{"id":"https://openalex.org/W1980139451","doi":"https://doi.org/10.1109/tac.2011.2168129","title":"Various Ways to Compute the Continuous-Discrete Extended Kalman Filter","display_name":"Various Ways to Compute the Continuous-Discrete Extended Kalman Filter","publication_year":2011,"publication_date":"2011-09-22","ids":{"openalex":"https://openalex.org/W1980139451","doi":"https://doi.org/10.1109/tac.2011.2168129","mag":"1980139451"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2011.2168129","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2168129","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00904376","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077547823","display_name":"Paul Frogerais","orcid":null},"institutions":[{"id":"https://openalex.org/I154526488","display_name":"Inserm","ror":"https://ror.org/02vjkv261","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488"]},{"id":"https://openalex.org/I4210105651","display_name":"Laboratoire Traitement du Signal et de l'Image","ror":"https://ror.org/01f1amm71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I154526488","https://openalex.org/I4210105651","https://openalex.org/I4210105774","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"P. Frogerais","raw_affiliation_strings":["LTSI, Universit\u00e9 de Rennes 1, Rennes, France","UMR 1099, INSERM, Rennes, France"],"affiliations":[{"raw_affiliation_string":"LTSI, Universit\u00e9 de Rennes 1, Rennes, France","institution_ids":["https://openalex.org/I4210105651","https://openalex.org/I56067802"]},{"raw_affiliation_string":"UMR 1099, INSERM, Rennes, France","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I154526488"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076298725","display_name":"Jean-Jacques Bellanger","orcid":null},"institutions":[{"id":"https://openalex.org/I154526488","display_name":"Inserm","ror":"https://ror.org/02vjkv261","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488"]},{"id":"https://openalex.org/I4210105651","display_name":"Laboratoire Traitement du Signal et de l'Image","ror":"https://ror.org/01f1amm71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I154526488","https://openalex.org/I4210105651","https://openalex.org/I4210105774","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Jacques Bellanger","raw_affiliation_strings":["LTSI, Universit\u00e9 de Rennes 1, Rennes, France","UMR 1099, INSERM, Rennes, France"],"affiliations":[{"raw_affiliation_string":"LTSI, Universit\u00e9 de Rennes 1, Rennes, France","institution_ids":["https://openalex.org/I4210105651","https://openalex.org/I56067802"]},{"raw_affiliation_string":"UMR 1099, INSERM, Rennes, France","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I154526488"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028457159","display_name":"Lotfi Senhadji","orcid":"https://orcid.org/0000-0001-9434-6341"},"institutions":[{"id":"https://openalex.org/I154526488","display_name":"Inserm","ror":"https://ror.org/02vjkv261","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488"]},{"id":"https://openalex.org/I4210105651","display_name":"Laboratoire Traitement du Signal et de l'Image","ror":"https://ror.org/01f1amm71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I154526488","https://openalex.org/I4210105651","https://openalex.org/I4210105774","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L. Senhadji","raw_affiliation_strings":["LTSI, Universit\u00e9 de Rennes 1, Rennes, France","UMR 1099, INSERM, Rennes, France"],"affiliations":[{"raw_affiliation_string":"LTSI, Universit\u00e9 de Rennes 1, Rennes, France","institution_ids":["https://openalex.org/I4210105651","https://openalex.org/I56067802"]},{"raw_affiliation_string":"UMR 1099, INSERM, Rennes, France","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I154526488"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077547823"],"corresponding_institution_ids":["https://openalex.org/I154526488","https://openalex.org/I4210105651","https://openalex.org/I56067802"],"apc_list":null,"apc_paid":null,"fwci":4.4392,"has_fulltext":false,"cited_by_count":109,"citation_normalized_percentile":{"value":0.94329234,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"57","issue":"4","first_page":"1000","last_page":"1004"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9952999949455261,"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/T11236","display_name":"Control Systems and Identification","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/extended-kalman-filter","display_name":"Extended Kalman filter","score":0.8136789202690125},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6216261386871338},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6196304559707642},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6163352131843567},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6038330793380737},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.6015046238899231},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5132107734680176},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4840540289878845},{"id":"https://openalex.org/keywords/invariant-extended-kalman-filter","display_name":"Invariant