{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T02:41:25Z","timestamp":1775616085432,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,9]],"date-time":"2022-11-09T00:00:00Z","timestamp":1667952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013314","name":"111 project","doi-asserted-by":"publisher","award":["No.B18039"],"award-info":[{"award-number":["No.B18039"]}],"id":[{"id":"10.13039\/501100013314","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The previous multi-frame version of the generalized labeled multi-Bernoulli model (MF-GLMB) only accounts for standard measurement models. It is not suitable for application in the detection and tracking of multiple weak targets (low signal-to-noise ratio) due to the measurement information loss. In this paper, we introduce a MF-GLMB model that formally incorporates a track-before-detect scheme for point targets using an image sensor model. Furthermore, a belief propagation algorithm is adopted to approximately calculate the marginal association probabilities of the multi-target posterior density. In this formulation, an MF-GLMB model based on the track-before-detect measurement model (MF-GLMB-TBD smoothing) enables multi-target posterior recursion for multi-target state estimation. By taking the entire history of the state estimation into account, MF-GLMB-TBD smoothing achieves superior performance in estimation precision compared with the corresponding GLMB-TBD filter. The simulation results demonstrate that the performance of the proposed algorithm is comparable to or better than that of the Gibbs sampler-based version.<\/jats:p>","DOI":"10.3390\/rs14225666","type":"journal-article","created":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T02:07:48Z","timestamp":1668046068000},"page":"5666","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Multi-Frame GLMB Smoothing Based on the Image-Observation Sensor for Tracking Multiple Weak Targets Using Belief Propagation"],"prefix":"10.3390","volume":"14","author":[{"given":"Chenghu","family":"Cao","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an University of Posts & Telecommunications, Xi\u2019an 710121, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6453-0786","authenticated-orcid":false,"given":"Yongbo","family":"Zhao","sequence":"additional","affiliation":[{"name":"National Lab of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3460","DOI":"10.1109\/TSP.2013.2259822","article-title":"Labeled random finite sets and multi-object conjugate priors","volume":"61","author":"Vo","year":"2013","journal-title":"IEEE Trans. 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