{"id":"https://openalex.org/W2110873966","doi":"https://doi.org/10.1109/taes.2012.6324684","title":"Quaternion Estimation from Vector Observations using a Matrix Kalman Filter","display_name":"Quaternion Estimation from Vector Observations using a Matrix Kalman Filter","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W2110873966","doi":"https://doi.org/10.1109/taes.2012.6324684","mag":"2110873966"},"language":"en","primary_location":{"id":"doi:10.1109/taes.2012.6324684","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2012.6324684","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/A5091412192","display_name":"Daniel Choukroun","orcid":"https://orcid.org/0000-0002-3862-6899"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"D. Choukroun","raw_affiliation_strings":["Delft University of Technology, Delft, Netherlands","Fac. of Aerosp. Eng., TUD-Delft Univ. of Technol., Delft, Netherlands"],"affiliations":[{"raw_affiliation_string":"Delft University of Technology, Delft, Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Fac. of Aerosp. Eng., TUD-Delft Univ. of Technol., Delft, Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110820995","display_name":"H. Weiss","orcid":null},"institutions":[{"id":"https://openalex.org/I16362100","display_name":"Rafael Advanced Defense Systems (Israel)","ror":"https://ror.org/016mey390","country_code":"IL","type":"company","lineage":["https://openalex.org/I16362100"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"H. Weiss","raw_affiliation_strings":["Department 35, Rafael, Ministry of Defence, Haifa, Israel","RAFAEL, Minist. of Defense, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Department 35, Rafael, Ministry of Defence, Haifa, Israel","institution_ids":["https://openalex.org/I16362100"]},{"raw_affiliation_string":"RAFAEL, Minist. of Defense, Haifa, Israel","institution_ids":["https://openalex.org/I16362100"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041483494","display_name":"Itzhack Y. Bar\u2010Itzhack","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"I. Y. Bar-Itzhack","raw_affiliation_strings":["Research Institute, Technion-Israel Institute of Technology, Haifa, Israel","Asher Space Res. Inst., Technion - Israel Inst. of Technol., Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Research Institute, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Asher Space Res. Inst., Technion - Israel Inst. of Technol., Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054940454","display_name":"Yaakov Oshman","orcid":"https://orcid.org/0000-0001-9471-3789"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Y. Oshman","raw_affiliation_strings":["Faculty of AeroSpace Engineering, Technion-Israel Institute of Technology, Haifa, Israel","Fac. of Aerosp. Eng., Technion Israel Inst. of Technol., Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Faculty of AeroSpace Engineering, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Fac. of Aerosp. Eng., Technion Israel Inst. of Technol., Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5091412192"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":null,"apc_paid":null,"fwci":3.9792,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.93349452,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"48","issue":"4","first_page":"3133","last_page":"3158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11325","display_name":"Inertial Sensor and Navigation","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11325","display_name":"Inertial Sensor and Navigation","score":1.0,"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/T10655","display_name":"GNSS positioning and interference","score":0.9987000226974487,"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.7479285597801208},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.740864634513855},{"id":"https://openalex.org/keywords/invariant-extended-kalman-filter","display_name":"Invariant extended Kalman filter","score":0.6156970262527466},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"Matrix algebra","score":0.5540788769721985},{"id":"https://openalex.org/keywords/extended-kalman-filter","display_name":"Extended Kalman filter","score":0.5229207277297974},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4999568462371826},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4516535997390747},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43521058559417725},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4345203638076782},{"id":"https://openalex.org/keywords/fast-kalman-filter","display_name":"Fast Kalman filter","score":0.4338666796684265},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4218197464942932},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.4217376410961151},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3903970718383789},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38620197772979736},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.37435415387153625},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14152872562408447},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10060417652130127}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.7479285597801208},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.740864634513855},{"id":"https://openalex.org/C8639503","wikidata":"https://www.wikidata.org/wiki/Q6059511","display_name":"Invariant extended Kalman