{"id":"https://openalex.org/W2110489756","doi":"https://doi.org/10.1137/080717055","title":"Characterization of Exponential Divergence of the Kalman Filter for Time-Varying Systems","display_name":"Characterization of Exponential Divergence of the Kalman Filter for Time-Varying Systems","publication_year":2009,"publication_date":"2009-11-05","ids":{"openalex":"https://openalex.org/W2110489756","doi":"https://doi.org/10.1137/080717055","mag":"2110489756"},"language":"en","primary_location":{"id":"doi:10.1137/080717055","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080717055","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5047167568","display_name":"Eduardo F. Costa","orcid":"https://orcid.org/0000-0002-9067-9234"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eduardo F. Costa","raw_affiliation_strings":["efcosta@icmc.usp.br#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"efcosta@icmc.usp.br#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018225150","display_name":"Alessandro Astolfi","orcid":"https://orcid.org/0000-0002-4331-454X"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alessandro Astolfi","raw_affiliation_strings":["Electrical and Electronic Engineering Department, Imperial College London, SW7 2AZ , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Electronic Engineering Department, Imperial College London, SW7 2AZ , UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2207,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89488625,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"48","issue":"5","first_page":"2917","last_page":"2944"},"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":0.9994999766349792,"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":0.9994999766349792,"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":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9983999729156494,"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/mathematics","display_name":"Mathematics","score":0.808508038520813},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.7139842510223389},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5725164413452148},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.541990339756012},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5317636132240295},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.522851288318634},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.507925808429718},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4965978264808655},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.463178426027298},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.448234498500824},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16871404647827148},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16366896033287048},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11362585425376892},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07785749435424805},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07142531871795654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.808508038520813},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.7139842510223389},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5725164413452148},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.541990339756012},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5317636132240295},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.522851288318634},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.507925808429718},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4965978264808655},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.463178426027298},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.448234498500824},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16871404647827148},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16366896033287048},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11362585425376892},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07785749435424805},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07142531871795654},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080717055","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080717055","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:www.producao.usp.br:BDPI/15932","is_oa":false,"landing_page_url":"http://producao.usp.br/handle/BDPI/15932","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP","raw_type":"publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1282806495","display_name":null,"funder_award_id":"EP/E057438/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W2001332000","https://openalex.org/W2019063098","https://openalex.org/W2026750739","https://openalex.org/W2028808207","https://openalex.org/W2038295818","https://openalex.org/W2051234657","https://openalex.org/W2061903321","https://openalex.org/W2063799102","https://openalex.org/W2064861110","https://openalex.org/W2068090215","https://openalex.org/W2068257363","https://openalex.org/W2076712618","https://openalex.org/W2093735221","https://openalex.org/W2097509729","https://openalex.org/W2129695524","https://openalex.org/W2132937713","https://openalex.org/W2138953630","https://openalex.org/W2151231006","https://openalex.org/W2162719021","https://openalex.org/W2167091066","https://openalex.org/W2168022335"],"related_works":["https://openalex.org/W3208095355","https://openalex.org/W2177370417","https://openalex.org/W2052507016","https://openalex.org/W2180461068","https://openalex.org/W2051816080","https://openalex.org/W1580685205","https://openalex.org/W2760382975","https://openalex.org/W1990207062","https://openalex.org/W1566957016","https://openalex.org/W1596181035"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"semistability":[3,88,105,137],"of":[4,12,44,70,92,147],"the":[5,10,32,45,55,68,90,97,124,145],"recursive":[6],"Kalman":[7],"filter":[8,46,56],"in":[9,106,144],"context":[11,146],"linear":[13,125],"time-varying":[14],"(LTV),":[15],"possibly":[16],"nondetectable":[17],"systems":[18],"with":[19,89],"incorrect":[20,116],"noise":[21,117],"information.":[22],"Semistability":[23],"is":[24],"a":[25,49,107],"key":[26],"property,":[27],"as":[28,73,119],"it":[29],"ensures":[30],"that":[31,104],"actual":[33],"estimation":[34],"error":[35,99],"does":[36,62],"not":[37,63,83],"diverge":[38],"exponentially.":[39],"We":[40,85],"explore":[41],"structural":[42],"properties":[43],"to":[47,57,78,121,133],"obtain":[48,79,130],"necessary":[50],"and":[51,81,94,101,114,138],"sufficient":[52],"condition":[53,61],"for":[54,136],"be":[58,76],"semistable.":[59],"The":[60],"involve":[64],"limiting":[65],"gains":[66],"nor":[67],"solution":[69],"Riccati":[71],"equations,":[72],"they":[74],"can":[75],"difficult":[77],"numerically":[80],"may":[82],"exist.":[84],"also":[86],"compare":[87],"notions":[91],"stability":[93,95],"w.r.t.":[96],"initial":[98],"covariance,":[100],"we":[102,129],"show":[103],"sense":[108],"makes":[109],"no":[110],"distinction":[111],"between":[112],"persistent":[113],"nonpersistent":[115],"models,":[118],"opposed":[120],"stability.":[122],"In":[123],"time":[126],"invariant":[127],"scenario":[128],"algebraic,":[131],"easy":[132],"test":[134],"conditions":[135],"stability,":[139],"which":[140],"complement":[141],"results":[142],"available":[143],"detectable":[148],"systems.":[149],"Illustrative":[150],"examples":[151],"are":[152],"included.":[153]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}