{"id":"https://openalex.org/W3100014800","doi":"https://doi.org/10.1007/s00498-015-0154-1","title":"Nonlinear filtering via stochastic PDE projection on mixture manifolds in $$L^2$$ L 2 direct metric","display_name":"Nonlinear filtering via stochastic PDE projection on mixture manifolds in $$L^2$$ L 2 direct metric","publication_year":2015,"publication_date":"2015-12-08","ids":{"openalex":"https://openalex.org/W3100014800","doi":"https://doi.org/10.1007/s00498-015-0154-1","mag":"3100014800"},"language":"en","primary_location":{"id":"doi:10.1007/s00498-015-0154-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00498-015-0154-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00498-015-0154-1.pdf","source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00498-015-0154-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031520227","display_name":"John Armstrong","orcid":"https://orcid.org/0000-0002-4232-9555"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"John Armstrong","raw_affiliation_strings":["Department of Mathematics, King\u2019s College, London, UK","Department of Mathematics, King's College, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King\u2019s College, London, UK","institution_ids":["https://openalex.org/I183935753"]},{"raw_affiliation_string":"Department of Mathematics, King's College, London, UK","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005254246","display_name":"Damiano Brigo","orcid":"https://orcid.org/0000-0003-1636-8654"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Damiano Brigo","raw_affiliation_strings":["Department of Mathematics, Imperial College, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College, London, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005254246"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":3.5745,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.93172548,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"28","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.983299970626831,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9811999797821045,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7627757787704468},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5694301724433899},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.5466055870056152},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5235352516174316},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48839038610458374},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4753248989582062},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4461379051208496},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4213102459907532},{"id":"https://openalex.org/keywords/filtering-problem","display_name":"Filtering problem","score":0.4131205677986145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.358642578125},{"id":"https://openalex.org/keywords/filter-design","display_name":"Filter design","score":0.3288625478744507},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2651326656341553},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15745946764945984}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7627757787704468},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5694301724433899},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.5466055870056152},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5235352516174316},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48839038610458374},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4753248989582062},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4461379051208496},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4213102459907532},{"id":"https://openalex.org/C41614226","wikidata":"https://www.wikidata.org/wiki/Q5449244","display_name":"Filtering problem","level":4,"score":0.4131205677986145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.358642578125},{"id":"https://openalex.org/C22597639","wikidata":"https://www.wikidata.org/wiki/Q5449227","display_name":"Filter design","level":3,"score":0.3288625478744507},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2651326656341553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15745946764945984},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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":4,"locations":[{"id":"doi:10.1007/s00498-015-0154-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00498-015-0154-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00498-015-0154-1.pdf","source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:openaire/439861dd-667a-4aa8-8d5c-c4c6638ea54c","is_oa":true,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/439861dd-667a-4aa8-8d5c-c4c6638ea54c","pdf_url":null,"source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Armstrong, J & Brigo, D 2016, 'Nonlinear filtering via stochastic PDE projection on mixture manifolds in L 2 direct metric', MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, vol. 28, no. 1, 5, pp. 1-33. https://doi.org/10.1007/s00498-015-0154-1","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/439861dd-667a-4aa8-8d5c-c4c6638ea54c","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=84949560349&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Armstrong , J &amp; Brigo , D 2016 , ' Nonlinear filtering via stochastic PDE projection on mixture manifolds in L 2 direct metric ' , MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS , vol. 28 , no. 1 , 5 , pp. 1-33 . https://doi.org/10.1007/s00498-015-0154-1","raw_type":"article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/30130","is_oa":true,"landing_page_url":"http://hdl.handle.net/10044/1/30130","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s00498-015-0154-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00498-015-0154-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00498-015-0154-1.pdf","source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3100014800.pdf","grobid_xml":"https://content.openalex.org/works/W3100014800.