Result: Calculation of multi-target conditional mean and covariance based on gaussian random fields

Title:
Calculation of multi-target conditional mean and covariance based on gaussian random fields
Authors:
Leroy, Idyano, Clark, Daniel
Contributors:
Institut Polytechnique de Paris (IP Paris), Communications, Images et Traitement de l'Information (TSP - CITI), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Institut Mines-Télécom [Paris] (IMT)-Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris), Statistiques, Optimisation, Probabilités (SOP - SAMOVAR), Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR), Institut Mines-Télécom [Paris] (IMT)-Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), University of Southampton, NITSM-MTS project with award no. 202265005
Source:
2025 28th International Conference on Information Fusion (FUSION). :1-7
Publisher Information:
CCSD; IEEE, 2025.
Publication Year:
2025
Collection:
collection:TELECOM-SUDPARIS
collection:IP_PARIS
collection:INSTITUTS-TELECOM
collection:INSTITUT-MINES-TELECOM
collection:INTERDISCIPLINARITES
collection:IP-PARIS-MATHEMATIQUES
collection:IP-PARIS-INFORMATION-COMMUNICATION-ELECTRONIQUE
collection:IP-PARIS-INFORMATIQUE-DONNEES-ET-IA
collection:SAMOVAR
Subject Terms:
Gaussian random field, point processes, multi-target tracking, [MATH]Mathematics [math], [INFO]Computer Science [cs]
Subject Geographic:
Rio de Janeiro, Brazil
Original Identifier:
HAL: hal-05308307
Document Type:
Conference conferenceObject<br />Conference papers
Language:
English
ISBN:
978-1-03-705623-9
Relation:
info:eu-repo/semantics/altIdentifier/doi/10.23919/FUSION65864.2025.11124063
DOI:
10.23919/FUSION65864.2025.11124063
Access URL:
https://hal.science/hal-05308307
https://hal.science/hal-05308307v1/document
https://hal.science/hal-05308307v1/file/grf_filter_fusion2025-7.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.05308307v1
Database:
HAL

Further Information

A conditional multi-target mean and covariance are calculated based on a Gaussian random field approximation of point processes. We derive a particular solution based on a multi-target model commonly used for multi-target tracking. The resulting conditional mean is shown to coincide with the classical first-order filter, while the posterior covariance-owing to the Gaussian approximation-exhibits a refined, localized representation of spatial correlations that contrasts with previous point process derivations. The proposed framework opens new avenues for interdisciplinary research in multi-target tracking, bridging point process theory and field theoretic methods.