{"id":"https://openalex.org/W2590870493","doi":"https://doi.org/10.1109/tac.2017.2774444","title":"Gaussian Process Quadrature Moment Transform","display_name":"Gaussian Process Quadrature Moment Transform","publication_year":2017,"publication_date":"2017-11-17","ids":{"openalex":"https://openalex.org/W2590870493","doi":"https://doi.org/10.1109/tac.2017.2774444","mag":"2590870493"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2774444","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2774444","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic 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/A5020274843","display_name":"Jakub Pr\u00fcher","orcid":"https://orcid.org/0000-0002-5448-3760"},"institutions":[{"id":"https://openalex.org/I92715842","display_name":"University of West Bohemia","ror":"https://ror.org/040t43x18","country_code":"CZ","type":"education","lineage":["https://openalex.org/I92715842"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Jakub Pruher","raw_affiliation_strings":["New Technologies for the Information Society, European Centre of Excellence, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic"],"affiliations":[{"raw_affiliation_string":"New Technologies for the Information Society, European Centre of Excellence, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic","institution_ids":["https://openalex.org/I92715842"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024372115","display_name":"Ond\u0159ej Straka","orcid":"https://orcid.org/0000-0003-3066-5882"},"institutions":[{"id":"https://openalex.org/I92715842","display_name":"University of West Bohemia","ror":"https://ror.org/040t43x18","country_code":"CZ","type":"education","lineage":["https://openalex.org/I92715842"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Ondrej Straka","raw_affiliation_strings":["New Technologies for the Information Society, European Centre of Excellence, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic"],"affiliations":[{"raw_affiliation_string":"New Technologies for the Information Society, European Centre of Excellence, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic","institution_ids":["https://openalex.org/I92715842"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020274843"],"corresponding_institution_ids":["https://openalex.org/I92715842"],"apc_list":null,"apc_paid":null,"fwci":1.5602,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.86850686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"63","issue":"9","first_page":"2844","last_page":"2854"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9991000294685364,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9991000294685364,"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9968000054359436,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/clenshaw\u2013curtis-quadrature","display_name":"Clenshaw\u2013Curtis quadrature","score":0.7199492454528809},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.6241335868835449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6212306022644043},{"id":"https://openalex.org/keywords/tanh-sinh-quadrature","display_name":"Tanh-sinh quadrature","score":0.6162267327308655},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.5877129435539246},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.5487951040267944},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.525883138179779},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5183647274971008},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.48361316323280334},{"id":"https://openalex.org/keywords/gauss\u2013laguerre-quadrature","display_name":"Gauss\u2013Laguerre quadrature","score":0.4835188388824463},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.48044535517692566},{"id":"https://openalex.org/keywords/adaptive-quadrature","display_name":"Adaptive quadrature","score":0.47364938259124756},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.4626404345035553},{"id":"https://openalex.org/keywords/gauss\u2013hermite-quadrature","display_name":"Gauss\u2013Hermite quadrature","score":0.45120561122894287},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.45108091831207275},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4059205651283264},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3575270175933838},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.3494657576084137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26931172609329224},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.24797338247299194},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13694146275520325},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.12897413969039917},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11534035205841064},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08357056975364685},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.07719886302947998}],"concepts":[{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.7199492454528809},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.6241335868835449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6212306022644043},{"id":"https://openalex.org/C162046254","wikidata":"https://www.wikidata.org/wiki/Q7683194","display_name":"Tanh-sinh quadrature","level":5,"score":0.6162267327308655},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.5877129435539246},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.5487951040267944},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.525883138179779},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5183647274971008},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.48361316323280334},{"id":"https://openalex.org/C6866599","wikidata":"https://www.wikidata.org/wiki/Q4218412","display_name":"Gauss\u2013Laguerre