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W9651693","https://openalex.org/W179920635","https://openalex.org/W347146154","https://openalex.org/W585779234","https://openalex.org/W1490150974","https://openalex.org/W1520168181","https://openalex.org/W1532184046","https://openalex.org/W1573874356","https://openalex.org/W1575104486","https://openalex.org/W1579485993","https://openalex.org/W1986892149","https://openalex.org/W1998999025","https://openalex.org/W2003318329","https://openalex.org/W2024900789","https://openalex.org/W2026462166","https://openalex.org/W2036422857","https://openalex.org/W2045889823","https://openalex.org/W2073283839","https://openalex.org/W2074056953","https://openalex.org/W2077802959","https://openalex.org/W2077991515","https://openalex.org/W2080273507","https://openalex.org/W2081877251","https://openalex.org/W2082265352","https://openalex.org/W2094011292","https://openalex.org/W2095440665","https://openalex.org/W2099867508","https://openalex.org/W2116228907","https://openalex.org/W2122512809","https://openalex.org/W2134714495","https://openalex.org/W2136186628","https://openalex.org/W2139561597","https://openalex.org/W2152767074","https://openalex.org/W2154626663","https://openalex.org/W2156579302","https://openalex.org/W2209834891","https://openalex.org/W2218963353","https://openalex.org/W2478586622","https://openalex.org/W2799758885","https://openalex.org/W2802739963","https://openalex.org/W3101921698","https://openalex.org/W3102097014","https://openalex.org/W4206222179","https://openalex.org/W4231019034","https://openalex.org/W4231021340","https://openalex.org/W4235816940","https://openalex.org/W4297584681"],"related_works":["https://openalex.org/W2351452215","https://openalex.org/W2617963432","https://openalex.org/W3202199134","https://openalex.org/W1574341164","https://openalex.org/W4294164186","https://openalex.org/W2803811596","https://openalex.org/W3038506845","https://openalex.org/W2514619848","https://openalex.org/W2034367127","https://openalex.org/W4386452853"],"abstract_inverted_index":{"We":[0,64,103,129,169,192,214],"examine":[1],"some":[2],"differential":[3,32,59],"geometric":[4,60],"approaches":[5],"to":[6,10,62,69,237],"finding":[7],"approximate":[8,54],"solutions":[9],"the":[11,26,37,58,75,84,94,100,108,111,119,122,137,140,156,162,176,189,230,233,239],"continuous":[12],"time":[13],"nonlinear":[14],"filtering":[15],"problem.":[16],"Our":[17],"primary":[18],"focus":[19],"is":[20,166,200],"a":[21,43,51,90,133,147,195,203,226],"new":[22,52,67,180,240],"projection":[23,71,87,143],"method":[24,92],"for":[25,110,121,132,151,202],"optimal":[27,190],"filter":[28,55,68,88,144,165,181,209,241],"infinite-dimensional":[29],"stochastic":[30],"partial":[31],"equation":[33],"(SPDE),":[34],"based":[35,56,73],"on":[36,42,57,74],"direct":[38],"$$L^2$$":[39,85,141,163],"metric":[40,78],"and":[41,79,82,118,161,210],"family":[44],"of":[45,97,136,178,207,225],"normal":[46],"mixtures.":[47],"This":[48],"results":[49],"in":[50,223,229],"finite-dimensional":[53],"approach":[61],"statistics.":[63],"compare":[65,83],"this":[66,179,208],"earlier":[70],"methods":[72],"Hellinger":[76],"distance/Fisher":[77],"exponential":[80],"families,":[81],"mixture":[86,138,142,154,164],"with":[89,93,146,188],"particle":[91],"same":[95],"number":[96],"parameters,":[98],"using":[99],"Levy":[101],"metric.":[102],"discuss":[104],"differences":[105],"between":[106],"projecting":[107],"SPDE":[109,120],"normalized":[112],"density,":[113],"known":[114,125],"as":[115,126],"Kushner\u2013Stratonovich":[116],"equation,":[117],"unnormalized":[123],"density":[124],"Zakai":[127],"equation.":[128],"prove":[130],"that":[131,173,199,222],"simple":[134],"choice":[135],"manifold":[139],"coincides":[145],"Galerkin":[148],"method,":[149],"whereas":[150],"more":[152,167],"general":[153],"manifolds":[155],"equivalence":[157],"does":[158],"not":[159],"hold":[160],"general.":[168],"study":[170],"particular":[171],"systems":[172],"may":[174],"illustrate":[175],"advantages":[177],"over":[182],"other":[183],"algorithms":[184],"when":[185],"comparing":[186],"outputs":[187],"filter.":[191],"finally":[193],"consider":[194],"specific":[196],"software":[197],"design":[198],"suited":[201],"numerically":[204],"efficient":[205],"implementation":[206],"provide":[211],"numerical":[212],"examples.":[213],"leverage":[215],"an":[216],"algebraic":[217],"ring":[218],"structure":[219,228],"by":[220],"proving":[221],"presence":[224],"given":[227],"system":[231],"coefficients":[232],"key":[234],"integrations":[235],"needed":[236],"implement":[238],"equations":[242],"can":[243],"be":[244],"executed":[245],"offline.":[246]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2020-11-23T00:00:00"}
