{"id":"https://openalex.org/W2050183293","doi":"https://doi.org/10.1109/tsmc.1971.4308288","title":"Linear Estimation in an Unknown Quasi-Stationary Environment","display_name":"Linear Estimation in an Unknown Quasi-Stationary Environment","publication_year":1971,"publication_date":"1971-07-01","ids":{"openalex":"https://openalex.org/W2050183293","doi":"https://doi.org/10.1109/tsmc.1971.4308288","mag":"2050183293"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.1971.4308288","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.1971.4308288","pdf_url":null,"source":{"id":"https://openalex.org/S76152103","display_name":"IEEE Transactions on Systems Man and Cybernetics","issn_l":"0018-9472","issn":["0018-9472","2168-2909"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Systems, Man, and Cybernetics","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/A5016527410","display_name":"P. Monsen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Peter Monsen","raw_affiliation_strings":["Bell Telephone Laboratories, Inc., Holmdel, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Telephone Laboratories, Inc., Holmdel, NJ, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5016527410"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8307,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.93803506,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"SMC-1","issue":"3","first_page":"216","last_page":"222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9959999918937683,"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"}},"topics":[{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9959999918937683,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9908999800682068,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9833999872207642,"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/rate-of-convergence","display_name":"Rate of convergence","score":0.6675025224685669},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6135825514793396},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5630335807800293},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5515904426574707},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5434456467628479},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5126306414604187},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5119541883468628},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.498457670211792},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.46148768067359924},{"id":"https://openalex.org/keywords/regression-function","display_name":"Regression function","score":0.46082863211631775},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.4526389539241791},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.438687264919281},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.4211609661579132},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3033876419067383},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.30188941955566406},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.2996771037578583},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09776058793067932},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.07899618148803711}],"concepts":[{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6675025224685669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6135825514793396},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5630335807800293},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5515904426574707},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5434456467628479},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5126306414604187},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5119541883468628},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.498457670211792},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.46148768067359924},{"id":"https://openalex.org/C2988035592","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression function","level":3,"score":0.46082863211631775},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.4526389539241791},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.438687264919281},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.4211609661579132},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3033876419067383},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.30188941955566406},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2996771037578583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09776058793067932},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.07899618148803711},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.1971.4308288","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.1971.4308288","pdf_url":null,"source":{"id":"https://openalex.org/S76152103","display_name":"IEEE Transactions on Systems Man and Cybernetics","issn_l":"0018-9472","issn":["0018-9472","2168-2909"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Systems, Man, and Cybernetics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6200000047683716,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1507360076","https://openalex.org/W1535810436","https://openalex.org/W1986077759","https://openalex.org/W1994616650","https://openalex.org/W2010586736","https://openalex.org/W2080621963","https://openalex.org/W2086322016","https://openalex.org/W2119072328","https://openalex.org/W2887248546","https://openalex.org/W4235448973","https://openalex.org/W6753500494"],"related_works":["https://openalex.org/W1907128005","https://openalex.org/W2514909387","https://openalex.org/W2120339885","https://openalex.org/W4309210394","https://openalex.org/W2084443610","https://openalex.org/W2048605715","https://openalex.org/W2032229253","https://openalex.org/W4246247437","https://openalex.org/W1982172364","https://openalex.org/W1604670796"],"abstract_inverted_index":{"Linear":[0],"estimation":[1,112],"under":[2],"a":[3,8,59,77,93],"minimum":[4,34],"mean-square-error":[5],"criterion":[6],"in":[7],"quasi-stationary":[9,111],"environment":[10],"is":[11,20,26,40,56],"considered.":[12],"A":[13,37],"generalized":[14],"form":[15],"of":[16,79,83,92,100],"the":[17,23,29,33,54,69,74,80,90,98],"Widrow-Hoff":[18],"algorithm":[19,55,70,87],"employed":[21],"for":[22,53,88],"estimation.":[24],"Performance":[25],"measured":[27],"by":[28],"excess":[30],"error":[31],"over":[32],"meansquare":[35],"error.":[36],"Gaussian":[38],"assumption":[39],"used":[41,66],"to":[42,67,107],"determine":[43,47],"this":[44],"performance":[45,75],"and":[46,58,72],"simple":[48],"bounds.":[49],"The":[50,85],"transient":[51],"solution":[52],"investigated":[57],"convergence":[60],"rate":[61,82],"determined.":[62],"These":[63],"results":[64],"are":[65],"optimize":[68],"parameters":[71],"bound":[73],"as":[76],"function":[78,96],"environmental":[81],"change.":[84],"Robbins-Monro":[86],"finding":[89],"root":[91],"linear":[94],"regression":[95],"suggests":[97],"use":[99],"fixed":[101],"step":[102],"size":[103],"stochastic":[104],"approximation":[105],"algorithms":[106],"solve":[108],"more":[109],"general":[110],"problems.":[113]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}