{"id":"https://openalex.org/W2110856480","doi":"https://doi.org/10.1109/tac.2010.2089753","title":"Square Root Modified Bryson\u2013Frazier Smoother","display_name":"Square Root Modified Bryson\u2013Frazier Smoother","publication_year":2010,"publication_date":"2010-11-05","ids":{"openalex":"https://openalex.org/W2110856480","doi":"https://doi.org/10.1109/tac.2010.2089753","mag":"2110856480"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2089753","doi":"https://doi.org/10.1109/tac.2010.2089753","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2089753","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":["cwts-core","jufo-3","ki-jl-1","norway-2"],"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"},"volume":null,"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/A5108507670","display_name":"Richard G. Gibbs","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]},{"id":"https://openalex.org/I2802946424","display_name":"Johns Hopkins University Applied Physics Laboratory","ror":"https://ror.org/029pp9z10","country_code":"US","type":"facility","lineage":["https://openalex.org/I145311948","https://openalex.org/I2802946424"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard G. Gibbs","raw_affiliation_strings":["Applied Physics Laboratory, Johns Hopkins University, Laurel, MD, USA","Appl. Phys. Lab. Johns Hopkins Univ., Laurel, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Physics Laboratory, Johns Hopkins University, Laurel, MD, USA","institution_ids":["https://openalex.org/I145311948","https://openalex.org/I2802946424"]},{"raw_affiliation_string":"Appl. Phys. Lab. Johns Hopkins Univ., Laurel, MD, USA","institution_ids":["https://openalex.org/I2802946424"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108507670"],"corresponding_institution_ids":["https://openalex.org/I145311948","https://openalex.org/I2802946424"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":2.0363,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.87910602,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"56","issue":"2","first_page":"452","last_page":"456"},"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":0.8539999723434448,"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":0.8539999723434448,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.08730000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.025299999862909317,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/square-root-algorithm","display_name":"square root algorithm","score":0.7229999899864197},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.8960000276565552},{"id":"https://openalex.org/keywords/state-estimation","display_name":"state estimation","score":0.4000000059604645}],"concepts":[{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.7572954893112183},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6543360352516174},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5636547803878784},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5363226532936096},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4959343373775482},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.48385846614837646},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.459867924451828},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4537986218929291},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4149990975856781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37162134051322937},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22862505912780762},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07761496305465698},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2010.2089753","doi":"https://doi.org/10.1109/tac.2010.2089753","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2089753","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":["cwts-core","jufo-3","ki-jl-1","norway-2"],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1650765400","https://openalex.org/W1969634731","https://openalex.org/W2010941966","https://openalex.org/W2067908011","https://openalex.org/W2069348048","https://openalex.org/W2094227853","https://openalex.org/W2098876649","https://openalex.org/W2172190709","https://openalex.org/W2567383493","https://openalex.org/W2798500587"],"related_works":["https://openalex.org/W2217961521","https://openalex.org/W2001134355","https://openalex.org/W1595735471","https://openalex.org/W2364423705","https://openalex.org/W3120038327","https://openalex.org/W1561772133","https://openalex.org/W3029623871","https://openalex.org/W933873750","https://openalex.org/W2200340134","https://openalex.org/W4308789280"],"abstract_inverted_index":{"We":[0,70],"derive":[1],"here":[2],"an":[3,84],"algorithm":[4,19],"for":[5],"a":[6],"complete":[7],"square":[8,55,76],"root":[9,56,77],"implementation":[10],"of":[11,27,51,67,78],"the":[12,21,25,39,49,61,65,75,79,87],"modified":[13],"Bryson-Frazier":[14],"(MBF)":[15],"smoother.":[16],"The":[17],"MBF":[18],"computes":[20],"smoothed":[22,62,80],"covariance":[23,40,63,81],"as":[24,64],"difference":[26,66],"two":[28,68],"symmetric":[29],"matrices.":[30,69],"Numerical":[31],"errors":[32],"in":[33,38,54,86],"this":[34],"differencing":[35],"can":[36],"result":[37],"matrix":[41],"not":[42],"being":[43],"positive":[44],"semi-definite.":[45],"Earlier":[46],"algorithms":[47],"implemented":[48],"computation":[50],"intermediate":[52],"quantities":[53],"form":[57],"but":[58],"still":[59],"computed":[60],"show":[71],"how":[72],"to":[73],"compute":[74],"by":[82],"solving":[83],"equation":[85],"formCCT=AAT-BBTusing":[88],"QR":[89],"decomposition":[90],"with":[91],"hyperbolic":[92],"Householder":[93],"transformations.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
