{"id":"https://openalex.org/W2004432665","doi":"https://doi.org/10.1080/00207170701216303","title":"Practical estimation of Volterra filters of arbitrary degree","display_name":"Practical estimation of Volterra filters of arbitrary degree","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2004432665","doi":"https://doi.org/10.1080/00207170701216303","mag":"2004432665"},"language":"en","primary_location":{"id":"doi:10.1080/00207170701216303","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701216303","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","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/A5008271568","display_name":"Tony J. Dodd","orcid":"https://orcid.org/0000-0001-6820-4526"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"T. J. Dodd","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield S1 3JD, UK","Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield, S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield, S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111628253","display_name":"Yufeng Wan","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Y. Wan","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield S1 3JD, UK","Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield, S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield, S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079339747","display_name":"P. Drezet","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"P. Drezet","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield S1 3JD, UK","Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield, S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield, S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042852708","display_name":"Robert F. Harrison","orcid":"https://orcid.org/0000-0002-9323-8637"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"R. F. Harrison","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield S1 3JD, UK","Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield, S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering , The University of Sheffield , Sheffield, S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5008271568"],"corresponding_institution_ids":["https://openalex.org/I91136226"],"apc_list":null,"apc_paid":null,"fwci":1.253,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.78426157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"80","issue":"6","first_page":"908","last_page":"918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11236","display_name":"Control Systems and Identification","score":0.9998999834060669,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.8230045437812805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5955045223236084},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5622668862342834},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.559822142124176},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5431067943572998},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.49598369002342224},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4720657169818878},{"id":"https://openalex.org/keywords/volterra-series","display_name":"Volterra series","score":0.4504399001598358},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.42587989568710327},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.41749921441078186},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40336373448371887},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31694069504737854},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.28400206565856934},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2389380931854248},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23475134372711182},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15153923630714417},{"id":"https://openalex.org/keywords/data-modeling","display_name":"Data modeling","score":0.08715096116065979}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.8230045437812805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5955045223236084},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5622668862342834},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.559822142124176},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5431067943572998},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.49598369002342224},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4720657169818878},{"id":"https://openalex.org/C2778532037","wikidata":"https://www.wikidata.org/wiki/Q3957891","display_name":"Volterra series","level":3,"score":0.4504399001598358},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.42587989568710327},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.41749921441078186},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40336373448371887},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31694069504737854},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.28400206565856934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2389380931854248},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23475134372711182},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15153923630714417},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.08715096116065979},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207170701216303","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701216303","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320342","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W135764817","https://openalex.org/W1537662695","https://openalex.org/W1568892534","https://openalex.org/W1604938182","https://openalex.org/W1629040618","https://openalex.org/W2012098495","https://openalex.org/W2015904350","https://openalex.org/W2018366188","https://openalex.org/W2043477928","https://openalex.org/W2045173605","https://openalex.org/W2046373728","https://openalex.org/W2052398345","https://openalex.org/W2065902930","https://openalex.org/W2108930555","https://openalex.org/W2119043701","https://openalex.org/W2131985863","https://openalex.org/W2141038809","https://openalex.org/W2146766088","https://openalex.org/W2147398347","https://openalex.org/W2156512439","https://openalex.org/W2160068178","https://openalex.org/W2160442460","https://openalex.org/W2169692087","https://openalex.org/W2170076406","https://openalex.org/W2537909172","https://openalex.org/W4298876635"],"related_works":["https://openalex.org/W2374023116","https://openalex.org/W4299118182","https://openalex.org/W4285290579","https://openalex.org/W1986863144","https://openalex.org/W3134083315","https://openalex.org/W2018264451","https://openalex.org/W2128584444","https://openalex.org/W183296071","https://openalex.org/W2896419989","https://openalex.org/W2119865606"],"abstract_inverted_index":{"Generalized":[0],"Fock":[1],"spaces":[2,29],"(GFS)":[3],"were":[4],"proposed":[5],"some":[6],"time":[7],"ago":[8],"as":[9,123],"a":[10,22,33,56,157,160,167,199,212],"general":[11],"framework":[12,35,58,207],"for":[13,36,163],"non-linear":[14],"system":[15,146],"identification":[16,147],"and":[17,41,49,79,181,197,211],"signal":[18],"analysis.":[19],"Corresponding":[20],"to":[21,102,144,208],"particular":[23,152,161],"class":[24],"of":[25,39,68,85,114,132,141,151,159,173,189,201,216,219],"reproducing":[26,170],"kernel":[27],"Hubert":[28],"(RKHS)":[30],"they":[31],"provide":[32],"natural":[34],"the":[37,65,103,108,118,124,139,145,174,187,190,194,205,217],"estimation":[38,67,218],"continuous-":[40],"discrete-time":[42],"Volterra":[43,178,191],"filters":[44],"(VF).":[45],"Whilst":[46],"both":[47],"finite":[48,94],"infinite":[50,69],"degree":[51,70,87],"VF":[52,84,105,164],"are":[53,98,154],"treated":[54],"in":[55,117],"single":[57],"using":[59],"GFS":[60,162,206],"an":[61],"open":[62],"question":[63],"is":[64,77,81,112],"practical":[66],"VF.":[71,220],"In":[72],"this":[73,75,142],"paper":[74,136],"problem":[76],"resolved":[78],"it":[80],"shown":[82],"how":[83],"arbitrary":[86],"(including":[88],"infinite)":[89],"can":[90],"be":[91],"computed":[92],"with":[93],"resources.":[95],"The":[96],"solutions":[97],"global":[99],"best":[100],"approximations":[101],"entire":[104],"based":[106],"on":[107],"available":[109],"data.":[110],"Use":[111],"made":[113,155],"recent":[115],"advances":[116],"machine":[119],"learning":[120],"community,":[121],"such":[122],"support":[125],"vector":[126],"machine,":[127],"which":[128,165,185],"make":[129],"extensive":[130],"use":[131],"RKHS":[133,182,195],"ideas.":[134],"This":[135],"also":[137],"highlights":[138],"importance":[140],"work":[143],"community.":[148],"A":[149],"number":[150],"contributions":[153],"including":[156],"derivation":[158],"permits":[166],"simply":[168],"computable":[169],"kernel,":[171],"derivations":[172],"associated":[175],"mappings":[176],"between":[177],"parameter":[179,183],"space":[180,184],"permit":[186],"extraction":[188],"parameters":[192],"from":[193],"approximation":[196],"solve":[198],"set":[200],"\u201cfree\u201d":[202],"parameters,":[203],"extending":[204],"include":[209],"regularization":[210],"detailed":[213],"simulation-based":[214],"comparison":[215]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}