extended Kalman filter","score":0.4415074586868286},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4383418560028076},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.4163423776626587},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4144030511379242},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4043794870376587},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.30925774574279785},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13578146696090698}],"concepts":[{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.8136789202690125},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6216261386871338},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6196304559707642},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6163352131843567},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6038330793380737},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.6015046238899231},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5132107734680176},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4840540289878845},{"id":"https://openalex.org/C8639503","wikidata":"https://www.wikidata.org/wiki/Q6059511","display_name":"Invariant extended Kalman filter","level":4,"score":0.4415074586868286},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4383418560028076},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4163423776626587},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4144030511379242},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4043794870376587},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30925774574279785},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13578146696090698},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2011.2168129","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2168129","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00904376v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00904376","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2012, 57 (4), pp.1000 - 1004. &#x27E8;10.1109/TAC.2011.2168129&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00904376v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00904376","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2012, 57 (4), pp.1000 - 1004. &#x27E8;10.1109/TAC.2011.2168129&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W126785765","https://openalex.org/W1603631609","https://openalex.org/W1969933072","https://openalex.org/W1986294597","https://openalex.org/W2020934227","https://openalex.org/W2036522227","https://openalex.org/W2069270950","https://openalex.org/W2070765152","https://openalex.org/W2076186907","https://openalex.org/W2097610177","https://openalex.org/W2098613108","https://openalex.org/W2122512809","https://openalex.org/W2139857744","https://openalex.org/W2171322001","https://openalex.org/W2267072639","https://openalex.org/W2790374560","https://openalex.org/W4244746866"],"related_works":["https://openalex.org/W2162299404","https://openalex.org/W2103062922","https://openalex.org/W1035502194","https://openalex.org/W2182059946","https://openalex.org/W2164404293","https://openalex.org/W4206024512","https://openalex.org/W2966342863","https://openalex.org/W2483158495","https://openalex.org/W2053335193","https://openalex.org/W4300476109"],"abstract_inverted_index":{"The":[0,49,101,117],"Extended":[1],"Kalman":[2],"Filter":[3],"(EKF)":[4],"is":[5,29,38,104,111,120,129,153],"a":[6,32,41,58,67,115,121],"very":[7],"popular":[8],"tool":[9],"dealing":[10],"with":[11],"state":[12,20,28],"estimation.":[13],"Its":[14],"continuous-discrete":[15],"version":[16],"(CD-EKF)":[17],"estimates":[18],"the":[19,46,53,77,105,136,147,150],"trajectory":[21],"of":[22,45,52,76,90,135,143,149],"continuous-time":[23],"nonlinear":[24,43,96],"models,":[25],"whose":[26],"internal":[27],"described":[30],"by":[31],"stochastic":[33],"differential":[34,59],"equation":[35,60],"and":[36],"which":[37,110,146],"observed":[39],"through":[40],"noisy":[42],"form":[44],"sampled":[47],"state.":[48],"prediction":[50,151],"step":[51],"CD-EKF":[54],"leads":[55],"to":[56,85,131],"solve":[57],"that":[61],"cannot":[62],"be":[63],"generally":[64],"solved":[65],"in":[66],"closed":[68],"form.":[69],"This":[70,125],"technical":[71],"note":[72],"presents":[73],"an":[74],"overview":[75],"numerical":[78],"methods,":[79],"including":[80],"recent":[81],"works,":[82],"usually":[83],"implemented":[84],"approximate":[86],"this":[87],"filter.":[88],"Comparisons":[89],"theses":[91],"methods":[92],"on":[93],"two":[94],"different":[95],"models":[97],"are":[98],"finally":[99],"presented.":[100],"first":[102],"one":[103,119],"Van":[106],"der":[107],"Pol":[108],"oscillator":[109],"widely":[112],"used":[113,130],"as":[114],"benchmark.":[116],"second":[118],"neuronal":[122],"population":[123],"model.":[124],"more":[126],"original":[127],"model":[128],"simulate":[132],"EEG":[133],"activity":[134],"cortex.":[137],"Experiments":[138],"showed":[139],"better":[140],"stability":[141],"properties":[142],"implementations":[144],"for":[145],"positivity":[148],"matrix":[152],"guaranteed.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}
