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This paper proposes an efficient implementation of the Poisson multi-Bernoulli mixture (PMBM) trajectory filter. The proposed implementation performs track-oriented N-scan pruning to limit complexity, and uses dual decomposition to solve…

Signal Processing · Electrical Eng. & Systems 2018-11-30 Yuxuan Xia , Karl Granström , Lennart Svensson , Ángel F. García-Fernández

The Poisson multi-Bernoulli mixture (PMBM) is an unlabelled multi-target distribution for which the prediction and update are closed. It has a Poisson birth process, and new Bernoulli components are generated on each new measurement as a…

Signal Processing · Electrical Eng. & Systems 2018-12-14 Karl Granström , Lennart Svensson , Yuxuan Xia , Jason Williams , Angel F Garcia-Fernandez

This paper presents two trajectory Poisson multi-Bernoulli (TPMB) filters for multi-target tracking: one to estimate the set of alive trajectories at each time step and another to estimate the set of all trajectories, which includes alive…

Computer Vision and Pattern Recognition · Computer Science 2020-09-18 Ángel F. García-Fernández , Lennart Svensson , Jason L. Williams , Yuxuan Xia , Karl Granström

This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter on the space of sets of tree trajectories for multiple target tracking with spawning targets. A tree trajectory contains all trajectory information of a target and its…

Methodology · Statistics 2022-05-04 Ángel F. García-Fernández , Lennart Svensson

This paper presents a Poisson multi-Bernoulli mixture (PMBM) filter for multi-target filtering based on sensor measurements that are sets of trajectories in the last two-time step window. The proposed filter, the trajectory measurement PMBM…

Signal Processing · Electrical Eng. & Systems 2025-11-25 Marco Fontana , Ángel F. García-Fernández , Simon Maskell

The Poisson multi-Bernoulli mixture (PMBM) filter is conjugate prior composed of the union of a Poisson point process (PPP) and a multi-Bernoulli mixture (MBM). In this paper, a new PMBM filter for tracking multiple targets with randomly…

Systems and Control · Computer Science 2019-04-09 Guchong Li

The Poisson Multi-Bernoulli Mixture (PMBM) density is a conjugate multi-target density for the standard point target model with Poisson point process birth. This means that both the filtering and predicted densities for the set of targets…

Signal Processing · Electrical Eng. & Systems 2024-12-17 Karl Granström , Lennart Svensson , Yuxuan Xia , Jason Williams , Ángel F. García-Fernández

The Poisson multi-Bernoulli mixture (PMBM) is a multi-target distribution for which the prediction and update are closed. By applying the random finite set (RFS) framework to multi-target tracking with sets of trajectories as the variable…

Signal Processing · Electrical Eng. & Systems 2019-11-21 Yuxuan Xia , Karl Granström , Lennart Svensson , Ángel F. García-Fernández , Jason L. Williams

This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter for coexisting point and extended targets, i.e., for scenarios where there may be simultaneous point and extended targets. The PMBM filter provides a recursion to compute…

Methodology · Statistics 2021-05-19 Ángel F. García-Fernández , Jason L. Williams , Lennart Svensson , Yuxuan Xia

Multi-Bernoulli mixture (MBM) filter is one of the exact closed-form multi-target Bayes filters in the random finite sets (RFS) framework, which utilizes multi-Bernoulli mixture density as the multi-target conjugate prior. This filter is…

Signal Processing · Electrical Eng. & Systems 2019-11-12 Sen Wang

The Poisson multi-Bernoulli mixture (PMBM) is a multi-object conjugate prior for the closed-form Bayes random finite sets filter. The extended object PMBM filter provides a closed-form solution for multiple extended object filtering with…

Signal Processing · Electrical Eng. & Systems 2021-08-16 Yuxuan Xia , Karl Granström , Lennart Svensson , Maryam Fatemi , Ángel F. García-Fernández , Jason L. Williams

This paper proposes a clustering and merging approach for the Poisson multi-Bernoulli mixture (PMBM) filter to lower its computational complexity and make it suitable for multiple target tracking with a high number of targets. We define a…

Signal Processing · Electrical Eng. & Systems 2024-09-16 Marco Fontana , Ángel F. García-Fernández , Simon Maskell

This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior for multiple extended object filtering. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture…

Computation · Statistics 2019-12-09 Karl Granstrom , Maryam Fatemi , Lennart Svensson

This paper considers a batch solution to the multi-object tracking problem based on sets of trajectories. Specifically, we present two offline implementations of the trajectory Poisson multi-Bernoulli mixture (TPMBM) filter for batch data…

Signal Processing · Electrical Eng. & Systems 2024-06-25 Yuxuan Xia , Ángel F. García-Fernández , Lennart Svensson

This paper considers multiple extended object tracking based on Poisson multi-Bernoulli mixture (PMBM) filtering, which gives the closed-form Bayesian solution for standard multiple extended object models with Poisson birth. To efficiently…

Methodology · Statistics 2026-04-28 Yuxuan Xia , Ángel F. García-Fernández , Lennart Svensson

We provide a derivation of the Poisson multi-Bernoulli mixture (PMBM) filter for multi-target tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish…

Computer Vision and Pattern Recognition · Computer Science 2018-09-14 Ángel F. García-Fernández , Jason L. Williams , Karl Granström , Lennart Svensson

This paper shows that the Poisson multi-Bernoulli mixture (PMBM) density is a multi-target conjugate prior for general target-generated measurement distributions and arbitrary clutter distributions. That is, for this multi-target…

Applications · Statistics 2023-05-25 Ángel F. García-Fernández , Yuxuan Xia , Lennart Svensson

In this paper, we propose a Poisson multi-Bernoulli (PMB) filter for extended object tracking (EOT), which directly estimates the set of object trajectories, using belief propagation (BP). The proposed filter propagates a PMB density on the…

Signal Processing · Electrical Eng. & Systems 2023-09-20 Yuxuan Xia , Ángel F. García-Fernández , Florian Meyer , Jason L. Williams , Karl Granström , Lennart Svensson

This paper presents the Gaussian implementation of the multi-Bernoulli mixture (MBM) filter. The MBM filter provides the filtering (multi-target) density for the standard dynamic and radar measurement models when the birth model is…

Signal Processing · Electrical Eng. & Systems 2019-08-26 Ángel F. García-Fernández , Yuxuan Xia , Karl Granström , Lennart Svensson , Jason L. Williams

This paper uses multi-object tracking methods known from the radar tracking community to address the problem of pedestrian tracking using 2D bounding box detections. The standard point-object (SPO) model is adopted, and the posterior…

Systems and Control · Electrical Eng. & Systems 2025-08-29 Jan Krejčí , Oliver Kost , Yuxuan Xia , Lennart Svensson , Ondřej Straka
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