{"id":"https://openalex.org/W2166887835","doi":"https://doi.org/10.1109/tsp.2010.2104147","title":"A New Derivation of Constrained Cram\u00e9r\u2013Rao Bound Via Norm Minimization","display_name":"A New Derivation of Constrained Cram\u00e9r\u2013Rao Bound Via Norm Minimization","publication_year":2011,"publication_date":"2011-01-07","ids":{"openalex":"https://openalex.org/W2166887835","doi":"https://doi.org/10.1109/tsp.2010.2104147","mag":"2166887835"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2010.2104147","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2010.2104147","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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/A5100868012","display_name":"Zhiguang Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shi Zhiguang","raw_affiliation_strings":["ATR Laboratory, National University of Defense Technology, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"ATR Laboratory, National University of Defense Technology, Changsha, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101813221","display_name":"Jianxiong Zhou","orcid":"https://orcid.org/0000-0002-7800-5173"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou Jianxiong","raw_affiliation_strings":["ATR Laboratory, National University of Defense Technology, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"ATR Laboratory, National University of Defense Technology, Changsha, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091321590","display_name":"Lei Hu","orcid":"https://orcid.org/0000-0003-3562-9178"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hu Lei","raw_affiliation_strings":["ATR Laboratory, National University of Defense Technology, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"ATR Laboratory, National University of Defense Technology, Changsha, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100653936","display_name":"Jicheng Li","orcid":"https://orcid.org/0000-0001-5000-1069"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Jicheng","raw_affiliation_strings":["ATR Laboratory, National University of Defense Technology, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"ATR Laboratory, National University of Defense Technology, Changsha, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100868012"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":null,"apc_paid":null,"fwci":0.6125,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.69565507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"59","issue":"4","first_page":"1879","last_page":"1882"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9966999888420105,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.994700014591217,"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/mathematics","display_name":"Mathematics","score":0.6651389598846436},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6610216498374939},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5369617342948914},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5175463557243347},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5007281303405762},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49880456924438477},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.48976588249206543},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.48066651821136475},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.41461318731307983},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3978230357170105},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.397177129983902},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11856651306152344},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08500373363494873}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6651389598846436},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6610216498374939},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5369617342948914},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5175463557243347},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5007281303405762},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49880456924438477},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.48976588249206543},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.48066651821136475},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.41461318731307983},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3978230357170105},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.397177129983902},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11856651306152344},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08500373363494873},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2010.2104147","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2010.2104147","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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":13,"referenced_works":["https://openalex.org/W1981286291","https://openalex.org/W2049063033","https://openalex.org/W2066629267","https://openalex.org/W2089486168","https://openalex.org/W2096038066","https://openalex.org/W2109515693","https://openalex.org/W2128203095","https://openalex.org/W2137493182","https://openalex.org/W2152044198","https://openalex.org/W2170215665","https://openalex.org/W2171750915","https://openalex.org/W2172277024","https://openalex.org/W3143031901"],"related_works":["https://openalex.org/W1980381208","https://openalex.org/W2364594919","https://openalex.org/W2219338811","https://openalex.org/W2167092671","https://openalex.org/W2149583853","https://openalex.org/W1861706286","https://openalex.org/W2143002539","https://openalex.org/W1120847856","https://openalex.org/W4293472652","https://openalex.org/W2038812594"],"abstract_inverted_index":{"The":[0,42,116],"constrained":[1],"Cram\u00e9r-Rao":[2],"bound":[3,98],"(CCRB)":[4],"is":[5,25,108,118],"widely":[6],"used":[7,81],"to":[8,56,82,120],"evaluate":[9],"the":[10,23,28,48,58,74,79,84,90,94,97,106,110,114],"estimation":[11,59,85],"performance":[12],"for":[13],"deterministic":[14],"parameters":[15],"with":[16],"parametric":[17,43,75],"constraints.":[18,41],"An":[19],"alternative":[20],"derivation":[21,62],"of":[22,30,39,93],"CCRB":[24],"presented":[26],"from":[27],"perspective":[29],"solving":[31],"a":[32,37,53,69],"norm":[33,92],"minimization":[34],"problem":[35],"under":[36],"set":[38],"linear":[40,49],"constraints":[44,50,76],"are":[45],"embedded":[46],"in":[47,109],"by":[51,113],"constructing":[52],"proper":[54],"basis":[55],"represent":[57,83],"error.":[60],"This":[61],"avoids":[63],"sophisticated":[64],"matrix":[65],"manipulations":[66],"and":[67,87,96,103,123],"has":[68],"clear":[70],"physical":[71],"meaning":[72],"that":[73],"cut":[77],"down":[78],"bases":[80],"error":[86,107],"hence":[88],"reduce":[89],"minimum":[91],"error,":[95],"can":[99],"be":[100],"achieved":[101],"if":[102,105],"only":[104],"subspace":[111],"spanned":[112],"bases.":[115],"result":[117],"applicable":[119],"biased":[121],"estimators":[122],"singular":[124],"Fisher":[125],"information":[126],"matrices.":[127]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}