{"id":"https://openalex.org/W2014265599","doi":"https://doi.org/10.1109/tits.2014.2347415","title":"A Macroscopic Traffic Data-Assimilation Framework Based on the Fourier\u2013Galerkin Method and Minimax Estimation","display_name":"A Macroscopic Traffic Data-Assimilation Framework Based on the Fourier\u2013Galerkin Method and Minimax Estimation","publication_year":2014,"publication_date":"2014-09-17","ids":{"openalex":"https://openalex.org/W2014265599","doi":"https://doi.org/10.1109/tits.2014.2347415","mag":"2014265599"},"language":"en","primary_location":{"id":"doi:10.1109/tits.2014.2347415","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tits.2014.2347415","pdf_url":null,"source":{"id":"https://openalex.org/S144771191","display_name":"IEEE Transactions on Intelligent Transportation Systems","issn_l":"1524-9050","issn":["1524-9050","1558-0016"],"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 Intelligent Transportation 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/A5036461550","display_name":"Tigran Tchrakian","orcid":null},"institutions":[{"id":"https://openalex.org/I4210145784","display_name":"IBM Research - Ireland","ror":"https://ror.org/04jnxr720","country_code":"IE","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210145784"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Tigran T. Tchrakian","raw_affiliation_strings":["IBM Research, Dublin, Ireland"],"affiliations":[{"raw_affiliation_string":"IBM Research, Dublin, Ireland","institution_ids":["https://openalex.org/I4210145784"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042402060","display_name":"Sergiy Zhuk","orcid":"https://orcid.org/0000-0002-0956-8909"},"institutions":[{"id":"https://openalex.org/I4210145784","display_name":"IBM Research - Ireland","ror":"https://ror.org/04jnxr720","country_code":"IE","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210145784"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Sergiy Zhuk","raw_affiliation_strings":["IBM Research, Dublin, Ireland"],"affiliations":[{"raw_affiliation_string":"IBM Research, Dublin, Ireland","institution_ids":["https://openalex.org/I4210145784"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036461550"],"corresponding_institution_ids":["https://openalex.org/I4210145784"],"apc_list":null,"apc_paid":null,"fwci":3.6518,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.92901816,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"1","first_page":"452","last_page":"464"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","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"}},"topics":[{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","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/T11371","display_name":"Wind and Air Flow Studies","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9779000282287598,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.674762487411499},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6608235836029053},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.5602806210517883},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5550042390823364},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.5383345484733582},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.529560387134552},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5233444571495056},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5174387097358704},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5136734843254089},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4619576930999756},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4430393576622009},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.439864844083786},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.41918373107910156},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32834434509277344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3280123472213745},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19253253936767578},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1738644242286682},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09309461712837219}],"concepts":[{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.674762487411499},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6608235836029053},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.5602806210517883},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5550042390823364},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.5383345484733582},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.529560387134552},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5233444571495056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5174387097358704},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5136734843254089},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4619576930999756},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4430393576622009},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.439864844083786},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.41918373107910156},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32834434509277344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3280123472213745},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19253253936767578},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1738644242286682},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09309461712837219},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tits.2014.2347415","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tits.2014.2347415","pdf_url":null,"source":{"id":"https://openalex.org/S144771191","display_name":"IEEE Transactions on Intelligent Transportation Systems","issn_l":"1524-9050","issn":["1524-9050","1558-0016"],"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 Intelligent Transportation Systems","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":29,"referenced_works":["https://openalex.org/W16548326","https://openalex.org/W1500191616","https://openalex.org/W1514578609","https://openalex.org/W1536111662","https://openalex.org/W1589702657","https://openalex.org/W1635622277","https://openalex.org/W1965186506","https://openalex.org/W1967633238","https://openalex.org/W1968719911","https://openalex.org/W2010685672","https://openalex.org/W2011504567","https://openalex.org/W2037141248","https://openalex.org/W2051241238","https://openalex.org/W2053110557","https://openalex.org/W2090360015","https://openalex.org/W2093921901","https://openalex.org/W2095515828","https://openalex.org/W2095797625","https://openalex.org/W2126150914","https://openalex.org/W2127520982","https://openalex.org/W2156145130","https://openalex.org/W2157916375","https://openalex.org/W2167999909","https://openalex.org/W2169991130","https://openalex.org/W2298541619","https://openalex.org/W6600645789","https://openalex.org/W6678929640","https://openalex.org/W6683030227","https://openalex.org/W6697460077"],"related_works":["https://openalex.org/W2016058626","https://openalex.org/W2474724840","https://openalex.org/W2895916002","https://openalex.org/W1814049089","https://openalex.org/W1977348009","https://openalex.org/W2369683208","https://openalex.org/W2084836983","https://openalex.org/W2025983798","https://openalex.org/W2162026849","https://openalex.org/W2394687667"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,62],"propose":[4],"a":[5,16,34,39,47,55,89,101,131,143],"new":[6],"framework":[7],"for":[8,58,72,125],"macroscopic":[9,40,94],"traffic":[10,43,149],"state":[11,30,70],"estimation.":[12,31],"Our":[13],"approach":[14,99],"is":[15],"robust":[17],"\u201cdiscretize\u201d":[18],"then":[19],"\u201coptimize\u201d":[20],"strategy,":[21],"based":[22],"on":[23],"the":[24,59,64,69,73,81,84,92,137,147],"Fourier-Galerkin":[25,35,85],"projection":[26,60],"method":[27,66,135],"and":[28,114],"minimax":[29,65],"We":[32,96,121],"assign":[33],"reduced":[36,74],"model":[37,41,75],"to":[38,67,142],"of":[42,83,91,133,146],"flow,":[44],"described":[45],"by":[46],"hyperbolic":[48],"partial":[49],"differential":[50],"equation.":[51],"Taking":[52],"into":[53],"account":[54],"priori":[56],"estimates":[57],"error,":[61],"apply":[63],"construct":[68],"estimate":[71,82],"that":[76,104],"gives":[77],"us,":[78],"in":[79,118],"turn,":[80],"coefficients":[86],"associated":[87],"with":[88,100],"solution":[90],"original":[93],"model.":[95,151],"illustrate":[97],"our":[98,126,134],"numerical":[102],"example":[103],"demonstrates":[105],"its":[106],"shock":[107],"capturing":[108],"capability":[109],"using":[110],"only":[111],"sparse":[112],"measurements":[113],"under":[115],"high":[116],"uncertainty":[117],"initial":[119],"conditions.":[120],"present":[122],"implementation":[123],"details":[124],"algorithm,":[127],"as":[128,130],"well":[129],"comparison":[132],"against":[136],"ensemble":[138],"Kalman":[139],"filter":[140],"applied":[141],"\u201clocal\u201d":[144],"discretization":[145],"same":[148],"flow":[150]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
