{"id":"https://openalex.org/W2914013421","doi":"https://doi.org/10.1109/tsp.2019.2897967","title":"Comments on \u201cThe Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes\u201d","display_name":"Comments on \u201cThe Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes\u201d","publication_year":2019,"publication_date":"2019-02-06","ids":{"openalex":"https://openalex.org/W2914013421","doi":"https://doi.org/10.1109/tsp.2019.2897967","mag":"2914013421"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2019.2897967","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2897967","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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/A5100688670","display_name":"Gang Wang","orcid":"https://orcid.org/0000-0002-7150-1000"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gang Wang","raw_affiliation_strings":["Center for Robotics, School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-7150-1000","affiliations":[{"raw_affiliation_string":"Center for Robotics, School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085284295","display_name":"Rui Xue","orcid":"https://orcid.org/0000-0002-9188-175X"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Xue","raw_affiliation_strings":["School of Electronics and Information Engineering, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-9188-175X","affiliations":[{"raw_affiliation_string":"School of Electronics and Information Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9711,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72002489,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"67","issue":"7","first_page":"1957","last_page":"1958"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11325","display_name":"Inertial Sensor and Navigation","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.9614053964614868},{"id":"https://openalex.org/keywords/hypercomplex-number","display_name":"Hypercomplex number","score":0.9498121738433838},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6206258535385132},{"id":"https://openalex.org/keywords/adaptive-filter","display_name":"Adaptive filter","score":0.573361873626709},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5574249029159546},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.44599345326423645},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43353360891342163},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40769147872924805},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19606128334999084},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07483679056167603}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.9614053964614868},{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.9498121738433838},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6206258535385132},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.573361873626709},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5574249029159546},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.44599345326423645},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43353360891342163},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40769147872924805},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19606128334999084},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07483679056167603},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2019.2897967","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2897967","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2398572347","display_name":null,"funder_award_id":"91438207","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2648016464","display_name":"\u57fa\u4e8e\u76f2\u6e90\u63d0\u53d6\u7684\u9ad8\u5149\u8c31\u77ff\u7269\u8bc6\u522b\u65b9\u6cd5\u4e0e\u673a\u5236\u7814\u7a76","funder_award_id":"41301459","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4210490095","display_name":null,"funder_award_id":"ZYGX2016J154","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4643353661","display_name":"\u57fa\u4e8e\u538b\u7f29\u611f\u77e5\u7684\u7279\u5b9a\u4fe1\u53f7\u76f2\u6e90\u63d0\u53d6\u95ee\u9898\u7814\u7a76","funder_award_id":"61371182","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1921661266","https://openalex.org/W1991017496","https://openalex.org/W2058693698","https://openalex.org/W2077598042","https://openalex.org/W2090550497","https://openalex.org/W2091669036","https://openalex.org/W2094646141","https://openalex.org/W2099057098","https://openalex.org/W2108704185","https://openalex.org/W2108812136","https://openalex.org/W2118369318","https://openalex.org/W2556598801","https://openalex.org/W2766233463","https://openalex.org/W2780313524","https://openalex.org/W3098588011"],"related_works":["https://openalex.org/W2916518000","https://openalex.org/W2916498667","https://openalex.org/W2917906954","https://openalex.org/W2572893131","https://openalex.org/W2917330019","https://openalex.org/W2917006597","https://openalex.org/W2916884673","https://openalex.org/W1897251165","https://openalex.org/W2423267406","https://openalex.org/W2020324309"],"abstract_inverted_index":{"In":[0],"a":[1,8],"previous":[2],"paper,":[3],"Took":[4],"et.":[5],"Al.":[6],"proposed":[7],"quaternion":[9,40,47,55],"least":[10],"mean":[11],"square":[12],"algorithm":[13],"for":[14],"adaptive":[15],"filters.":[16],"The":[17,31,57],"gradients":[18],"can":[19],"be":[20],"obtained":[21,58],"in":[22,60],"two":[23],"different":[24],"solutions":[25],"from":[26],"the":[27,34,39,46,53,61],"same":[28],"cost":[29],"function.":[30],"derivation":[32],"of":[33],"gradient":[35,48,59],"is":[36,42],"incorrect":[37],"because":[38],"product":[41],"non-commutative.":[43],"We":[44],"study":[45],"update":[49],"rules":[50],"and":[51],"derive":[52],"right":[54],"gradient.":[56],"correction":[62],"has":[63],"only":[64],"one":[65],"solution.":[66]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
