{"id":"https://openalex.org/W2016765436","doi":"https://doi.org/10.1142/s0218127404010345","title":"NONLINEAR DYNAMICAL SYSTEM IDENTIFICATION FROM UNCERTAIN AND INDIRECT MEASUREMENTS","display_name":"NONLINEAR DYNAMICAL SYSTEM IDENTIFICATION FROM UNCERTAIN AND INDIRECT MEASUREMENTS","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W2016765436","doi":"https://doi.org/10.1142/s0218127404010345","mag":"2016765436"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127404010345","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404010345","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5021823169","display_name":"Henning U. Voss","orcid":"https://orcid.org/0000-0003-2811-2074"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"HENNING U. VOSS","raw_affiliation_strings":["Freiburg Center for Data Analysis and Modeling, University of Freiburg, 79104 Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"Freiburg Center for Data Analysis and Modeling, University of Freiburg, 79104 Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052831097","display_name":"Jens Timmer","orcid":"https://orcid.org/0000-0003-4517-1383"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"JENS TIMMER","raw_affiliation_strings":["Freiburg Center for Data Analysis and Modeling, University of Freiburg, 79104 Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"Freiburg Center for Data Analysis and Modeling, University of Freiburg, 79104 Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085207296","display_name":"J\u00fcrgen Kurths","orcid":"https://orcid.org/0000-0002-5926-4276"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J\u00dcRGEN KURTHS","raw_affiliation_strings":["Center for Dynamics of Complex Systems, University of Potsdam, 14469 Potsdam, Germany"],"affiliations":[{"raw_affiliation_string":"Center for Dynamics of Complex Systems, University of Potsdam, 14469 Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021823169"],"corresponding_institution_ids":["https://openalex.org/I161046081"],"apc_list":null,"apc_paid":null,"fwci":7.3852,"has_fulltext":false,"cited_by_count":297,"citation_normalized_percentile":{"value":0.97804193,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"14","issue":"06","first_page":"1905","last_page":"1933"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9908000230789185,"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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9908000230789185,"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"}},{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9814000129699707,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9747999906539917,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6378898620605469},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.5890789031982422},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5851384401321411},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.5707045197486877},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5605369210243225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5408023595809937},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5248354077339172},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5122939348220825},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.4490264356136322},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.44527605175971985},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42199116945266724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41328543424606323},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39973247051239014},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36447399854660034},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3140183091163635},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11103317141532898},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.10869422554969788},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.09581616520881653},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09191012382507324}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6378898620605469},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.5890789031982422},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5851384401321411},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.5707045197486877},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5605369210243225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5408023595809937},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5248354077339172},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5122939348220825},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.4490264356136322},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.44527605175971985},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