{"id":"https://openalex.org/W1988031792","doi":"https://doi.org/10.1109/lsp.2015.2394301","title":"A Novel Generalization of Modified LMS Algorithm to Fractional Order","display_name":"A Novel Generalization of Modified LMS Algorithm to Fractional Order","publication_year":2015,"publication_date":"2015-01-20","ids":{"openalex":"https://openalex.org/W1988031792","doi":"https://doi.org/10.1109/lsp.2015.2394301","mag":"1988031792"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2015.2394301","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2394301","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":["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/A5024949205","display_name":"Yun Tan","orcid":"https://orcid.org/0000-0002-9855-8234"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yun Tan","raw_affiliation_strings":["Beijing University of Posts and Telecommunications, Beijing, China","Beijing University of Posts and Telecommunications,Beijing,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"Beijing University of Posts and Telecommunications,Beijing,China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100689912","display_name":"Zhiqiang He","orcid":"https://orcid.org/0000-0002-5010-3118"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiqiang He","raw_affiliation_strings":["Beijing University of Posts and Telecommunications, Beijing, China","Beijing University of Posts and Telecommunications,Beijing,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"Beijing University of Posts and Telecommunications,Beijing,China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113818722","display_name":"Baoyu Tian","orcid":null},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Baoyu Tian","raw_affiliation_strings":["Beijing University of Posts and Telecommunications, Beijing, China","Beijing University of Posts and Telecommunications,Beijing,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"Beijing University of Posts and Telecommunications,Beijing,China","institution_ids":["https://openalex.org/I139759216"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I139759216"],"apc_list":null,"apc_paid":null,"fwci":9.3819,"has_fulltext":false,"cited_by_count":78,"citation_normalized_percentile":{"value":0.98520594,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"22","issue":"9","first_page":"1244","last_page":"1248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11081","display_name":"Advanced Control Systems Design","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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.8231338262557983},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7087604999542236},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6144217848777771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6141698360443115},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5680133700370789},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5574375987052917},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5124323964118958},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48752519488334656},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30148518085479736},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19980919361114502},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1660158634185791}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8231338262557983},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7087604999542236},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6144217848777771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6141698360443115},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5680133700370789},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5574375987052917},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5124323964118958},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48752519488334656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30148518085479736},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19980919361114502},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1660158634185791},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2015.2394301","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2394301","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W2000310218","https://openalex.org/W2005010408","https://openalex.org/W2007422900","https://openalex.org/W2014725445","https://openalex.org/W2062181178","https://openalex.org/W2086646907","https://openalex.org/W2100819955","https://openalex.org/W2108132547","https://openalex.org/W2126318433","https://openalex.org/W2132611513","https://openalex.org/W2133247229","https://openalex.org/W2143991194","https://openalex.org/W2144213565","https://openalex.org/W2150903299","https://openalex.org/W2154405161","https://openalex.org/W2157347895","https://openalex.org/W2228698783","https://openalex.org/W2787959293","https://openalex.org/W4236087597","https://openalex.org/W6654265202","https://openalex.org/W6676186167"],"related_works":["https://openalex.org/W1971753667","https://openalex.org/W2052275678","https://openalex.org/W1997271576","https://openalex.org/W2348187822","https://openalex.org/W2068208308","https://openalex.org/W2946992918","https://openalex.org/W2082669437","https://openalex.org/W2885094885","https://openalex.org/W1675928192","https://openalex.org/W1593514994"],"abstract_inverted_index":{"In":[0],"this":[1],"letter,":[2],"the":[3,33,38,55,70,75,78],"modified":[4],"least":[5],"mean":[6],"squares":[7],"(MLMS)":[8],"algorithm":[9,59],"proposed":[10],"by":[11,31],"Kretschmer":[12],"is":[13,29,63],"generalized":[14,56],"to":[15],"fractional":[16,44,71],"order":[17,35,72],"\u03b1":[18,21,73,86,95],"(0":[19],"<;":[20],"<sub":[22],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[23],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u2264":[24],"1</sub>":[25],").":[26],"Such":[27],"generalization":[28],"achieved":[30],"replacing":[32],"first":[34],"difference":[36],"of":[37,54],"weight":[39,49,90],"updating":[40],"equation":[41],"with":[42],"a":[43,84,93],"one.":[45],"The":[46],"convergence":[47,99],"speed,":[48],"noise":[50,91],"and":[51],"implementation":[52],"issue":[53],"MLMS":[57],"(GMLMS)":[58],"are":[60],"examined.":[61],"It":[62],"shown":[64],"that":[65,83],"for":[66],"smaller":[67,85,89],"step":[68,79],"size,":[69,80],"functions":[74],"same":[76],"as":[77],"which":[81],"means":[82],"will":[87,96],"give":[88,97],"while":[92],"bigger":[94],"faster":[98],"speed.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":8}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}