{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:32:35Z","timestamp":1760239955263,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,31]],"date-time":"2019-01-31T00:00:00Z","timestamp":1548892800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China National Natural Science Foundation","award":["61141009"],"award-info":[{"award-number":["61141009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Most multi-target tracking filters assume that one target and its observation follow a Hidden Markov Chain (HMC) model, but the implicit independence assumption of the HMC model is invalid in many practical applications, and a Pairwise Markov Chain (PMC) model is more universally suitable than the traditional HMC model. A set of weighted particles is used to approximate the probability hypothesis density of multi-targets in the framework of the PMC model, and a particle probability hypothesis density filter based on the PMC model (PF-PMC-PHD) is proposed for the nonlinear multi-target tracking system. Simulation results show the effectiveness of the PF-PMC-PHD filter and that the tracking performance of the PF-PMC-PHD filter is superior to the particle PHD filter based on the HMC model in a scenario where we kept the local physical properties of nonlinear and Gaussian HMC models while relaxing their independence assumption.<\/jats:p>","DOI":"10.3390\/a12020031","type":"journal-article","created":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T03:08:05Z","timestamp":1548990485000},"page":"31","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Particle Probability Hypothesis Density Filter Based on Pairwise Markov Chains"],"prefix":"10.3390","volume":"12","author":[{"given":"Jiangyi","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Electronic and optical engineering, Shijiazhuang Campus of Army Engineering University, Shijiazhuang 050000, China"}]},{"given":"Chunping","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Electronic and optical engineering, Shijiazhuang Campus of Army Engineering University, Shijiazhuang 050000, China"}]},{"given":"Wei","family":"Wang","sequence":"additional","affiliation":[{"name":"China Huayin Ordnance Test Center, Huayin 714200, China"}]},{"given":"Zheng","family":"Li","sequence":"additional","affiliation":[{"name":"Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing 100000, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,31]]},"reference":[{"key":"ref_1","unstructured":"Mahler, R. (2000). An Introduction to Multisource-Multitarget Statistics and Its Applications, Technical Monograph for Lockheed Martin."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mahler, R.P. (2007). Statistical Multisource-Multitarget Information Fusion, Artech House, Inc.","DOI":"10.1201\/9781420053098.ch16"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1109\/TAES.2003.1261119","article-title":"Multitarget Bayes Filtering via First-Order Multitarget Moments","volume":"39","author":"Mahler","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1109\/TAES.2005.1561884","article-title":"Sequential Monte Carlo methods for multi-target filtering with random finite sets","volume":"41","author":"Vo","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.sigpro.2016.06.017","article-title":"Particle-gating SMC-PHD Filter","volume":"130","author":"Gao","year":"2017","journal-title":"Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4091","DOI":"10.1109\/TSP.2006.881190","article-title":"The Gaussian mixture probability hypothesis density filter","volume":"54","author":"Vo","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1007\/s12555-015-0193-x","article-title":"An Improved ET-GM-PHD Filter for Multiple Closely-spaced Extended Target Tracking","volume":"15","author":"Yang","year":"2017","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Pieczynski, W. (2000, January 10\u201313). Pairwise Markov chains and Bayesian unsupervised fusion. 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Stat."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/2\/31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:30:01Z","timestamp":1760185801000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/2\/31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,31]]},"references-count":15,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["a12020031"],"URL":"https:\/\/doi.org\/10.3390\/a12020031","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2019,1,31]]}}}