information

Latest update

1/5/2021 8