{"id":"https://openalex.org/W2139960514","doi":"https://doi.org/10.1109/tit.1956.1056800","title":"Final-value systems with Gaussian inputs","display_name":"Final-value systems with Gaussian inputs","publication_year":1956,"publication_date":"1956-09-01","ids":{"openalex":"https://openalex.org/W2139960514","doi":"https://doi.org/10.1109/tit.1956.1056800","mag":"2139960514"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1956.1056800","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1956.1056800","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":["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/A5007615875","display_name":"Richard C. Booton","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. Booton","raw_affiliation_strings":["Department of Electrical Eugineering, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Eugineering, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007615875"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":3.9575,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.93106535,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"3","first_page":"173","last_page":"175"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.972000002861023,"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/T11236","display_name":"Control Systems and Identification","score":0.972000002861023,"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/T10320","display_name":"Neural Networks and Applications","score":0.9498000144958496,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9401999711990356,"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/estimator","display_name":"Estimator","score":0.5678781270980835},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5341044664382935},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44530245661735535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3567952513694763},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3150045871734619},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2181481122970581},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.15505772829055786}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5678781270980835},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5341044664382935},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44530245661735535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3567952513694763},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3150045871734619},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2181481122970581},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.15505772829055786}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1956.1056800","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1956.1056800","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"A":[0],"final-value":[1],"system":[2,48,82,94,129,157],"controls":[3],"a":[4,11,25,76,93,101,128,185],"response":[5,34,56,122,172],"variable":[6],"<tex":[7,14,28,36,50,57,84,116,145],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,15,29,37,51,58,85,117,146],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r(t)</tex>":[9],"over":[10],"time":[12],"interval":[13],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(O,T)</tex>":[16],"with":[17,138],"the":[18,22,32,47,54,70,81,110,120,124,139,143,159,163,167,170,176,182,189,192],"objective":[19],"of":[20,42,69,96,119,166,181,184,188,191],"minimizing":[21],"difference":[23,144],"between":[24],"desired":[26,55,121,171],"value":[27,35,78],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\rho</tex>":[30,59],"and":[31,46,53,123,137,169,175],"final":[33],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r(T)</tex>":[38],".":[39,88,150],"An":[40],"ensemble":[41],"situations":[43],"is":[44,104,158,173,179],"considered,":[45],"input":[49,111,168],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i(t)</tex>":[52],"are":[60,64],"random":[61],"variables":[62],"that":[63,92,155],"statistically":[65],"related.":[66],"Physical":[67],"limitations":[68],"element":[71],"being":[72],"controlled":[73],"result":[74],"in":[75,127,133],"maximum":[77],"constraint":[79],"on":[80],"velocity":[83,130],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r\\prime":[86],"(t)</tex>":[87],"Earlier":[89],"results":[90,126],"suggest":[91],"consisting":[95],"an":[97,114],"estimator":[98,108],"followed":[99],"by":[100],"\"bang-bang\"":[102],"servo":[103,125],"approximately":[105],"optimum.":[106],"The":[107,151],"uses":[109],"to":[112],"produce":[113],"estimate":[115],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\rho^{\\ast}</tex>":[118],"as":[131,135,142],"large":[132],"magnitude":[134,190],"possible":[136],"same":[140],"sign":[141],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\rho^{\\ast}":[147],"-":[148],"r</tex>":[149],"present":[152],"paper":[153],"shows":[154],"this":[156],"true":[160],"optimum":[161],"when":[162],"joint":[164],"distribution":[165],"Gaussian":[174],"error":[177],"criterion":[178],"minimization":[180],"average":[183],"nondecreasing":[186],"function":[187],"error.":[193]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}