42199116945266724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41328543424606323},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39973247051239014},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36447399854660034},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3140183091163635},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11103317141532898},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.10869422554969788},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.09581616520881653},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09191012382507324},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127404010345","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404010345","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.137.5259","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.5259","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://webber.physik.uni-freiburg.de/~jeti/papers/IJBC_edi.pdf","raw_type":"text"},{"id":"pmh:oai:kobv.de-opus4-uni-potsdam:15404","is_oa":false,"landing_page_url":"https://publishup.uni-potsdam.de/frontdoor/index/index/docId/15404","pdf_url":null,"source":{"id":"https://openalex.org/S4306400594","display_name":"publish.UP (University of Potsdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I176453806","host_organization_name":"University of Potsdam","host_organization_lineage":["https://openalex.org/I176453806"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":177,"referenced_works":["https://openalex.org/W75512829","https://openalex.org/W185885492","https://openalex.org/W200858817","https://openalex.org/W291003596","https://openalex.org/W304861154","https://openalex.org/W579208263","https://openalex.org/W608647825","https://openalex.org/W613224089","https://openalex.org/W833440777","https://openalex.org/W1486034269","https://openalex.org/W1502042205","https://openalex.org/W1507322379","https://openalex.org/W1517729176","https://openalex.org/W1531218787","https://openalex.org/W1531532259","https://openalex.org/W1532679390","https://openalex.org/W1540723801","https://openalex.org/W1540941301","https://openalex.org/W1544097513","https://openalex.org/W1549386224","https://openalex.org/W1552529795","https://openalex.org/W1567052132","https://openalex.org/W1572031236","https://openalex.org/W1575104486","https://openalex.org/W1963718895","https://openalex.org/W1964360919","https://openalex.org/W1964740397","https://openalex.org/W1965403106","https://openalex.org/W1965901723","https://openalex.org/W1967557690","https://openalex.org/W1967666158","https://openalex.org/W1970022570","https://openalex.org/W1971947347","https://openalex.org/W1974346839","https://openalex.org/W1975911643","https://openalex.org/W1976620978","https://openalex.org/W1977569390","https://openalex.org/W1978497463","https://openalex.org/W1979957032","https://openalex.org/W1980625815","https://openalex.org/W1982119348","https://openalex.org/W1984391316","https://openalex.org/W1984581891","https://openalex.org/W1985037657","https://openalex.org/W1985940938","https://openalex.org/W1986294597","https://openalex.org/W1987531565","https://openalex.org/W1988663218","https://openalex.org/W1990765697","https://openalex.org/W1992074539","https://openalex.org/W1992967649","https://openalex.org/W1994616650","https://openalex.org/W1995228946","https://openalex.org/W1997190589","https://openalex.org/W1998824936","https://openalex.org/W1999524646","https://openalex.org/W2000329349","https://openalex.org/W2000356602","https://openalex.org/W2001483689","https://openalex.org/W2001698084","https://openalex.org/W2006260142","https://openalex.org/W2007571690","https://openalex.org/W2007979658","https://openalex.org/W2008995486","https://openalex.org/W2009375605","https://openalex.org/W2009751220","https://openalex.org/W2011703323","https://openalex.org/W2012231377","https://openalex.org/W2015451024","https://openalex.org/W2017592766","https://openalex.org/W2018582985","https://openalex.org/W2019744409","https://openalex.org/W2022800953","https://openalex.org/W2024318216","https://openalex.org/W2027689606","https://openalex.org/W2029000318","https://openalex.org/W2029401646","https://openalex.org/W2030255580","https://openalex.org/W2030748132","https://openalex.org/W2031365860","https://openalex.org/W2033410765","https://openalex.org/W2035895971","https://openalex.org/W2037505161","https://openalex.org/W2037807929","https://openalex.org/W2039813141","https://openalex.org/W2044257293","https://openalex.org/W2044503966","https://openalex.org/W2045407900","https://openalex.org/W2045807947","https://openalex.org/W2049633694","https://openalex.org/W2050617311","https://openalex.org/W2054126693","https://openalex.org/W2056428637","https://openalex