{"id":"https://openalex.org/W4406321556","doi":"https://doi.org/10.1109/tsp.2025.3529468","title":"Cram\u00e9r-Rao Lower Bounds for Unconstrained and Constrained Quaternion Parameters","display_name":"Cram\u00e9r-Rao Lower Bounds for Unconstrained and Constrained Quaternion Parameters","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4406321556","doi":"https://doi.org/10.1109/tsp.2025.3529468"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2025.3529468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3529468","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/A5044069210","display_name":"Shuning Sun","orcid":"https://orcid.org/0009-0002-1901-5942"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shuning Sun","raw_affiliation_strings":["Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China"],"raw_orcid":"https://orcid.org/0009-0002-1901-5942","affiliations":[{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012826227","display_name":"Dongpo Xu","orcid":"https://orcid.org/0000-0002-9663-9743"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongpo Xu","raw_affiliation_strings":["Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China"],"raw_orcid":"https://orcid.org/0000-0002-9663-9743","affiliations":[{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091932363","display_name":"Qiankun Diao","orcid":"https://orcid.org/0009-0000-6322-6312"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiankun Diao","raw_affiliation_strings":["Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China"],"raw_orcid":"https://orcid.org/0009-0000-6322-6312","affiliations":[{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103001848","display_name":"Danilo P. Mandic","orcid":"https://orcid.org/0000-0001-8432-3963"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Danilo P. Mandic","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","Department of Electrical and Electronic Engineering, Imperial College London, London, UK"],"raw_orcid":"https://orcid.org/0000-0001-8432-3963","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044069210"],"corresponding_institution_ids":["https://openalex.org/I184983240"],"apc_list":null,"apc_paid":null,"fwci":1.3257,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78327597,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"73","issue":null,"first_page":"508","last_page":"518"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955000281333923,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955000281333923,"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"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9742000102996826,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9736999869346619,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.6992307305335999},{"id":"https://openalex.org/keywords/cram\u00e9r\u2013rao-bound","display_name":"Cram\u00e9r\u2013Rao bound","score":0.613258957862854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6126258969306946},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4733041822910309},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.42992833256721497},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.424014151096344},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36691465973854065},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.3312758505344391},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3014198839664459},{"id":"https://openalex.org/keywords/radar","display_name":"Radar","score":0.1363801658153534},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.11140507459640503}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.6992307305335999},{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.613258957862854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6126258969306946},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4733041822910309},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.42992833256721497},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.424014151096344},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36691465973854065},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3312758505344391},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3014198839664459},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.1363801658153534},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.11140507459640503},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2025.3529468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3529468","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":[{"id":"https://openalex.org/G7302374699","display_name":null,"funder_award_id":"62176051","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8487639614","display_name":null,"funder_award_id":"20240101370JC","funder_id":"https://openalex.org/F4320310121","funder_display_name":"Natural Science Foundation of Jilin