filter","level":4,"score":0.6156970262527466},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.5540788769721985},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.5229207277297974},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4999568462371826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4516535997390747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43521058559417725},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4345203638076782},{"id":"https://openalex.org/C150679823","wikidata":"https://www.wikidata.org/wiki/Q5436946","display_name":"Fast Kalman filter","level":4,"score":0.4338666796684265},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4218197464942932},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4217376410961151},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3903970718383789},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38620197772979736},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.37435415387153625},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14152872562408447},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10060417652130127},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/taes.2012.6324684","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2012.6324684","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":22,"referenced_works":["https://openalex.org/W50340912","https://openalex.org/W1488435683","https://openalex.org/W1507322379","https://openalex.org/W1628100432","https://openalex.org/W1967795974","https://openalex.org/W2006863675","https://openalex.org/W2014774230","https://openalex.org/W2049186971","https://openalex.org/W2062608425","https://openalex.org/W2063005413","https://openalex.org/W2074117332","https://openalex.org/W2080247258","https://openalex.org/W2094201513","https://openalex.org/W2110728483","https://openalex.org/W2114942378","https://openalex.org/W2117102490","https://openalex.org/W2131752723","https://openalex.org/W2140454437","https://openalex.org/W2164268880","https://openalex.org/W2170940176","https://openalex.org/W3172279961","https://openalex.org/W4236774793"],"related_works":["https://openalex.org/W4310470578","https://openalex.org/W2756636025","https://openalex.org/W2079005675","https://openalex.org/W2140268640","https://openalex.org/W2112936906","https://openalex.org/W2013066175","https://openalex.org/W2005477509","https://openalex.org/W2036128127","https://openalex.org/W2062946220","https://openalex.org/W2498868696"],"abstract_inverted_index":{"A":[0,172,186],"novel":[1,214],"two-stage":[2],"quaternion":[3,43],"estimator":[4,174,234],"from":[5,45],"vector":[6],"observations":[7],"that":[8,65,117,131,162,231],"is":[9,20,72,119,160,175,199],"a":[10,34,42,67,89,94,108,113,217,224,247,251],"synthesis":[11],"between":[12],"Wahba's":[13],"approach":[14,19],"and":[15,116,193,219,250,266],"the":[16,31,46,59,76,80,84,102,124,132,144,165,169,182,191,196,202,210,213,232,243,256,264],"Kalman":[17,62,69,158],"filtering":[18],"presented.":[21],"The":[22,38],"first":[23],"stage":[24,40,106],"features":[25],"an":[26],"optimal":[27],"denoising":[28,60],"procedure":[29],"of":[30,33,78,83,93,135,195,212],"elements":[32],"time-varying":[35],"noisy":[36],"K-matrix.":[37],"second":[39],"produces":[41],"estimate":[44],"filtered":[47],"K-matrix":[48,103],"via":[49,61],"any":[50],"eigenvalue-eigenvector":[51],"solver.":[52],"This":[53,128,148],"work's":[54],"contribution":[55],"consists":[56],"in":[57,143,151,168,263],"performing":[58],"filtering.":[63],"For":[64],"purpose,":[66],"matrix":[68,85,109],"filter":[70,159,183,258],"(MKF)":[71],"developed,":[73],"which":[74,189],"has":[75],"advantage":[77],"preserving":[79],"natural":[81],"formulation":[82],"plant":[86],"equations.":[87],"As":[88,237],"result,":[90],"two":[91],"aspects":[92],"previous":[95],"algorithm,":[96],"called":[97],"Optimal-REQUEST":[98],"(OPREQ),":[99],"are":[100,138],"improved:":[101],"update":[104],"estimation":[105],"uses":[107],"gain":[110,118],"rather":[111],"than":[112,255],"scalar":[114],"gain,":[115],"optimized":[120],"with":[121,216],"respect":[122],"to":[123],"classical":[125],"minimum-variance":[126],"cost.":[127],"work":[129],"assumes":[130],"sensed":[133],"lines":[134],"sight":[136],"(LOS)":[137],"time":[139],"invariant":[140],"as":[141,223],"seen":[142],"chosen":[145],"reference":[146],"frame.":[147],"assumption":[149],"fits":[150],"various":[152],"operational":[153],"mission":[154],"architectures.":[155],"An":[156],"exact":[157],"developed":[161,177],"accounts":[163],"for":[164,181,259],"state-multiplicative":[166],"noise":[167],"process":[170],"equation.":[171],"reduced":[173],"also":[176],"assuming":[178],"simple":[179],"expressions":[180],"covariance":[184],"matrices.":[185],"constrained":[187,244],"estimator,":[188],"enforces":[190],"symmetry":[192,265],"null-trace":[194,267],"estimated":[197],"matrix,":[198],"designed":[200],"using":[201],"pseudomeasurement":[203],"(PM)":[204],"technique.":[205],"Extensive":[206,227],"Monte-Carlo":[207,228,241],"simulations":[208,229],"illustrate":[209],"performance":[211],"filters":[215],"spinning":[218],"nutating":[220],"spacecraft":[221],"(SC)":[222],"case":[225],"study.":[226],"show":[230],"proposed":[233],"outperforms":[235],"OPREQ.":[236],"illustrated":[238],"by":[239],"additional":[240],"simulations,":[242],"MKF":[245],"exhibits":[246],"better":[248,252],"transient":[249],"steady-state":[253],"accuracy":[254],"unconstrained":[257],"large":[260],"initial":[261],"disturbances":[262],"properties.":[268]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}