{"id":"https://openalex.org/W2293860863","doi":"https://doi.org/10.1109/lsp.2016.2558461","title":"Geometric-Algebra LMS Adaptive Filter and Its Application to Rotation Estimation","display_name":"Geometric-Algebra LMS Adaptive Filter and Its Application to Rotation Estimation","publication_year":2016,"publication_date":"2016-04-28","ids":{"openalex":"https://openalex.org/W2293860863","doi":"https://doi.org/10.1109/lsp.2016.2558461","mag":"2293860863"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2016.2558461","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2016.2558461","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.06044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Wilder B. Lopes","orcid":null},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Wilder B. Lopes","raw_affiliation_strings":["Department of Electronic Systems Engineering, University of Sao Paulo, Sao Paulo, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Systems Engineering, University of Sao Paulo, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Anas Al-Nuaimi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anas Al-Nuaimi","raw_affiliation_strings":["Chair of Media Technology (LMT), TU M\u00fcnchen Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Media Technology (LMT), TU M\u00fcnchen Munich, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Cassio G. Lopes","orcid":null},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Cassio G. Lopes","raw_affiliation_strings":["Department of Electronic Systems Engineering, University of Sao Paulo, Sao Paulo, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Systems Engineering, University of Sao Paulo, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0574,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.94903846,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"23","issue":"6","first_page":"858","last_page":"862"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.3634999990463257,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.3634999990463257,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.06430000066757202,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.03889999911189079,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/adaptive-filter","display_name":"Adaptive filter","score":0.7087000012397766},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.6395000219345093},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.6008999943733215},{"id":"https://openalex.org/keywords/hypercomplex-number","display_name":"Hypercomplex number","score":0.5105999708175659},{"id":"https://openalex.org/keywords/kernel-adaptive-filter","display_name":"Kernel adaptive filter","score":0.4797999858856201},{"id":"https://openalex.org/keywords/rotor","display_name":"Rotor (electric)","score":0.4065999984741211},{"id":"https://openalex.org/keywords/filter-design","display_name":"Filter design","score":0.36730000376701355},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.3644999861717224}],"concepts":[{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.7087000012397766},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.6395000219345093},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.6008999943733215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5180000066757202},{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.5105999708175659},{"id":"https://openalex.org/C13107197","wikidata":"https://www.wikidata.org/wiki/Q6394192","display_name":"Kernel adaptive filter","level":4,"score":0.4797999858856201},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45179998874664307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4431000053882599},{"id":"https://openalex.org/C17281054","wikidata":"https://www.wikidata.org/wiki/Q193466","display_name":"Rotor (electric)","level":2,"score":0.4065999984741211},{"id":"https://openalex.org/C22597639","wikidata":"https://www.wikidata.org/wiki/Q5449227","display_name":"Filter design","level":3,"score":0.36730000376701355},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.35920000076293945},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3504999876022339},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C207570611","wikidata":"https://www.wikidata.org/wiki/Q1256500","display_name":"Rotation group SO","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C2776003309","wikidata":"https://www.wikidata.org/wiki/Q1988072","display_name":"Adaptive algorithm","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.30090001225471497},{"id":"https://openalex.org/C52970973","wikidata":"https://www.wikidata.org/wiki/Q2497134","display_name":"Adaptive system","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C198386975","wikidata":"https://www.wikidata.org/wiki/Q117785","display_name":"Finite impulse response","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C36390408","wikidata":"https://www.wikidata.org/wiki/Q1163067","display_name":"Digital filter","level":3,"score":0.25949999690055847}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2016.2558461","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2016.2558461","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1601.06044","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.06044","pdf_url":"https://arxiv.org/pdf/1601.06044","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.06044","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.06044","pdf_url":"https://arxiv.org/pdf/1601.06044","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1557571532","https://openalex.org/W1595823061","https://openalex.org/W1967895609","https://openalex.org/W1976167430","https://openalex.org/W1993267444","https://openalex.org/W1993985351","https://openalex.org/W2049981393","https://openalex.org/W2077598042","https://openalex.org/W2090550497","https://openalex.org/W2099057098","https://openalex.org/W2118104180","https://openalex.org/W2126537583","https://openalex.org/W2126773478","https://openalex.org/W2128019145","https://openalex.org/W2152864241","https://openalex.org/W2159593339","https://openalex.org/W2164544312","https://openalex.org/W2515973928","https://openalex.org/W2962901069","https://openalex.org/W2963380050","https://openalex.org/W4210475733","https://openalex.org/W4239240501","https://openalex.org/W6677898303","https://openalex.org/W6774258613"],"related_works":[],"abstract_inverted_index":{"This":[0],"letter":[1],"exploits":[2],"geometric":[3,29],"(Clifford)":[4],"algebra":[5],"(GA)":[6],"theory":[7],"to":[8,36,61,71,106,122,138],"devise":[9],"and":[10,39,56],"introduce":[11],"a":[12,18,64,67,85,92,111],"new":[13],"adaptive":[14,47,54,78],"filtering":[15],"strategy.":[16],"From":[17],"least-squares":[19],"cost":[20,109],"function,":[21],"the":[22,32,97,108,118,127,135],"gradient":[23],"is":[24,59,82],"calculated":[25],"following":[26],"results":[27],"from":[28,52,57],"calculus":[30],"(GC),":[31],"extension":[33],"of":[34,110,120],"GA":[35,44],"handle":[37],"differential":[38],"integral":[40],"calculus.":[41],"The":[42,77],"novel":[43],"least-mean-squares":[45],"(GA-LMS)":[46],"filter,":[48],"which":[49,90],"inherits":[50],"properties":[51],"standard":[53],"filters":[55],"GA,":[58],"developed":[60],"recursively":[62],"estimate":[63],"rotor":[65],"(multivector),":[66],"hypercomplex":[68],"quantity":[69],"able":[70],"describe":[72],"rotations":[73],"in":[74,141],"any":[75],"dimension.":[76],"filter":[79,137],"(AF)":[80],"performance":[81],"assessed":[83],"via":[84],"3-D":[86,113],"point-clouds":[87],"registration":[88,114],"problem,":[89],"contains":[91],"rotation":[93],"estimation":[94],"step.":[95],"Calculating":[96],"AF":[98],"computational":[99],"complexity":[100],"suggests":[101],"that":[102],"it":[103],"can":[104],"contribute":[105],"reduce":[107],"full-blown":[112],"algorithm,":[115],"especially":[116],"when":[117],"number":[119],"points":[121],"be":[123],"processed":[124],"grows.":[125],"Moreover,":[126],"employed":[128],"GA/GC":[129],"framework":[130],"allows":[131],"for":[132],"easily":[133],"applying":[134],"resulting":[136],"estimating":[139],"rotors":[140],"higher":[142],"dimensions.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":8},{"year":2016,"cited_by_count":2}],"updated_date":"2026-07-12T07:33:03.550515","created_date":"2016-06-24T00:00:00"}