{"id":"https://openalex.org/W3128001846","doi":"https://doi.org/10.1109/tit.2021.3050342","title":"Nonstationary Gauss-Markov Processes: Parameter Estimation and Dispersion","display_name":"Nonstationary Gauss-Markov Processes: Parameter Estimation and Dispersion","publication_year":2021,"publication_date":"2021-02-10","ids":{"openalex":"https://openalex.org/W3128001846","doi":"https://doi.org/10.1109/tit.2021.3050342","mag":"3128001846"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3050342","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3050342","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1907.00304","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029942376","display_name":"Peida Tian","orcid":"https://orcid.org/0000-0003-3665-8173"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peida Tian","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":"https://orcid.org/0000-0003-3665-8173","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001633086","display_name":"Victoria Kostina","orcid":"https://orcid.org/0000-0002-2406-7440"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Victoria Kostina","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-2406-7440","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1399,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51985945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"67","issue":"4","first_page":"2426","last_page":"2449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9994999766349792,"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9994999766349792,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3807486295700073},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3361761271953583},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3352966606616974},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3242855668067932},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25986671447753906}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3807486295700073},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3361761271953583},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3352966606616974},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3242855668067932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25986671447753906}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2021.3050342","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3050342","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1907.00304","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.00304","pdf_url":"https://arxiv.org/pdf/1907.00304","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"},{"id":"pmh:oai:authors.library.caltech.edu:108012","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/108012/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1907.00304","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.00304","pdf_url":"https://arxiv.org/pdf/1907.00304","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":[{"id":"https://openalex.org/G2580377013","display_name":null,"funder_award_id":"CCF-1751356","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":93,"referenced_works":["https://openalex.org/W105181866","https://openalex.org/W1484170624","https://openalex.org/W1608472120","https://openalex.org/W1881945330","https://openalex.org/W1965324089","https://openalex.org/W1975994995","https://openalex.org/W1978432233","https://openalex.org/W1980656704","https://openalex.org/W1990992471","https://openalex.org/W2003848332","https://openalex.org/W2005447187","https://openalex.org/W2017379196","https://openalex.org/W2019646731","https://openalex.org/W2028488313","https://openalex.org/W2029910124","https://openalex.org/W2030080040","https://openalex.org/W2038876117","https://openalex.org/W2045463928","https://openalex.org/W2052690615","https://openalex.org/W2059120410","https://openalex.org/W2083263610","https://openalex.org/W2091369032","https://openalex.org/W2097645910","https://openalex.org/W2100541918","https://openalex.org/W2106864314","https://openalex.org/W2109400143","https://openalex.org/W2110478863","https://openalex.org/W2114715837","https://openalex.org/W2128505914","https://openalex.org/W2132105090","https://openalex.org/W2134392502","https://openalex.org/W2134723731","https://openalex.org/W2137243344","https://openalex.org/W2138428663","https://openalex.org/W2138605525","https://openalex.org/W2143270289","https://openalex.org/W2143648696","https://openalex.org/W2145072343","https://openalex.org/W2148986322","https://openalex.org/W2153815969","https://openalex.org/W2156216606","https://openalex.org/W2157076370","https://openalex.org/W2158395931","https://openalex.org/W2158566595","https://openalex.org/W2159649593","https://openalex.org/W2163714951","https://openalex.org/W2166571310","https://openalex.org/W2166965702","https://openalex.org/W2169249327","https://openalex.org/W2196937749","https://openalex.org/W2210387432","https://openalex.org/W2249746297","https://openalex.org/W2254578071","https://openalex.org/W2312497442","https://openalex.org/W2313470939","https://openalex.org/W2313953460","https://openalex.org/W2321541861","https://openalex.org/W2762498633","https://openalex.org/W2798949107","https://openalex.org/W2885546979","https://openalex.org/W2903088609","https://openalex.org/W2912099989","https://openalex.org/W2941237017","https://openalex.org/W2949470205","https://openalex.org/W2962915224","https://openalex.org/W2963412706","https://openalex.org/W2972915637","https://openalex.org/W2976432654","https://openalex.org/W2981735749","https://openalex.org/W3007035353","https://openalex.org/W3015420945","https://openalex.org/W3098376640","https://openalex.org/W3098926852","https://openalex.org/W3099463922","https://openalex.org/W3100528221","https://openalex.org/W3101293504","https://openalex.org/W3105659800","https://openalex.org/W3146166473","https://openalex.org/W4206196235","https://openalex.org/W4210869902","https://openalex.org/W4211030719","https://openalex.org/W4230644069","https://openalex.org/W4238674002","https://openalex.org/W4243833160","https://openalex.org/W4245338064","https://openalex.org/W4251333191","https://openalex.org/W4292483811","https://openalex.org/W4388534025","https://openalex.org/W6604201397","https://openalex.org/W6639294111","https://openalex.org/W6748537339","https://openalex.org/W6756955122","https://openalex.org/W6770028373"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W4391913857"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"a":[3,23,46,65,91,114],"precise":[4],"error":[5,209],"analysis":[6],"for":[7,113,132,155],"the":[8,21,98,102,118,124,130,142,147,156,166,172,179,193,197,204],"maximum":[9,173],"likelihood":[10],"estimate":[11],"\u00e2_(ML)(u":[12],"<sub":[13,27,35,60],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,17,28,31,36,42,61,71,86],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[15,29,37],"<sup":[16,30,41,70,85],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[18,32],")":[19],"of":[20,101,117,120,135,192,196,206],"parameter":[22],"given":[24,145],"samples":[25],"u":[26],"=":[33,51,63],"(u":[34],",":[38],"...,":[39],"u_n)":[40],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sup>":[43,72],"drawn":[44],"from":[45],"nonstationary":[47,136,167],"Gauss-Markov":[48,137,159],"process":[49],"U_i":[50],"aU_(i-1)":[52],"+":[53],"Z)_i,":[54],"i":[55],"\u2265":[56],"1,":[57,67],"where":[58],"U":[59],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[62],"0,":[64],">":[66],"and":[68,82,178,200],"Zi":[69],"s":[73],"are":[74,183],"independent":[75],"Gaussian":[76],"random":[77],"variables":[78],"with":[79],"zero":[80],"mean":[81],"variance":[83],"\u03c3":[84],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[87],".":[88],"We":[89,122,139],"show":[90,140],"tight":[92,111],"nonasymptotic":[93],"exponentially":[94],"decaying":[95],"bound":[96,109,127],"on":[97,190],"tail":[99],"probability":[100],"estimation":[103,126,208],"error.":[104],"Unlike":[105],"previous":[106],"works,":[107],"our":[108,207],"is":[110,144],"already":[112],"sample":[115],"size":[116],"order":[119],"hundreds.":[121],"apply":[123],"new":[125,201],"to":[128],"find":[129],"dispersion":[131,143],"lossy":[133],"compression":[134],"sources.":[138],"that":[141,151,187],"by":[146,185],"same":[148],"integral":[149],"formula":[150],"we":[152],"derived":[153],"previously":[154],"asymptotically":[157],"stationary":[158],"sources,":[160],"i.e.,":[161],"|a|<;1.":[162],"New":[163],"ideas":[164],"in":[165,203],"case":[168],"include":[169],"separately":[170],"bounding":[171],"eigenvalue":[174],"(which":[175,182],"scales":[176],"exponentially)":[177],"other":[180],"eigenvalues":[181],"bounded":[184],"constants":[186],"depend":[188],"only":[189],"a)":[191],"covariance":[194],"matrix":[195],"source":[198],"sequence,":[199],"techniques":[202],"derivation":[205],"bound.":[210]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
