{"id":"https://openalex.org/W2568724943","doi":"https://doi.org/10.1109/cdc.2016.7799247","title":"Equilibrium distributions and stability analysis of Gaussian Process State Space Models","display_name":"Equilibrium distributions and stability analysis of Gaussian Process State Space Models","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2568724943","doi":"https://doi.org/10.1109/cdc.2016.7799247","mag":"2568724943"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2016.7799247","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7799247","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.06653","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Thomas Beckers","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Thomas Beckers","raw_affiliation_strings":["Chair of Information-oriented Control (ITR), Technical University of Munich, Munich"],"affiliations":[{"raw_affiliation_string":"Chair of Information-oriented Control (ITR), Technical University of Munich, Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":null,"display_name":"Sandra Hirche","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sandra Hirche","raw_affiliation_strings":["Chair of Information-oriented Control (ITR), Technical University of Munich, Munich"],"affiliations":[{"raw_affiliation_string":"Chair of Information-oriented Control (ITR), Technical University of Munich, Munich","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":3.5472,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.9408275,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"6355","last_page":"6361"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9660999774932861,"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/T11236","display_name":"Control Systems and Identification","score":0.9643999934196472,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6801000237464905},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5625},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.5322999954223633},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49000000953674316},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4880000054836273},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4796000123023987},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4205999970436096},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.39579999446868896},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.3952000141143799}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7432000041007996},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6801000237464905},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.576200008392334},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5625},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.5322999954223633},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49000000953674316},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4880000054836273},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4796000123023987},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4205999970436096},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.3952000141143799},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.37549999356269836},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3750999867916107},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.36660000681877136},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3215999901294708},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29170000553131104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2854999899864197},{"id":"https://openalex.org/C123954133","wikidata":"https://www.wikidata.org/wiki/Q7595775","display_name":"Stable process","level":3,"score":0.2797999978065491},{"id":"https://openalex.org/C116930293","wikidata":"https://www.wikidata.org/wiki/Q5265717","display_name":"Deterministic system (philosophy)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.265500009059906}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2016.7799247","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7799247","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1811.06653","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.06653","pdf_url":"https://arxiv.org/pdf/1811.06653","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.06653","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.06653","pdf_url":"https://arxiv.org/pdf/1811.06653","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1968749873","https://openalex.org/W2014208709","https://openalex.org/W2026915383","https://openalex.org/W2038581140","https://openalex.org/W2052551665","https://openalex.org/W2124609748","https://openalex.org/W2126877537","https://openalex.org/W2480512873","https://openalex.org/W2572801168","https://openalex.org/W6602145669","https://openalex.org/W6631830761","https://openalex.org/W6675740164","https://openalex.org/W6682906688","https://openalex.org/W6684451488"],"related_works":[],"abstract_inverted_index":{"Gaussian":[0],"Process":[1],"State":[2],"Space":[3],"Models":[4],"(GP-SSM)":[5],"are":[6],"a":[7,31,83,117],"data-driven":[8],"stochastic":[9],"model":[10],"class":[11],"suitable":[12,93],"to":[13],"represent":[14],"nonlinear":[15],"dynamics.":[16],"They":[17],"have":[18],"become":[19],"increasingly":[20],"popular":[21],"in":[22],"non-parametric":[23],"modeling":[24],"approaches":[25],"since":[26],"they":[27],"provide":[28],"not":[29],"only":[30],"prediction":[32],"of":[33,41,47,52,68,73,82,87],"the":[34,42,45,50,69,79,88,102],"system":[35,54],"behavior":[36],"but":[37],"also":[38],"an":[39],"accuracy":[40],"prediction.":[43],"For":[44],"application":[46],"these":[48],"models,":[49],"analysis":[51],"fundamental":[53],"properties":[55,67],"is":[56,76,92,109,120],"required.":[57],"In":[58],"this":[59],"paper,":[60],"we":[61,99],"analyze":[62],"equilibrium":[63,74],"distributions":[64,75],"and":[65,91,114],"stability":[66],"GP-SSM.":[70],"The":[71],"computation":[72],"based":[77],"on":[78],"numerical":[80],"solution":[81],"Fredholm":[84],"integral":[85],"equation":[86],"second":[89],"kind":[90],"for":[94],"any":[95],"covariance":[96,107],"function.":[97],"Besides,":[98],"show":[100],"that":[101],"GP-SSM":[103],"with":[104],"squared":[105],"exponential":[106],"function":[108],"always":[110],"mean":[111],"square":[112],"bounded":[113],"there":[115],"exists":[116],"set":[118],"which":[119],"positive":[121],"recurrent.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2017-01-13T00:00:00"}