Province"}],"funders":[{"id":"https://openalex.org/F4320310121","display_name":"Natural Science Foundation of Jilin Province","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W107110140","https://openalex.org/W1855615675","https://openalex.org/W1921661266","https://openalex.org/W2043592505","https://openalex.org/W2049063033","https://openalex.org/W2078314058","https://openalex.org/W2090550497","https://openalex.org/W2094646141","https://openalex.org/W2096038066","https://openalex.org/W2096142642","https://openalex.org/W2114765937","https://openalex.org/W2120662572","https://openalex.org/W2127949350","https://openalex.org/W2161500056","https://openalex.org/W2330070481","https://openalex.org/W2523056272","https://openalex.org/W2751499108","https://openalex.org/W2798239553","https://openalex.org/W2884244916","https://openalex.org/W2923872554","https://openalex.org/W2949977657","https://openalex.org/W2952791331","https://openalex.org/W2964095833","https://openalex.org/W2978437779","https://openalex.org/W2990201147","https://openalex.org/W3017988012","https://openalex.org/W3047915604","https://openalex.org/W3092753424","https://openalex.org/W3093252450","https://openalex.org/W3095945879","https://openalex.org/W3120384044","https://openalex.org/W3127605436","https://openalex.org/W4200537477","https://openalex.org/W4205463000","https://openalex.org/W4223418869","https://openalex.org/W4251652949","https://openalex.org/W4285288115","https://openalex.org/W4292971241","https://openalex.org/W4299868912","https://openalex.org/W4309673631","https://openalex.org/W4313188585","https://openalex.org/W4313449746","https://openalex.org/W4385819679","https://openalex.org/W4386523188","https://openalex.org/W4387730071","https://openalex.org/W4388104002","https://openalex.org/W4394585906","https://openalex.org/W4394698864","https://openalex.org/W4396699589","https://openalex.org/W4399665812","https://openalex.org/W4400448596","https://openalex.org/W4401747751","https://openalex.org/W4401870858","https://openalex.org/W4401870872"],"related_works":["https://openalex.org/W3127350447","https://openalex.org/W3108700312","https://openalex.org/W4225472102","https://openalex.org/W2382948573","https://openalex.org/W2585557503","https://openalex.org/W2169354510","https://openalex.org/W1967296369","https://openalex.org/W2057485678","https://openalex.org/W4389474210","https://openalex.org/W1971427935"],"abstract_inverted_index":{"The":[0,140],"Cram\u00e9r-Rao":[1,32],"lower":[2,33],"bound":[3,34],"(CRLB)":[4],"is":[5,19,46,106,146],"a":[6,49,88,99],"fundamental":[7],"result":[8],"in":[9,48,194,197],"statistical":[10],"signal":[11,220],"processing,":[12,221],"however,":[13],"the":[14,28,38,54,62,65,70,77,80,83,91,94,104,111,124,129,144,156,161,164,168,175,186,198,204,213,226],"CRLB":[15],"for":[16,79,90,101,113,163,203],"quaternion":[17,31,66,71,115,125,169,187,219,227],"parameters":[18],"not":[20],"yet":[21],"established.":[22],"To":[23],"this":[24,45],"end,":[25],"we":[26],"develop":[27],"theory":[29,214],"of":[30,64,82,93,123,143,218],"(QCRLB),":[35],"based":[36],"on":[37],"generalized":[39],"Hamilton-real":[40],"(GHR)":[41],"calculus.":[42],"For":[43],"generality,":[44],"achieved":[47],"way":[50,78],"that":[51,155],"conforms":[52],"with":[53,180],"real":[55],"and":[56,69,98,120,132,167,215],"complex":[57],"CRLB.":[58],"We":[59,108,183],"first":[60],"provide":[61],"properties":[63],"covariance":[67],"matrix":[68,74],"Fisher":[72],"information":[73],"(FIM),":[75],"paving":[76],"derivation":[81],"QCRLB.":[84],"This":[85],"serves":[86],"as":[87],"basis":[89],"formulation":[92],"QCRLB":[95,105,112,145,162,176],"without":[96],"constraints":[97],"criterion":[100],"determining":[102],"whether":[103],"attained.":[107],"also":[109,184],"establish":[110],"constrained":[114,188,200],"parameters,":[116],"including":[117],"both":[118,212],"nonsingular":[119],"singular":[121],"cases":[122],"FIM.":[126],"These":[127,207],"broaden":[128],"theoretical":[130,181],"framework":[131],"enhance":[133],"its":[134],"applicability":[135],"to":[136,211],"diverse":[137],"practical":[138,141,216],"scenarios.":[139],"efficacy":[142],"demonstrated":[147],"through":[148],"two":[149],"illustrative":[150],"examples.":[151],"Numerical":[152],"validations":[153],"confirm":[154],"maximum-likelihood":[157],"estimator":[158],"(MLE)":[159],"attains":[160],"linear":[165,199,205],"model,":[166],"gradient":[170],"ascent":[171],"(QGA)":[172],"algorithm":[173],"achieves":[174],"at":[177],"each":[178],"iteration":[179],"guarantees.":[182],"propose":[185],"scoring":[189],"(QCS)":[190],"algorithm,":[191],"which":[192],"converges":[193],"one":[195],"step":[196],"MLE":[201],"case,":[202],"model.":[206],"results":[208],"significantly":[209],"contribute":[210],"application":[217],"bringing":[222],"valuable":[223],"insights":[224],"into":[225],"parameter":[228],"estimation.":[229]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
