{"id":"https://openalex.org/W7113897432","doi":"https://doi.org/10.1109/lsp.2025.3642765","title":"P-Norm Based Fractional-Order Robust Subband Adaptive Filtering Algorithm for Impulsive Noise and Noisy Input","display_name":"P-Norm Based Fractional-Order Robust Subband Adaptive Filtering Algorithm for Impulsive Noise and Noisy Input","publication_year":2025,"publication_date":"2025-12-10","ids":{"openalex":"https://openalex.org/W7113897432","doi":"https://doi.org/10.1109/lsp.2025.3642765"},"language":null,"primary_location":{"id":"doi:10.1109/lsp.2025.3642765","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2025.3642765","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/2601.10074","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jianhong Ye","orcid":"https://orcid.org/0009-0009-5544-0912"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianhong Ye","raw_affiliation_strings":["Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China"],"raw_orcid":"https://orcid.org/0009-0009-5544-0912","affiliations":[{"raw_affiliation_string":"Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Haiquan Zhao","orcid":"https://orcid.org/0000-0003-0198-1384"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiquan Zhao","raw_affiliation_strings":["Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0003-0198-1384","affiliations":[{"raw_affiliation_string":"Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yi Peng","orcid":"https://orcid.org/0009-0001-5001-4035"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Peng","raw_affiliation_strings":["Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China"],"raw_orcid":"https://orcid.org/0009-0001-5001-4035","affiliations":[{"raw_affiliation_string":"Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4800084"],"apc_list":null,"apc_paid":null,"fwci":0.8506,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76953006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"33","issue":null,"first_page":"281","last_page":"285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9955000281333923,"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":0.9955000281333923,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.0013000000035390258,"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/T11248","display_name":"Advanced Power Amplifier Design","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/robustness","display_name":"Robustness (evolution)","score":0.7692000269889832},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5929999947547913},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.5166000127792358},{"id":"https://openalex.org/keywords/adaptive-filter","display_name":"Adaptive filter","score":0.5157999992370605},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5016999840736389},{"id":"https://openalex.org/keywords/noise-measurement","display_name":"Noise measurement","score":0.5012999773025513},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.49230000376701355},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.48410001397132874},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4821000099182129}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7692000269889832},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6618000268936157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6226999759674072},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5929999947547913},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.5166000127792358},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.5157999992370605},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5016999840736389},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.5012999773025513},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.49230000376701355},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.48410001397132874},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4821000099182129},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.4684000015258789},{"id":"https://openalex.org/C32617633","wikidata":"https://www.wikidata.org/wiki/Q1426666","display_name":"Least mean squares filter","level":3,"score":0.40400001406669617},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.3878999948501587},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.37209999561309814},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C31441030","wikidata":"https://www.wikidata.org/wiki/Q4291882","display_name":"Least absolute deviations","level":3,"score":0.3287999927997589},{"id":"https://openalex.org/C2776003309","wikidata":"https://www.wikidata.org/wiki/Q1988072","display_name":"Adaptive algorithm","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30250000953674316},{"id":"https://openalex.org/C55352655","wikidata":"https://www.wikidata.org/wiki/Q304247","display_name":"Median filter","level":4,"score":0.30000001192092896},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C2988709989","wikidata":"https://www.wikidata.org/wiki/Q85784623","display_name":"Mean square","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C2988922011","wikidata":"https://www.wikidata.org/wiki/Q5449244","display_name":"Filtering theory","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C188154048","wikidata":"https://www.wikidata.org/wiki/Q6803609","display_name":"Mean absolute error","level":3,"score":0.2581999897956848}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2025.3642765","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2025.3642765","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:2601.10074","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2601.10074","pdf_url":"https://arxiv.org/pdf/2601.10074","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:2601.10074","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2601.10074","pdf_url":"https://arxiv.org/pdf/2601.10074","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":[{"id":"https://openalex.org/G2030446458","display_name":null,"funder_award_id":"61871461","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3184487484","display_name":null,"funder_award_id":"62171388","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4514581901","display_name":"\u9ad8\u6548\u7a33\u5065\u7684\u5206\u5e03\u5f0f\u7ea6\u675f\u81ea\u9002\u5e94\u6ee4\u6ce2\u65b0\u65b9\u6cd5\u4e0e\u5e94\u7528\u7814\u7a76","funder_award_id":"61871461","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6148365373","display_name":"\u591a\u6838\u81ea\u9002\u5e94\u6ee4\u6ce2\u65b0\u65b9\u6cd5\u53ca\u5e94\u7528\u7814\u7a76","funder_award_id":"61571374","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7020212242","display_name":null,"funder_award_id":"61571374","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8776338496","display_name":null,"funder_award_id":"62171388","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7113897432.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Building":[0],"upon":[1],"the":[2,11,88,96,104,110,116,124,140,143],"mean":[3,127],"<inline-formula":[4,14,24,62,118],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,15,25,31,63,68,119],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[6,16,26,32,64,69,120],"notation=\"LaTeX\">$p$</tex-math></inline-formula>-power":[7],"error":[8],"(MPE)":[9],"criterion,":[10],"normalized":[12],"subband":[13],"notation=\"LaTeX\">$p$</tex-math></inline-formula>-norm":[17],"(NSPN)":[18],"algorithm":[19,85,146],"demonstrates":[20],"superior":[21],"robustness":[22],"in":[23,44,134],"notation=\"LaTeX\">$\\alpha$</tex-math></inline-formula>-stable":[27,65],"noise":[28,55,59,137],"environments":[29,138],"(<inline-formula":[30,67],"notation=\"LaTeX\">$1&lt;":[33],"\\alpha":[34,71],"\\leq":[35,72],"2$</tex-math></inline-formula>)":[36],"through":[37],"effective":[38],"utilization":[39],"of":[40,107,113,142],"low-order":[41],"moment":[42],"hidden":[43],"robust":[45],"loss":[46],"functions.":[47],"Nevertheless,":[48],"its":[49,108],"performance":[50],"degrades":[51],"significantly":[52],"when":[53],"processing":[54],"input":[56],"or":[57],"additive":[58],"characterized":[60],"by":[61],"processes":[66],"notation=\"LaTeX\">$0&lt;":[70],"1$</tex-math></inline-formula>).":[73],"To":[74],"overcome":[75],"these":[76],"limitations,":[77],"we":[78],"propose":[79],"a":[80],"novel":[81],"fractional-order":[82,89,117],"NSPN":[83],"(FoNSPN)":[84],"that":[86],"incorporates":[87],"stochastic":[90],"gradient":[91],"descent":[92],"(FoSGD)":[93],"method":[94],"into":[95],"MPE":[97],"framework.":[98],"Additionally,":[99],"this":[100],"paper":[101],"also":[102],"analyzes":[103],"convergence":[105],"range":[106],"step-size,":[109],"theoretical":[111,125],"domain":[112],"values":[114],"for":[115],"notation=\"LaTeX\">$\\beta$</tex-math></inline-formula>,":[121],"and":[122],"establishes":[123],"steady-state":[126],"square":[128],"deviation":[129],"(MSD)":[130],"model.":[131],"Simulations":[132],"conducted":[133],"diverse":[135],"impulsive":[136],"confirm":[139],"superiority":[141],"proposed":[144],"FoNSPN":[145],"against":[147],"existing":[148],"state-of-the-art":[149],"algorithms.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-12-11T00:00:00"}