{"id":"https://openalex.org/W2086085567","doi":"https://doi.org/10.1109/tsp.2012.2204258","title":"Computing Constrained Cram\u00e9r-Rao Bounds","display_name":"Computing Constrained Cram\u00e9r-Rao Bounds","publication_year":2012,"publication_date":"2012-06-11","ids":{"openalex":"https://openalex.org/W2086085567","doi":"https://doi.org/10.1109/tsp.2012.2204258","mag":"2086085567"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2012.2204258","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2204258","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1204.2033","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023909481","display_name":"Paul Tune","orcid":"https://orcid.org/0000-0002-2459-3168"},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Paul Tune","raw_affiliation_strings":["School of Mathematical Sciences, University of Adelaide, Australia","Sch. of Math. Sci., Univ. of Adelaide, Adelaide, SA, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Adelaide, Australia","institution_ids":["https://openalex.org/I5681781"]},{"raw_affiliation_string":"Sch. of Math. Sci., Univ. of Adelaide, Adelaide, SA, Australia","institution_ids":["https://openalex.org/I5681781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023909481"],"corresponding_institution_ids":["https://openalex.org/I5681781"],"apc_list":null,"apc_paid":null,"fwci":0.3403,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.63192147,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"60","issue":"10","first_page":"5543","last_page":"5548"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9987999796867371,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.7821977138519287},{"id":"https://openalex.org/keywords/cram\u00e9r\u2013rao-bound","display_name":"Cram\u00e9r\u2013Rao bound","score":0.6344835758209229},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6128976345062256},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5946556329727173},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5848068594932556},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5358433127403259},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5339177250862122},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.49175170063972473},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46498578786849976},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.46236637234687805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4567602276802063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45583605766296387},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4531559944152832},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.42293378710746765},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.42085665464401245},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.39486390352249146},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09312725067138672}],"concepts":[{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.7821977138519287},{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.6344835758209229},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6128976345062256},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5946556329727173},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5848068594932556},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5358433127403259},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5339177250862122},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.49175170063972473},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46498578786849976},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.46236637234687805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4567602276802063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45583605766296387},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4531559944152832},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.42293378710746765},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.42085665464401245},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.39486390352249146},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09312725067138672},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"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":3,"locations":[{"id":"doi:10.1109/tsp.2012.2204258","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2204258","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"},{"id":"pmh:oai:arXiv.org:1204.2033","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.2033","pdf_url":"https://arxiv.org/pdf/1204.2033","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:digital.library.adelaide.edu.au:2440/73883","is_oa":false,"landing_page_url":"http://hdl.handle.net/2440/73883","pdf_url":null,"source":{"id":"https://openalex.org/S4306401835","display_name":"Adelaide Research & Scholarship (AR&S) (University of Adelaide)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5681781","host_organization_name":"The University of Adelaide","host_organization_lineage":["https://openalex.org/I5681781"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dx.doi.org/10.1109/tsp.2012.2204258","raw_type":"Journal article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1204.2033","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.2033","pdf_url":"https://arxiv.org/pdf/1204.2033","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1965392255","https://openalex.org/W1977054492","https://openalex.org/W2010973140","https://openalex.org/W2016834185","https://openalex.org/W2026032151","https://openalex.org/W2036200304","https://openalex.org/W2049063033","https://openalex.org/W2052921087","https://openalex.org/W2068425868","https://openalex.org/W2075621462","https://openalex.org/W2128203095","https://openalex.org/W2149414429","https://openalex.org/W2161570458","https://openalex.org/W2162826379","https://openalex.org/W2172271905","https://openalex.org/W2296319761","https://openalex.org/W2500965032","https://openalex.org/W2610857016","https://openalex.org/W2797925981","https://openalex.org/W4206180546","https://openalex.org/W4210921710","https://openalex.org/W4239146293","https://openalex.org/W4250589301","https://openalex.org/W4300029251","https://openalex.org/W4300579247"],"related_works":["https://openalex.org/W4297911919","https://openalex.org/W2585557503","https://openalex.org/W1994676335","https://openalex.org/W2066487328","https://openalex.org/W2494111473","https://openalex.org/W2876132667","https://openalex.org/W2126985620","https://openalex.org/W1853313042","https://openalex.org/W2111557694","https://openalex.org/W2135503105"],"abstract_inverted_index":{"We":[0,27,74,110],"revisit":[1],"the":[2,8,15,36,46,56,61,98,113,117,120,123,131,144],"problem":[3],"of":[4,7,17,21,35,48,55,88,93,119,146],"computing":[5],"submatrices":[6],"Cram\u00e9r-Rao":[9],"bound":[10,57,99],"(CRB),":[11],"which":[12,40],"lower":[13],"bounds":[14],"variance":[16],"any":[18],"unbiased":[19],"estimator":[20],"a":[22,147],"vector":[23],"parameter":[24,132],"\\mbi":[25,49,133],"\u03b8.":[26],"explore":[28],"iterative":[29],"methods":[30,70,95],"that":[31,80],"avoid":[32],"direct":[33],"inversion":[34],"Fisher":[37,124],"information":[38,125],"matrix,":[39],"can":[41],"be":[42],"computationally":[43],"expensive":[44],"when":[45,122,130],"dimension":[47],"\u03b8":[50,134],"is":[51,58,127,135],"large.":[52],"The":[53],"computation":[54,118],"related":[59],"to":[60,97,115,137],"quadratic":[62],"matrix":[63,126],"program,":[64],"where":[65],"there":[66],"are":[67,85,107],"highly":[68],"efficient":[69],"for":[71,151],"solving":[72],"it.":[73],"present":[75],"several":[76],"methods,":[77],"and":[78,129],"show":[79],"algorithms":[81,104],"in":[82,102],"prior":[83],"work":[84,114],"special":[86],"instances":[87],"existing":[89],"optimization":[90],"algorithms.":[91],"Some":[92],"these":[94],"converge":[96],"monotonically,":[100],"but":[101],"particular,":[103],"converging":[105],"nonmonotonically":[106],"much":[108],"faster.":[109],"then":[111],"extend":[112],"encompass":[116],"CRB":[121],"singular":[128],"subject":[136],"constraints.":[138],"As":[139],"an":[140],"application,":[141],"we":[142],"consider":[143],"design":[145],"data":[148],"streaming":[149],"algorithm":[150],"network":[152],"measurement.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
