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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 provides a scalable, multi-sensor measurement adaptive track initiation technique for labeled random finite set filters. A naive construction of the multi-sensor measurement adaptive birth set distribution leads to an exponential…

Signal Processing · Electrical Eng. & Systems 2022-05-02 Anthony Trezza , Donald J. Bucci , Pramod K. Varshney

This paper introduces a Poisson multi-Bernoulli mixture (PMBM) filter in which the intensities of target birth and undetected targets are grid-based. A simplified version of the Rao-Blackwellized point mass filter is used to predict the…

Signal Processing · Electrical Eng. & Systems 2021-03-22 Per Boström-Rost , Daniel Axehill , Gustaf Hendeby

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

The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multi-target distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a…

Signal Processing · Electrical Eng. & Systems 2020-03-02 Yuxuan Xia , Karl Granström , Lennart Svensson , Ángel F. García-Fernández , Jason L. Williams

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

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 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

Adaptive track initiation remains a crucial component of many modern multi-target tracking systems. For labeled random finite sets multi-object filters, prior work has been established to construct a labeled multi-object birth density using…

Signal Processing · Electrical Eng. & Systems 2025-06-23 Jennifer Bondarchuk , Anthony Trezza , Donald J. Bucci

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) 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

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

Accurate 3D multi-object tracking (MOT) is crucial for autonomous driving, as it enables robust perception, navigation, and planning in complex environments. While deep learning-based solutions have demonstrated impressive 3D MOT…

Computer Vision and Pattern Recognition · Computer Science 2026-02-04 Guanhua Ding , Yuxuan Xia , Runwei Guan , Qinchen Wu , Tao Huang , Weiping Ding , Jinping Sun , Guoqiang Mao

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

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

Measurement-adaptive track initiation remains a critical design requirement of many practical multi-target tracking systems. For labeled random finite sets multi-object filters, prior work has been established to construct a labeled…

Signal Processing · Electrical Eng. & Systems 2023-07-14 Jennifer Bondarchuk , Anthony Trezza , Donald J. Bucci

This paper focuses on the joint multi-object tracking (MOT) and the estimate of detection probability with the \emph{Poisson multi-Bernoulli mixture} (PMBM) filter. In a majority of multi-object scenarios, the knowledge of detection…

Systems and Control · Electrical Eng. & Systems 2019-09-24 Guchong Li

Passive multi-target tracking applications require the integration of multiple spatially distributed sensor measurements to distinguish true tracks from ghost tracks. A popular multi-target tracking approach for these applications is the…

Systems and Control · Electrical Eng. & Systems 2021-08-11 Christopher Berry , Donald J. Bucci , Samuel W. Schmidt

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

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
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