{"id":"https://openalex.org/W2137448549","doi":"https://doi.org/10.1109/cdc.2007.4434662","title":"Left-invariant extended Kalman filter and attitude estimation","display_name":"Left-invariant extended Kalman filter and attitude estimation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2137448549","doi":"https://doi.org/10.1109/cdc.2007.4434662","mag":"2137448549"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434662","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434662","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","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/A5110083725","display_name":"Silv\u00e8re Bonnabel","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I32881790","https://openalex.org/I4210116740"]},{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Silvere Bonnabel","raw_affiliation_strings":["Centre Automatique et Syst\u00e9mes, Paris, France","\u00c9cole des Mines de Paris, Paris"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre Automatique et Syst\u00e9mes, Paris, France","institution_ids":["https://openalex.org/I4210116740"]},{"raw_affiliation_string":"\u00c9cole des Mines de Paris, Paris","institution_ids":["https://openalex.org/I70768539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110083725"],"corresponding_institution_ids":["https://openalex.org/I4210116740","https://openalex.org/I70768539"],"apc_list":null,"apc_paid":null,"fwci":3.4328,"has_fulltext":false,"cited_by_count":129,"citation_normalized_percentile":{"value":0.93151326,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"1027","last_page":"1032"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9987999796867371,"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/T11325","display_name":"Inertial Sensor and Navigation","score":0.9975000023841858,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9950000047683716,"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/invariant","display_name":"Invariant (physics)","score":0.7564413547515869},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.7449755668640137},{"id":"https://openalex.org/keywords/invariant-extended-kalman-filter","display_name":"Invariant extended Kalman filter","score":0.6199398636817932},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.567428469657898},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.554309070110321},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.5297703742980957},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.4951099455356598},{"id":"https://openalex.org/keywords/extended-kalman-filter","display_name":"Extended Kalman filter","score":0.4862991273403168},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.47873422503471375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47409114241600037},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.45521801710128784},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40023255348205566},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3367100954055786},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29431581497192383},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.25169891119003296},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24129432439804077},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16625693440437317},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10149523615837097},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.09281066060066223},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07401061058044434}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7564413547515869},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.7449755668640137},{"id":"https://openalex.org/C8639503","wikidata":"https://www.wikidata.org/wiki/Q6059511","display_name":"Invariant extended Kalman filter","level":4,"score":0.6199398636817932},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.567428469657898},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.554309070110321},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.5297703742980957},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.4951099455356598},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.4862991273403168},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.47873422503471375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47409114241600037},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45521801710128784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40023255348205566},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3367100954055786},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29431581497192383},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.25169891119003296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24129432439804077},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16625693440437317},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10149523615837097},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09281066060066223},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07401061058044434}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2007.4434662","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434662","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W155208371","https://openalex.org/W208000474","https://openalex.org/W1764149764","https://openalex.org/W1804494423","https://openalex.org/W1996077195","https://openalex.org/W2090147357","https://openalex.org/W2102787760","https://openalex.org/W2103095193","https://openalex.org/W2115930333","https://openalex.org/W2116394929","https://openalex.org/W2129980120","https://openalex.org/W2136517446","https://openalex.org/W2963459976","https://openalex.org/W3104122060","https://openalex.org/W7043003852"],"related_works":["https://openalex.org/W1035502194","https://openalex.org/W2164404293","https://openalex.org/W4206024512","https://openalex.org/W2966342863","https://openalex.org/W2053335193","https://openalex.org/W4300476109","https://openalex.org/W2772311278","https://openalex.org/W4205759170","https://openalex.org/W2354299011","https://openalex.org/W4385993860"],"abstract_inverted_index":{"We":[0,24],"consider":[1],"a":[2,6,26,44],"left-invariant":[3,40],"dynamics":[4],"on":[5],"Lie":[7],"group.":[8],"One":[9],"way":[10],"to":[11,18],"define":[12],"driving":[13],"and":[14,31],"observation":[15],"noises":[16],"is":[17,55],"make":[19],"them":[20],"preserve":[21],"the":[22,39,50],"symmetries.":[23],"propose":[25],"left-":[27],"invariant":[28],"(i.e,":[29],"intrinsic":[30],"thus":[32],"symmetry-preserving)":[33],"extended":[34],"Kalman":[35],"filter":[36],"such":[37],"that":[38],"estimation":[41,60],"error":[42],"obeys":[43],"stochastic":[45],"differential":[46],"equation":[47],"independent":[48],"of":[49],"system":[51],"trajectory.":[52],"The":[53],"theory":[54],"illustrated":[56],"by":[57],"an":[58],"attitude":[59],"example.":[61]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
