{"id":"https://openalex.org/W7133119843","doi":"https://doi.org/10.3390/e28030273","title":"A Novel Belief Propagation-Based Probabilistic Multiple Hypothesis Tracking Algorithm for Multiple Resolvable Group Targets","display_name":"A Novel Belief Propagation-Based Probabilistic Multiple Hypothesis Tracking Algorithm for Multiple Resolvable Group Targets","publication_year":2026,"publication_date":"2026-02-28","ids":{"openalex":"https://openalex.org/W7133119843","doi":"https://doi.org/10.3390/e28030273","pmid":"https://pubmed.ncbi.nlm.nih.gov/41899925"},"language":"en","primary_location":{"id":"doi:10.3390/e28030273","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030273","pdf_url":"https://www.mdpi.com/1099-4300/28/3/273/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/28/3/273/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127759981","display_name":"Tianli Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110558","display_name":"Xi'an Technological University","ror":"https://ror.org/01t8prc81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianli Ma","raw_affiliation_strings":["School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"],"raw_orcid":"https://orcid.org/0000-0002-1077-1656","affiliations":[{"raw_affiliation_string":"School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I4210110558"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022655628","display_name":"Peiling Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110558","display_name":"Xi'an Technological University","ror":"https://ror.org/01t8prc81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peiling Shi","raw_affiliation_strings":["School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I4210110558"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100611661","display_name":"Sai Liu","orcid":"https://orcid.org/0009-0009-1336-5539"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sai Liu","raw_affiliation_strings":["China International Engineering Consulting Corporation, Beijing 100089, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China International Engineering Consulting Corporation, Beijing 100089, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5127761347","display_name":"Peng Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110558","display_name":"Xi'an Technological University","ror":"https://ror.org/01t8prc81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng Wang","raw_affiliation_strings":["School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I4210110558"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2419609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":"273","last_page":"273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.8537999987602234,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.8537999987602234,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10331","display_name":"Video Surveillance and Tracking Methods","score":0.054499998688697815,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.01269999984651804,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/factor-graph","display_name":"Factor graph","score":0.7214000225067139},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5889999866485596},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5823000073432922},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5677000284194946},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5418999791145325},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"Belief propagation","score":0.5412999987602234},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.46470001339912415},{"id":"https://openalex.org/keywords/data-association","display_name":"Data association","score":0.4339999854564667},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.421099990606308},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41839998960494995}],"concepts":[{"id":"https://openalex.org/C159246509","wikidata":"https://www.wikidata.org/wiki/Q5428725","display_name":"Factor graph","level":3,"score":0.7214000225067139},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5889999866485596},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5823000073432922},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5677000284194946},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5418999791145325},{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.5412999987602234},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5235000252723694},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.46470001339912415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4528000056743622},{"id":"https://openalex.org/C2983325608","wikidata":"https://www.wikidata.org/wiki/Q17084606","display_name":"Data association","level":3,"score":0.4339999854564667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4219000041484833},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.421099990606308},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C142853389","wikidata":"https://www.wikidata.org/wiki/Q744778","display_name":"Association (psychology)","level":2,"score":0.40849998593330383},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3878999948501587},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.3546000123023987},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3472999930381775},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.3431999981403351},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.328900009393692},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.27219998836517334},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C33954974","wikidata":"https://www.wikidata.org/wiki/Q486494","display_name":"Sensor fusion","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C193524817","wikidata":"https://www.wikidata.org/wiki/Q386780","display_name":"Association rule learning","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28030273","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030273","pdf_url":"https://www.mdpi.com/1099-4300/28/3/273/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:41899925","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41899925","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:f3ea6412e018429499758bd7882625ed","is_oa":true,"landing_page_url":"https://doaj.org/article/f3ea6412e018429499758bd7882625ed","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 28, Iss 3, p 273 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13025329","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13025329/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e28030273","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28030273","pdf_url":"https://www.mdpi.com/1099-4300/28/3/273/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.45021116733551025}],"awards":[{"id":"https://openalex.org/G2828418383","display_name":null,"funder_award_id":"2023-ZDLNY-61","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6438380941","display_name":null,"funder_award_id":"62303368","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7133119843.pdf","grobid_xml":"https://content.openalex.org/works/W7133119843.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0,47],"key":[1],"challenge":[2],"in":[3,14,108],"multiple":[4],"group":[5,59,87],"target":[6,116],"tracking":[7],"is":[8,51],"to":[9,119],"maintain":[10],"consistent":[11],"data":[12],"association":[13,56,70],"the":[15,40,55,65,73,86,93,101,109,120],"presence":[16],"of":[17,67,112],"dynamic":[18],"evolutions,":[19],"i.e.,":[20],"splitting":[21],"and":[22,61,85,115,123],"merging.":[23],"This":[24],"paper":[25],"proposes":[26],"a":[27],"Belief":[28,74],"Propagation-based":[29],"Multiple":[30],"Hypothesis":[31],"Tracking":[32],"framework.":[33],"The":[34],"measurements":[35],"are":[36,78,89],"partitioned":[37],"by":[38,64,91],"using":[39],"Minimum":[41],"Spanning":[42],"Tree":[43],"divisive":[44],"clustering":[45],"algorithm.":[46],"factor":[48],"graph":[49],"model":[50],"then":[52],"constructed":[53],"for":[54],"hypotheses":[57],"between":[58],"targets":[60],"measurements,":[62],"followed":[63],"inference":[66],"marginal":[68],"posterior":[69],"probabilities":[71,77],"via":[72],"Propagation.":[75],"These":[76],"finally":[79],"integrated":[80],"into":[81],"an":[82],"Expectation-Maximization":[83],"framework,":[84],"states":[88,114],"updated":[90],"maximizing":[92],"expected":[94],"log-likelihood":[95],"function.":[96],"Simulation":[97],"results":[98],"demonstrate":[99],"that":[100],"proposed":[102],"algorithm":[103],"achieves":[104],"significantly":[105],"higher":[106],"accuracy":[107],"joint":[110],"estimation":[111],"kinematic":[113],"cardinality":[117],"compared":[118],"PMHT-based,":[121],"PHD-based,":[122],"JPDA-based":[124],"algorithms.":[125]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-03-02T00:00:00"}