quadrature","level":5,"score":0.4835188388824463},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.48044535517692566},{"id":"https://openalex.org/C184599523","wikidata":"https://www.wikidata.org/wiki/Q4680758","display_name":"Adaptive quadrature","level":4,"score":0.47364938259124756},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.4626404345035553},{"id":"https://openalex.org/C167590341","wikidata":"https://www.wikidata.org/wiki/Q5527850","display_name":"Gauss\u2013Hermite quadrature","level":5,"score":0.45120561122894287},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.45108091831207275},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4059205651283264},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3575270175933838},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.3494657576084137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26931172609329224},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.24797338247299194},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13694146275520325},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.12897413969039917},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11534035205841064},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08357056975364685},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.07719886302947998},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2017.2774444","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2774444","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1557325609","display_name":null,"funder_award_id":"GA15-12068S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W55912154","https://openalex.org/W88520345","https://openalex.org/W311952742","https://openalex.org/W561317618","https://openalex.org/W1003261049","https://openalex.org/W1558470758","https://openalex.org/W1593505867","https://openalex.org/W1746819321","https://openalex.org/W1996908140","https://openalex.org/W2007692097","https://openalex.org/W2051775893","https://openalex.org/W2054091988","https://openalex.org/W2055891640","https://openalex.org/W2065526349","https://openalex.org/W2077611006","https://openalex.org/W2095287147","https://openalex.org/W2098613108","https://openalex.org/W2098946742","https://openalex.org/W2099371695","https://openalex.org/W2104533781","https://openalex.org/W2105945651","https://openalex.org/W2110720940","https://openalex.org/W2119007379","https://openalex.org/W2120717581","https://openalex.org/W2121990344","https://openalex.org/W2126272934","https://openalex.org/W2137637613","https://openalex.org/W2138713746","https://openalex.org/W2146332636","https://openalex.org/W2152842312","https://openalex.org/W2167061265","https://openalex.org/W2179284380","https://openalex.org/W2185347192","https://openalex.org/W2294813034","https://openalex.org/W2337859546","https://openalex.org/W2470984501","https://openalex.org/W2486824498","https://openalex.org/W2515324445","https://openalex.org/W2515625217","https://openalex.org/W2545658386","https://openalex.org/W2964202371","https://openalex.org/W3103503690","https://openalex.org/W3104531771","https://openalex.org/W3140599801","https://openalex.org/W3171485246","https://openalex.org/W4211049957","https://openalex.org/W4232464081","https://openalex.org/W6615619314","https://openalex.org/W6675740164","https://openalex.org/W6679207738","https://openalex.org/W6685744914","https://openalex.org/W6686476780","https://openalex.org/W6703362890","https://openalex.org/W6726541495","https://openalex.org/W6729218549","https://openalex.org/W6786338897","https://openalex.org/W6796871250","https://openalex.org/W7026840405"],"related_works":["https://openalex.org/W2289189603","https://openalex.org/W4294281846","https://openalex.org/W2032097736","https://openalex.org/W4377005030","https://openalex.org/W3050590833","https://openalex.org/W4317584040","https://openalex.org/W2471455030","https://openalex.org/W2550867510","https://openalex.org/W4390128132","https://openalex.org/W4377968225"],"abstract_inverted_index":{"Computation":[0],"of":[1,3,46,64],"moments":[2],"transformed":[4],"random":[5,48,82],"variables":[6],"is":[7,38],"a":[8,41,81],"problem":[9],"appearing":[10],"in":[11,55],"many":[12],"engineering":[13],"applications.":[14],"The":[15],"current":[16],"methods":[17],"for":[18,32,43,52],"moment":[19,44,109],"transformation":[20,45,99],"are":[21],"mostly":[22],"based":[23],"on":[24,96],"the":[25,33,53,56,77,85,91,97,106,114],"classical":[26,115],"quadrature":[27,70],"rules,":[28],"which":[29,50,72],"cannot":[30],"account":[31],"approximation":[34],"errors.":[35],"Our":[36],"aim":[37],"to":[39,75],"design":[40],"method":[42],"Gaussian":[47,68],"variables,":[49],"accounts":[51],"error":[54],"numerically":[57],"computed":[58],"mean.":[59],"We":[60],"employ":[61],"an":[62],"instance":[63],"Bayesian":[65],"quadrature,":[66],"called":[67],"process":[69],"(GPQ),":[71],"allows":[73],"us":[74,89],"treat":[76],"integral":[78,86],"itself":[79],"as":[80],"variable,":[83],"where":[84],"variance":[87],"informs":[88],"about":[90],"incurred":[92],"integration":[93],"error.":[94],"Experiments":[95],"coordinate":[98],"and":[100],"nonlinear":[101],"filtering":[102],"examples":[103],"show":[104],"that":[105],"proposed":[107],"GPQ":[108],"transform":[110],"performs":[111],"better":[112],"than":[113],"transforms.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}