{"id":"https://openalex.org/W3094460945","doi":"https://doi.org/10.1109/taes.2020.3028487","title":"Nonlinear Filtering With a Polynomial Series of Gaussian Random Variables","display_name":"Nonlinear Filtering With a Polynomial Series of Gaussian Random Variables","publication_year":2020,"publication_date":"2020-10-23","ids":{"openalex":"https://openalex.org/W3094460945","doi":"https://doi.org/10.1109/taes.2020.3028487","mag":"3094460945"},"language":"en","primary_location":{"id":"doi:10.1109/taes.2020.3028487","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2020.3028487","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","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/A5002572323","display_name":"Simone Servadio","orcid":"https://orcid.org/0000-0001-6603-3858"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Simone Servadio","raw_affiliation_strings":["The University of Texas at Austin, Austin, TX, USA"],"affiliations":[{"raw_affiliation_string":"The University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052167629","display_name":"Renato Zanetti","orcid":"https://orcid.org/0000-0001-9669-7428"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Renato Zanetti","raw_affiliation_strings":["The University of Texas at Austin, Austin, TX, USA"],"affiliations":[{"raw_affiliation_string":"The University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076017664","display_name":"Brandon A. Jones","orcid":"https://orcid.org/0000-0003-3480-6320"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brandon A. Jones","raw_affiliation_strings":["The University of Texas at Austin, Austin, TX, USA"],"affiliations":[{"raw_affiliation_string":"The University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002572323"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":0.6633,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.76377304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"57","issue":"1","first_page":"647","last_page":"658"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9760000109672546,"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/mathematics","display_name":"Mathematics","score":0.648085355758667},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6086738109588623},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5720565915107727},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5273348093032837},{"id":"https://openalex.org/keywords/gaussian-filter","display_name":"Gaussian filter","score":0.5226975679397583},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.4849839210510254},{"id":"https://openalex.org/keywords/gaussian-function","display_name":"Gaussian function","score":0.43647825717926025},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.42349621653556824},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4135796129703522},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3744008541107178},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20838603377342224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.648085355758667},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6086738109588623},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5720565915107727},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5273348093032837},{"id":"https://openalex.org/C65892221","wikidata":"https://www.wikidata.org/wiki/Q1113935","display_name":"Gaussian filter","level":3,"score":0.5226975679397583},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.4849839210510254},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.43647825717926025},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.42349621653556824},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4135796129703522},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3744008541107178},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20838603377342224},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/taes.2020.3028487","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2020.3028487","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G141797481","display_name":null,"funder_award_id":"FA9550-18-1-0351","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W304861154","https://openalex.org/W1880751280","https://openalex.org/W1974537499","https://openalex.org/W2012368669","https://openalex.org/W2017952090","https://openalex.org/W2020383129","https://openalex.org/W2064756505","https://openalex.org/W2070898270","https://openalex.org/W2074878962","https://openalex.org/W2083402998","https://openalex.org/W2098613108","https://openalex.org/W2099867508","https://openalex.org/W2105934661","https://openalex.org/W2108001913","https://openalex.org/W2117614621","https://openalex.org/W2121990344","https://openalex.org/W2123487311","https://openalex.org/W2149842790","https://openalex.org/W2161358768","https://openalex.org/W2169409209","https://openalex.org/W2340001178","https://openalex.org/W2478708596","https://openalex.org/W2737395110","https://openalex.org/W2782072516","https://openalex.org/W2889709742","https://openalex.org/W2951980816","https://openalex.org/W3000413080","https://openalex.org/W3037316762","https://openalex.org/W3041866371","https://openalex.org/W3084552781","https://openalex.org/W4246139085","https://openalex.org/W6703832604","https://openalex.org/W6720551740","https://openalex.org/W6779732177","https://openalex.org/W6782825315"],"related_works":["https://openalex.org/W3205470106","https://openalex.org/W1978251635","https://openalex.org/W4220715471","https://openalex.org/W2104155200","https://openalex.org/W2609066529","https://openalex.org/W4295035285","https://openalex.org/W1977123013","https://openalex.org/W2082319654","https://openalex.org/W2171618211","https://openalex.org/W3084552781"],"abstract_inverted_index":{"Filters":[0],"relying":[1],"on":[2,34],"the":[3,8,12,15,24,31,35,40,43,58,61,90,104,107,110,134,139,142,145,148,157,162,167,174,191],"Gaussian":[4,32,53,71,123],"approximation":[5,124],"typically":[6,38],"incorporate":[7],"measurement":[9,16,101,108],"linearly,":[10],"i.e.,":[11,103],"value":[13,105],"of":[14,42,49,60,69,89,106,116,133,141,147,164],"is":[17,63,94,197],"premultiplied":[18],"by":[19,65],"a":[20,46,66,70,85,99,114,122,130],"matrix-valued":[21],"gain":[22],"in":[23,84,190],"state":[25,44,62],"update.":[26],"Nonlinear":[27],"filters":[28],"that":[29],"relax":[30],"assumption,":[33],"other":[36],"hand,":[37],"approximate":[39],"distribution":[41,59],"with":[45,125],"finite":[47],"sum":[48],"point":[50],"masses":[51],"or":[52],"distributions.":[54],"In":[55],"this":[56],"work,":[57],"approximated":[64],"polynomial":[67,100,115,203],"transformation":[68],"distribution,":[72],"allowing":[73],"for":[74,177],"all":[75],"moments,":[76],"central":[77],"and":[78,144,186],"raw,":[79],"to":[80,97,152,156,200],"be":[81],"rapidly":[82],"computed":[83],"closed":[86],"form.":[87],"Knowledge":[88],"higher":[91],"order":[92,140,146],"moments":[93],"then":[95],"employed":[96],"perform":[98],"update,":[102],"enters":[109],"update":[111,127,149],"function":[112],"as":[113],"arbitrary":[117],"order.":[118],"A":[119],"filter":[120],"employing":[121],"linear":[126],"is,":[128],"therefore,":[129],"special":[131],"case":[132],"proposed":[135],"algorithm":[136],"when":[137],"both":[138],"series":[143],"are":[150],"set":[151],"one:":[153],"it":[154,196],"reduces":[155],"extended":[158],"Kalman":[159],"filter.":[160],"At":[161],"cost":[163],"more":[165],"computations,":[166],"new":[168],"methodology":[169],"guarantees":[170],"performance":[171],"better":[172],"than":[173],"linear/Gaussian":[175],"approach":[176],"nonlinear":[178],"systems.":[179],"This":[180],"work":[181],"employs":[182],"monomial":[183],"basis":[184],"functions":[185],"Taylor":[187],"series,":[188],"developed":[189],"differential":[192],"algebra":[193],"framework,":[194],"but":[195],"readily":[198],"extendable":[199],"an":[201],"orthogonal":[202],"basis.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3}],"updated_date":"2026-03-02T08:37:19.008085","created_date":"2025-10-10T00:00:00"}