{"id":"https://openalex.org/W2105959128","doi":"https://doi.org/10.1109/tsp.2011.2168519","title":"Closed-Form Solutions to Forward\u2013Backward Smoothing","display_name":"Closed-Form Solutions to Forward\u2013Backward Smoothing","publication_year":2011,"publication_date":"2011-09-23","ids":{"openalex":"https://openalex.org/W2105959128","doi":"https://doi.org/10.1109/tsp.2011.2168519","mag":"2105959128"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2168519","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2168519","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072792589","display_name":"Ba\u2010Ngu Vo","orcid":"https://orcid.org/0000-0003-4202-7722"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Ba-Ngu Vo","raw_affiliation_strings":["Sch. of Electr., Electron., & Comput. Eng., Univ. of Western Australia, Crawley, WA, Australia"],"affiliations":[{"raw_affiliation_string":"Sch. of Electr., Electron., & Comput. Eng., Univ. of Western Australia, Crawley, WA, Australia","institution_ids":["https://openalex.org/I177877127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070960013","display_name":"Ba-Tuong Vo","orcid":"https://orcid.org/0000-0002-3954-238X"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ba-Tuong Vo","raw_affiliation_strings":["Sch. of Electr., Electron., & Comput. Eng., Univ. of Western Australia, Crawley, WA, Australia"],"affiliations":[{"raw_affiliation_string":"Sch. of Electr., Electron., & Comput. Eng., Univ. of Western Australia, Crawley, WA, Australia","institution_ids":["https://openalex.org/I177877127"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006022796","display_name":"Ronald Mahler","orcid":"https://orcid.org/0000-0003-1226-1104"},"institutions":[{"id":"https://openalex.org/I1287521167","display_name":"Lockheed Martin (United States)","ror":"https://ror.org/026er9r08","country_code":"US","type":"company","lineage":["https://openalex.org/I1287521167"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald P. S. Mahler","raw_affiliation_strings":["MS2 Tactical Syst., Adv. Technol. Group, Lockheed Martin, Eagan, MN, USA"],"affiliations":[{"raw_affiliation_string":"MS2 Tactical Syst., Adv. Technol. Group, Lockheed Martin, Eagan, MN, USA","institution_ids":["https://openalex.org/I1287521167"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072792589"],"corresponding_institution_ids":["https://openalex.org/I177877127"],"apc_list":null,"apc_paid":null,"fwci":9.6486,"has_fulltext":false,"cited_by_count":86,"citation_normalized_percentile":{"value":0.97999362,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"60","issue":"1","first_page":"2","last_page":"17"},"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":0.9993000030517578,"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":0.9993000030517578,"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/T12389","display_name":"Infrared Target Detection Methodologies","score":0.9668999910354614,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9379000067710876,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/smoothing","display_name":"Smoothing","score":0.6002867221832275},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5204551219940186},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40792039036750793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39853718876838684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3724626302719116},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3257195055484772},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.1974378228187561}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6002867221832275},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5204551219940186},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40792039036750793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39853718876838684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3724626302719116},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3257195055484772},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.1974378228187561}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2011.2168519","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2168519","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/ce1ccb64-8353-4e66-8119-409ea7452a40","is_oa":false,"landing_page_url":"https://research-repository.uwa.edu.au/en/publications/ce1ccb64-8353-4e66-8119-409ea7452a40","pdf_url":null,"source":{"id":"https://openalex.org/S4306402523","display_name":"UWA Profiles and Research Repository (University of Western Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177877127","host_organization_name":"The University of Western Australia","host_organization_lineage":["https://openalex.org/I177877127"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Vo , B-N , Vo , B-T &amp; Mahler , R P S 2012 , ' Closed-form solutions to forward-backward smoothing ' , IEEE Transactions on Signal Processing , vol. 60 , pp. 2-17 . https://doi.org/10.1109/TSP.2011.2168519","raw_type":"article"},{"id":"pmh:oai:espace.curtin.edu.au:20.500.11937/42215","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11937/42215","pdf_url":null,"source":{"id":"https://openalex.org/S4306401790","display_name":"eSpace (Curtin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205640436","host_organization_name":"Curtin University","host_organization_lineage":["https://openalex.org/I205640436"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W34992941","https://openalex.org/W1483307070","https://openalex.org/W1514443597","https://openalex.org/W1531532259","https://openalex.org/W1557595030","https://openalex.org/W1968422312","https://openalex.org/W1988827501","https://openalex.org/W2009331766","https://openalex.org/W2014787937","https://openalex.org/W2048796971","https://openalex.org/W2054734272","https://openalex.org/W2070898270","https://openalex.org/W2077611006","https://openalex.org/W2088117020","https://openalex.org/W2098296991","https://openalex.org/W2098613108","https://openalex.org/W2098973553","https://openalex.org/W2099867508","https://openalex.org/W2105905583","https://openalex.org/W2105934661","https://openalex.org/W2106873007","https://openalex.org/W2114822183","https://openalex.org/W2126736494","https://openalex.org/W2126885789","https://openalex.org/W2128266453","https://openalex.org/W2134494829","https://openalex.org/W2137190649","https://openalex.org/W2137585588","https://openalex.org/W2146485022","https://openalex.org/W2149532992","https://openalex.org/W2151926297","https://openalex.org/W2155012790","https://openalex.org/W2161435744","https://openalex.org/W2293807537","https://openalex.org/W2509410776","https://openalex.org/W2571446175","https://openalex.org/W4229793772","https://openalex.org/W4240108704","https://openalex.org/W4297888513","https://openalex.org/W4307492541","https://openalex.org/W6633511732","https://openalex.org/W6642584951"],"related_works":["https://openalex.org/W2590671464","https://openalex.org/W2388501007","https://openalex.org/W4225891298","https://openalex.org/W2004492308","https://openalex.org/W4385485567","https://openalex.org/W1970987673","https://openalex.org/W2386767533","https://openalex.org/W3005990459","https://openalex.org/W3127884516","https://openalex.org/W2141783658"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2],"closed-form":[3,10],"Gaussian":[4,86],"sum":[5],"smoother":[6],"and,":[7],"more":[8],"importantly,":[9],"smoothing":[11,49],"solutions":[12,42,72],"for":[13],"increasingly":[14],"complex":[15],"problems":[16],"arising":[17],"from":[18],"practice,":[19],"including":[20],"tracking":[21,27,33],"in":[22],"clutter,":[23],"joint":[24],"detection":[25],"and":[26,30],"(in":[28,34],"clutter),":[29],"multiple":[31],"target":[32],"clutter)":[35],"via":[36],"the":[37,46,56,64,70,74,80,94],"probability":[38],"hypothesis":[39],"density.":[40],"The":[41,67],"are":[43,89],"based":[44],"on":[45],"corresponding":[47],"forward-backward":[48],"recursions":[50],"that":[51],"involve":[52],"forward":[53],"propagation":[54,62],"of":[55,63,76,79],"filtering":[57],"densities,":[58],"followed":[59],"by":[60],"backward":[61,81],"smoothed":[65],"densities.":[66],"key":[68],"to":[69,92],"exact":[71],"is":[73],"use":[75],"alternative":[77],"forms":[78],"propagations,":[82],"together":[83],"with":[84],"standard":[85],"identities.":[87],"Simulations":[88],"also":[90],"presented":[91],"verify":[93],"proposed":[95],"solutions.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
