{"id":"https://openalex.org/W2043592505","doi":"https://doi.org/10.1109/taes.2013.6621830","title":"A Particle Filter Approach to Approximate Posterior Cramer-Rao Lower Bound: The Case of Hidden States","display_name":"A Particle Filter Approach to Approximate Posterior Cramer-Rao Lower Bound: The Case of Hidden States","publication_year":2013,"publication_date":"2013-10-01","ids":{"openalex":"https://openalex.org/W2043592505","doi":"https://doi.org/10.1109/taes.2013.6621830","mag":"2043592505"},"language":"en","primary_location":{"id":"doi:10.1109/taes.2013.6621830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2013.6621830","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","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/A5046068826","display_name":"Aditya Tulsyan","orcid":"https://orcid.org/0000-0002-8915-2187"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Aditya Tulsyan","raw_affiliation_strings":["Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada","Dept. of Chem. & Mater. Eng., Univ. of Alberta, Edmonton, AB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Dept. of Chem. & Mater. Eng., Univ. of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100432851","display_name":"Biao Huang","orcid":"https://orcid.org/0000-0001-9082-2216"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Biao Huang","raw_affiliation_strings":["Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada","Dept. of Chem. & Mater. Eng., Univ. of Alberta, Edmonton, AB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Dept. of Chem. & Mater. Eng., Univ. of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008908321","display_name":"R. Bhushan Gopaluni","orcid":"https://orcid.org/0000-0002-4321-0468"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R. Bhushan Gopaluni","raw_affiliation_strings":["University of Alberta, Edmonton, AB, CA","Dept. of Chem. & Mater. Eng., Univ. of Alberta, Edmonton, AB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta, Edmonton, AB, CA","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Dept. of Chem. & Mater. Eng., Univ. of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037125619","display_name":"J. Fraser Forbes","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"J. Fraser Forbes","raw_affiliation_strings":["Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada","Dept. of Chem. & Mater. Eng., Univ. of Alberta, Edmonton, AB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Dept. of Chem. & Mater. Eng., Univ. of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":null,"apc_paid":null,"fwci":3.4074,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.92623426,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"49","issue":"4","first_page":"2478","last_page":"2495"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11698","display_name":"Underwater Acoustics Research","score":0.972599983215332,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/particle-filter","display_name":"Particle filter","score":0.7632228136062622},{"id":"https://openalex.org/keywords/cram\u00e9r\u2013rao-bound","display_name":"Cram\u00e9r\u2013Rao bound","score":0.635196328163147},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6224998831748962},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5806683301925659},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5435066819190979},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5141168236732483},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5097739100456238},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.49791646003723145},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49758556485176086},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.44949835538864136},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.44243112206459045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4414314925670624},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4180181324481964},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3866567015647888},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.36514756083488464},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3253940939903259},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.2768898606300354},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13320794701576233},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12041619420051575},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08504718542098999}],"concepts":[{"id":"https://openalex.org/C52421305","wikidata":"https://www.wikidata.org/wiki/Q1151499","display_name":"Particle filter","level":3,"score":0.7632228136062622},{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.635196328163147},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6224998831748962},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5806683301925659},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5435066819190979},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5141168236732483},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5097739100456238},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.49791646003723145},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49758556485176086},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44949835538864136},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.44243112206459045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4414314925670624},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4180181324481964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3866567015647888},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.36514756083488464},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3253940939903259},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2768898606300354},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13320794701576233},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12041619420051575},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08504718542098999},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/taes.2013.6621830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2013.6621830","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","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":37,"referenced_works":["https://openalex.org/W95577512","https://openalex.org/W116417043","https://openalex.org/W391578156","https://openalex.org/W1500551892","https://openalex.org/W1982711454","https://openalex.org/W1984197955","https://openalex.org/W1993722646","https://openalex.org/W2003967703","https://openalex.org/W2007998685","https://openalex.org/W2024712436","https://openalex.org/W2025106365","https://openalex.org/W2034663708","https://openalex.org/W2040896388","https://openalex.org/W2049795963","https://openalex.org/W2064480843","https://openalex.org/W2077611006","https://openalex.org/W2090562304","https://openalex.org/W2096887879","https://openalex.org/W2099235157","https://openalex.org/W2099996308","https://openalex.org/W2104130465","https://openalex.org/W2115543721","https://openalex.org/W2119668398","https://openalex.org/W2123211114","https://openalex.org/W2125945227","https://openalex.org/W2131598171","https://openalex.org/W2146091262","https://openalex.org/W2148681057","https://openalex.org/W2149074579","https://openalex.org/W2159590918","https://openalex.org/W2162182236","https://openalex.org/W2162733643","https://openalex.org/W2235585540","https://openalex.org/W4233487859","https://openalex.org/W4244486013","https://openalex.org/W4285719527","https://openalex.org/W6652085760"],"related_works":["https://openalex.org/W2164801693","https://openalex.org/W2120266201","https://openalex.org/W2585557503","https://openalex.org/W2389491004","https://openalex.org/W2384282517","https://openalex.org/W1976418043","https://openalex.org/W2378226311","https://openalex.org/W2035458027","https://openalex.org/W4252024964","https://openalex.org/W4253883008"],"abstract_inverted_index":{"The":[0,102,120,142],"posterior":[1],"Cramer-Rao":[2],"lower":[3],"bound":[4,11],"(PCRLB)":[5],"derived":[6],"in":[7,67,70,133],"[1]":[8],"provides":[9],"a":[10,54,88,113,155],"on":[12,92,150],"the":[13,25,58,79,82,109,116,131,145],"mean":[14],"square":[15],"error":[16],"(MSE)":[17],"obtained":[18],"with":[19,136],"any":[20,43],"nonlinear":[21,134],"state":[22,138],"filter.":[23],"Computing":[24],"PCRLB":[26,80,132],"involves":[27],"solving":[28],"complex,":[29],"multi-dimensional":[30],"expectations,":[31],"which":[32,61],"do":[33],"not":[34,63],"lend":[35],"themselves":[36],"to":[37,45,57,107,129],"an":[38],"easy":[39],"analytical":[40],"solution.":[41],"Furthermore,":[42],"attempt":[44],"approximate":[46,130],"it":[47],"using":[48,112],"numerical":[49],"or":[50,69,86,96],"simulation-based":[51],"approaches":[52],"require":[53],"priori":[55],"access":[56],"true":[59],"states,":[60],"may":[62],"be":[64,127],"available,":[65],"except":[66],"simulations":[68],"carefully":[71],"designed":[72],"experiments.":[73],"To":[74],"allow":[75],"recursive":[76],"approximation":[77],"of":[78,115,144,158],"when":[81],"states":[83,111],"are":[84],"hidden":[85,110],"unmeasured,":[87],"new":[89],"approach":[90,103],"based":[91],"sequential":[93],"Monte-Carlo":[94],"(SMC)":[95],"particle":[97],"filters":[98],"(PFs)":[99],"is":[100,123,148],"proposed.":[101],"uses":[104],"SMC":[105],"methods":[106],"estimate":[108],"sequence":[114],"available":[117],"sensor":[118,140],"measurements.":[119],"developed":[121,146],"method":[122,147],"general":[124],"and":[125,139],"can":[126],"used":[128],"systems":[135],"non-Gaussian":[137],"noise.":[141],"efficacy":[143],"illustrated":[149],"two":[151],"simulation":[152],"examples,":[153],"including":[154],"practical":[156],"problem":[157],"ballistic":[159],"target":[160],"tracking":[161],"at":[162],"reentry":[163],"phase.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}