.org/W2056651346","https://openalex.org/W2057515481","https://openalex.org/W2063387759","https://openalex.org/W2065017532","https://openalex.org/W2065508260","https://openalex.org/W2065725171","https://openalex.org/W2068844879","https://openalex.org/W2069888879","https://openalex.org/W2072964096","https://openalex.org/W2073283839","https://openalex.org/W2075628905","https://openalex.org/W2075788737","https://openalex.org/W2075921810","https://openalex.org/W2076147293","https://openalex.org/W2076186907","https://openalex.org/W2077611006","https://openalex.org/W2078892469","https://openalex.org/W2080175185","https://openalex.org/W2081068198","https://openalex.org/W2082842500","https://openalex.org/W2083402998","https://openalex.org/W2085461338","https://openalex.org/W2091822727","https://openalex.org/W2095109112","https://openalex.org/W2098613108","https://openalex.org/W2102078856","https://openalex.org/W2105934661","https://openalex.org/W2107327484","https://openalex.org/W2110370029","https://openalex.org/W2113373687","https://openalex.org/W2118760499","https://openalex.org/W2121451933","https://openalex.org/W2121990344","https://openalex.org/W2122512809","https://openalex.org/W2128396151","https://openalex.org/W2132427836","https://openalex.org/W2136186628","https://openalex.org/W2137043637","https://openalex.org/W2141394518","https://openalex.org/W2147929628","https://openalex.org/W2150218489","https://openalex.org/W2156254905","https://openalex.org/W2158870666","https://openalex.org/W2159996541","https://openalex.org/W2160430373","https://openalex.org/W2161129698","https://openalex.org/W2162854795","https://openalex.org/W2164004138","https://openalex.org/W2170120409","https://openalex.org/W2214810577","https://openalex.org/W2219026468","https://openalex.org/W2261442997","https://openalex.org/W2315740996","https://openalex.org/W2476928429","https://openalex.org/W2489605225","https://openalex.org/W2492794003","https://openalex.org/W2565198181","https://openalex.org/W2571050459","https://openalex.org/W2797508167","https://openalex.org/W2798500587","https://openalex.org/W2996433891","https://openalex.org/W2999129308","https://openalex.org/W3022106996","https://openalex.org/W3042168128","https://openalex.org/W3143949042","https://openalex.org/W3146166473","https://openalex.org/W3187867541","https://openalex.org/W4205687564","https://openalex.org/W4206419526","https://openalex.org/W4206428854","https://openalex.org/W4210509282","https://openalex.org/W4210616753","https://openalex.org/W4230348196","https://openalex.org/W4236400251","https://openalex.org/W4237554871","https://openalex.org/W4241115065","https://openalex.org/W4244491820","https://openalex.org/W4246808543","https://openalex.org/W4250079830","https://openalex.org/W4252112222","https://openalex.org/W4252639814","https://openalex.org/W4294967943","https://openalex.org/W4297663678","https://openalex.org/W4299637698"],"related_works":["https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2330535098","https://openalex.org/W2377513064","https://openalex.org/W2952544653"],"abstract_inverted_index":{"We":[0,79],"review":[1],"the":[2,34,57,82,87,91,106,110],"problem":[3,51,108,111],"of":[4,16,84,90,112],"estimating":[5],"parameters":[6,69],"and":[7,68,109,122],"unobserved":[8],"trajectory":[9],"components":[10],"from":[11],"noisy":[12,43],"time":[13],"series":[14],"measurements":[15,44],"continuous":[17],"nonlinear":[18],"dynamical":[19],"systems.":[20],"It":[21],"is":[22,52],"first":[23],"shown":[24],"that":[25,30,53,60,73,81],"in":[26,118],"parameter":[27,48,96],"estimation":[28,97,124],"techniques":[29],"do":[31],"not":[32],"take":[33,102],"measurement":[35],"errors":[36],"explicitly":[37],"into":[38,103],"account,":[39],"like":[40],"regression":[41],"approaches,":[42,100],"can":[45,94],"produce":[46],"inaccurate":[47],"estimates.":[49],"Another":[50],"for":[54],"chaotic":[55],"systems":[56],"cost":[58,114],"functions":[59],"have":[61],"to":[62,65],"be":[63],"minimized":[64],"estimate":[66],"states":[67],"are":[70,116,127],"so":[71],"complex":[72,113],"common":[74],"optimization":[75],"routines":[76],"may":[77],"fail.":[78],"show":[80],"inclusion":[83],"information":[85],"about":[86],"time-continuous":[88],"nature":[89],"underlying":[92],"trajectories":[93],"improve":[95],"considerably.":[98],"Two":[99],"which":[101],"account":[104],"both":[105],"errors-in-variables":[107],"functions,":[115],"described":[117],"detail:":[119],"shooting":[120],"approaches":[121],"recursive":[123],"techniques.":[125],"Both":[126],"demonstrated":[128],"on":[129],"numerical":[130],"examples.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":19},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":26}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}