{"id":"https://openalex.org/W1987156218","doi":"https://doi.org/10.1137/s0363012902363920","title":"Approximate Nonlinear Filtering for a Two-Dimensional Diffusion with One-Dimensional Observations in a Low Noise Channel","display_name":"Approximate Nonlinear Filtering for a Two-Dimensional Diffusion with One-Dimensional Observations in a Low Noise Channel","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1987156218","doi":"https://doi.org/10.1137/s0363012902363920","mag":"1987156218"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012902363920","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012902363920","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://repositorio-aberto.up.pt/handle/10216/530","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022742288","display_name":"Paula Milheiro\u2013Oliveira","orcid":"https://orcid.org/0000-0003-4166-9379"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Paula Milheiro de Oliveira","raw_affiliation_strings":["Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, P-4200-465 Porto, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, P-4200-465 Porto, Portugal","institution_ids":["https://openalex.org/I182534213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109928480","display_name":"Jean Picard","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I198244214","display_name":"Universit\u00e9 Clermont Auvergne","ror":"https://ror.org/01a8ajp46","country_code":"FR","type":"education","lineage":["https://openalex.org/I198244214"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean Picard","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Appliqu\u00e9es (CNRS-UMR 6620), Universit\u00e9 Blaise Pascal, F-63177 Aubi\u00e8re Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Appliqu\u00e9es (CNRS-UMR 6620), Universit\u00e9 Blaise Pascal, F-63177 Aubi\u00e8re Cedex, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210155549"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109928480"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210155549"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.06545105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"41","issue":"6","first_page":"1801","last_page":"1819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9948999881744385,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9948999881744385,"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9751999974250793,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.95660001039505,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8233381509780884},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.690686821937561},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6547380089759827},{"id":"https://openalex.org/keywords/nonlinear-filter","display_name":"Nonlinear filter","score":0.6478014588356018},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5668385028839111},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5161410570144653},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.45765766501426697},{"id":"https://openalex.org/keywords/filtering-problem","display_name":"Filtering problem","score":0.447201669216156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44306570291519165},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.441528856754303},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.4380713999271393},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.430331826210022},{"id":"https://openalex.org/keywords/linear-filter","display_name":"Linear filter","score":0.4296855032444},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4241965115070343},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4043448269367218},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3325660824775696},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.328469455242157},{"id":"https://openalex.org/keywords/filter-design","display_name":"Filter design","score":0.3073391318321228},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16314131021499634},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.11628064513206482},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10039669275283813},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06904938817024231},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06644400954246521}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8233381509780884},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.690686821937561},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6547380089759827},{"id":"https://openalex.org/C137685913","wikidata":"https://www.wikidata.org/wiki/Q4316763","display_name":"Nonlinear filter","level":4,"score":0.6478014588356018},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5668385028839111},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5161410570144653},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45765766501426697},{"id":"https://openalex.org/C41614226","wikidata":"https://www.wikidata.org/wiki/Q5449244","display_name":"Filtering problem","level":4,"score":0.447201669216156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44306570291519165},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.441528856754303},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.4380713999271393},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.430331826210022},{"id":"https://openalex.org/C139722471","wikidata":"https://www.wikidata.org/wiki/Q2619517","display_name":"Linear filter","level":3,"score":0.4296855032444},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4241965115070343},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4043448269367218},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3325660824775696},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.328469455242157},{"id":"https://openalex.org/C22597639","wikidata":"https://www.wikidata.org/wiki/Q5449227","display_name":"Filter design","level":3,"score":0.3073391318321228},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16314131021499634},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.11628064513206482},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10039669275283813},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06904938817024231},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06644400954246521},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0363012902363920","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012902363920","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.3377","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.3377","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wwwlma.univ-bpclermont.fr/preprint/1999/10-99.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.498.7426","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.498.7426","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mathinfo.univ-bpclermont.fr/~picard/SIAM2003.pdf","raw_type":"text"},{"id":"pmh:oai:repositorio-aberto.up.pt:10216/530","is_oa":true,"landing_page_url":"https://repositorio-aberto.up.pt/handle/10216/530","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:repositorio-aberto.up.pt:10216/530","is_oa":true,"landing_page_url":"https://repositorio-aberto.up.pt/handle/10216/530","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1978672152","https://openalex.org/W1985034462","https://openalex.org/W2003793708","https://openalex.org/W2018028661","https://openalex.org/W2021279192","https://openalex.org/W2094970485","https://openalex.org/W2095156483","https://openalex.org/W2175593785","https://openalex.org/W4241742894","https://openalex.org/W4249557314"],"related_works":["https://openalex.org/W585779234","https://openalex.org/W1970684742","https://openalex.org/W2151194595","https://openalex.org/W2245414322","https://openalex.org/W2002521569","https://openalex.org/W2108391895","https://openalex.org/W2162050050","https://openalex.org/W2057112466","https://openalex.org/W2160916790","https://openalex.org/W2034367127"],"abstract_inverted_index":{"The":[0,95],"asymptotic":[1],"behavior":[2],"of":[3,15,35,45,97,106,113,115],"a":[4,28,42,57],"nonlinear":[5],"continuous":[6],"time":[7],"filtering":[8,80],"problem":[9],"is":[10,27,38,54,64,93,101,127],"studied":[11],"when":[12],"the":[13,16,25,36,51,79,90,98,104,107,111,116,119,123],"variance":[14],"observation":[17,124],"noise":[18,59,125],"tends":[19],"to":[20,68,83],"0.":[21],"We":[22],"suppose":[23],"that":[24,41,78],"signal":[26],"two-dimensional":[29],"process":[30],"from":[31],"which":[32],"only":[33,49],"one":[34],"components":[37],"noisy":[39],"and":[40,85,110],"one-dimensional":[43],"function":[44],"this":[46,70],"signal,":[47],"depending":[48],"on":[50],"unnoisy":[52],"component,":[53],"observed":[55],"in":[56,66],"low":[58],"channel.":[60],"An":[61],"approximate":[62,99],"filter":[63,100],"considered":[65],"order":[67,112],"solve":[69],"problem.":[71],"Under":[72],"some":[73],"detectability":[74],"assumptions,":[75],"we":[76],"prove":[77],"error":[81,117],"converges":[82],"0,":[84],"an":[86],"upper":[87],"bound":[88],"for":[89],"convergence":[91],"rate":[92],"given.":[94],"efficiency":[96,105],"compared":[102],"with":[103],"optimal":[108],"filter,":[109],"magnitude":[114],"between":[118],"two":[120],"filters,":[121],"as":[122],"vanishes,":[126],"obtained.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}