{"id":"https://openalex.org/W2018295752","doi":"https://doi.org/10.1109/tac.1968.1099025","title":"An innovations approach to least-squares estimation--Part I: Linear filtering in additive white noise","display_name":"An innovations approach to least-squares estimation--Part I: Linear filtering in additive white noise","publication_year":1968,"publication_date":"1968-12-01","ids":{"openalex":"https://openalex.org/W2018295752","doi":"https://doi.org/10.1109/tac.1968.1099025","mag":"2018295752"},"language":"en","primary_location":{"id":"doi:10.1109/tac.1968.1099025","doi":"https://doi.org/10.1109/tac.1968.1099025","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.1968.1099025","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-200","russia-white-list-1"],"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 Automatic Control","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2018295752"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5014088470","display_name":"T. Kailath","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"T. Kailath","raw_affiliation_strings":["University of Stanford, Stamford, CA, USA","Stanford University Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Stanford, Stamford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014088470"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":18.7069,"has_fulltext":false,"cited_by_count":752,"citation_normalized_percentile":{"value":0.99682035,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"13","issue":"6","first_page":"646","last_page":"655"},"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":0.9541000127792358,"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":0.9541000127792358,"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":0.03959999978542328,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.0027000000700354576,"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/least-squares-estimation","display_name":"least squares estimation","score":0.8970000147819519},{"id":"https://openalex.org/keywords/linear-filtering","display_name":"linear filtering","score":0.9419999718666077},{"id":"https://openalex.org/keywords/additive-white-noise","display_name":"additive white noise","score":0.8669999837875366},{"id":"https://openalex.org/keywords/wiener-filter","display_name":"Wiener filter","score":0.847000002861023},{"id":"https://openalex.org/keywords/kalman-bucy-filter","display_name":"Kalman-Bucy filter","score":0.8299999833106995},{"id":"https://openalex.org/keywords/recursive-filters","display_name":"recursive filtering","score":0.9070000052452087},{"id":"https://openalex.org/keywords/nonstationary-processes","display_name":"non-stationary processes","score":0.9430000185966492},{"id":"https://openalex.org/keywords/finite-interval","display_name":"finite interval","score":0.6370000243186951},{"id":"https://openalex.org/keywords/continuous-time-processes","display_name":"continuous-time processes","score":0.6830000281333923},{"id":"https://openalex.org/keywords/discrete-time-processes","display_name":"discrete-time processes","score":0.9929999709129333}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7341245412826538},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.6757664680480957},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6692643761634827},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.6145006418228149},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5403497815132141},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.525086522102356},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.521817147731781},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.47685420513153076},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.44434037804603577},{"id":"https://openalex.org/C18537770","wikidata":"https://www.wikidata.org/wiki/Q25523","display_name":"Wiener filter","level":2,"score":0.433709979057312},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3928312361240387},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3276355266571045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2390720248222351},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14415082335472107},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09380024671554565},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06489342451095581},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.1968.1099025","doi":"https://doi.org/10.1109/tac.1968.1099025","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.1968.1099025","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-200","russia-white-list-1"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W130599074","https://openalex.org/W141081514","https://openalex.org/W1489872560","https://openalex.org/W1510355813","https://openalex.org/W1531578805","https://openalex.org/W1672455737","https://openalex.org/W1967907471","https://openalex.org/W1982755128","https://openalex.org/W1988559163","https://openalex.org/W1997825317","https://openalex.org/W2007339048","https://openalex.org/W2012992565","https://openalex.org/W2013891788","https://openalex.org/W2044144205","https://openalex.org/W2062973984","https://openalex.org/W2063470045","https://openalex.org/W2065736545","https://openalex.org/W2073486793","https://openalex.org/W2074143156","https://openalex.org/W2078806674","https://openalex.org/W2079232594","https://openalex.org/W2083402998","https://openalex.org/W2094070726","https://openalex.org/W2094227853","https://openalex.org/W2103435373","https://openalex.org/W2105934661","https://openalex.org/W2128457724","https://openalex.org/W2158082140","https://openalex.org/W2171612575","https://openalex.org/W2477871341","https://openalex.org/W2795805775","https://openalex.org/W2800702870","https://openalex.org/W2896322077","https://openalex.org/W3031081200","https://openalex.org/W3090704166","https://openalex.org/W3147179697","https://openalex.org/W4249925951","https://openalex.org/W6605697617"],"related_works":["https://openalex.org/W2125908809","https://openalex.org/W2033449798","https://openalex.org/W2037799710","https://openalex.org/W4249925951","https://openalex.org/W2038775671","https://openalex.org/W2090645496","https://openalex.org/W2018748051","https://openalex.org/W4232303111","https://openalex.org/W2138654000","https://openalex.org/W2107856431"],"abstract_inverted_index":{"The":[0],"innovations":[1],"approach":[2],"to":[3,10,23,40,64,80],"linear":[4],"least-squares":[5],"approximation":[6],"problems":[7],"is":[8],"first":[9],"\"whiten\"":[11],"the":[12,25,46,62,86],"observed":[13],"data":[14],"by":[15,36],"a":[16,42,55,82],"causal":[17],"and":[18,21,38,94,97],"invertible":[19],"operation,":[20],"then":[22],"treat":[24],"resulting":[26],"simpler":[27],"white-noise":[28],"observations":[29],"problem.":[30],"This":[31],"technique":[32,63],"was":[33],"successfully":[34],"used":[35],"Bode":[37],"Shannon":[39],"obtain":[41,81],"simple":[43,83],"derivation":[44,84],"of":[45,85],"classical":[47],"Wiener":[48],"filtering":[49,89],"problem":[50],"for":[51],"stationary":[52],"processes":[53,68],"over":[54,69],"semi-infinite":[56],"interval.":[57],"Here":[58],"we":[59,75],"shall":[60,76],"extend":[61],"handle":[65],"nonstationary":[66],"continuous-time":[67,93],"finite":[70],"intervals.":[71],"In":[72],"Part":[73],"I":[74],"apply":[77],"this":[78],"method":[79],"Kalman-Bucy":[87],"recursive":[88],"formulas":[90],"(for":[91],"both":[92],"discrete-time":[95],"processes)":[96],"also":[98],"some":[99],"minor":[100],"generalizations":[101],"thereof.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":21},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":18},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":12}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2016-06-24T00:00:00"}
