{"id":"https://openalex.org/W2955958653","doi":"https://doi.org/10.1109/tsp.2019.2925604","title":"Full Mean Square Performance Bounds on Quaternion Estimators for Improper Data","display_name":"Full Mean Square Performance Bounds on Quaternion Estimators for Improper Data","publication_year":2019,"publication_date":"2019-07-07","ids":{"openalex":"https://openalex.org/W2955958653","doi":"https://doi.org/10.1109/tsp.2019.2925604","mag":"2955958653"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2925604","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5005242197","display_name":"Yili Xia","orcid":"https://orcid.org/0000-0002-4402-8131"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"funder","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yili Xia","raw_affiliation_strings":["School of Information Science and Engineering, Southeast University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101966699","display_name":"Song Tao","orcid":"https://orcid.org/0000-0002-0944-0112"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"funder","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Song Tao","raw_affiliation_strings":["School of Information Science and Engineering, Southeast University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100356607","display_name":"Zhe Li","orcid":"https://orcid.org/0000-0001-7130-7876"},"institutions":[{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"funder","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhe Li","raw_affiliation_strings":["School of Electronic and Information Engineering, Soochow University, Suzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Soochow University, Suzhou, China","institution_ids":["https://openalex.org/I3923682"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071836863","display_name":"Min Xiang","orcid":"https://orcid.org/0000-0002-0239-3392"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"funder","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Min Xiang","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K."],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K.","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101830725","display_name":"Wenjiang Pei","orcid":"https://orcid.org/0000-0002-0776-4607"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"funder","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenjiang Pei","raw_affiliation_strings":["School of Information Science and Engineering, Southeast University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"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":"funder","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."],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K.","institution_ids":["https://openalex.org/I47508984"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.246,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":14,"citation_normalized_percentile":{"value":0.791588,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":89},"biblio":{"volume":"67","issue":"15","first_page":"4093","last_page":"4106"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11325","display_name":"Inertial Sensor and Navigation","score":0.9994,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T11325","display_name":"Inertial Sensor and Navigation","score":0.9994,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9988,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9961,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.83270496},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.71466225},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.6331562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.54981315},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4880985},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.43936136},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.43480414},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40557796},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4001028},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38763624},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3626861},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2925604","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.81,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, justice, and strong institutions"}],"grants":[{"funder":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China","award_id":"61771124"}],"datasets":[],"versions":[],"referenced_works_count":45,"referenced_works":["https://openalex.org/W142384176","https://openalex.org/W1527786550","https://openalex.org/W1855615675","https://openalex.org/W1965914766","https://openalex.org/W1972161577","https://openalex.org/W1987730473","https://openalex.org/W1999542175","https://openalex.org/W2002714615","https://openalex.org/W2040575700","https://openalex.org/W2062144489","https://openalex.org/W2067489830","https://openalex.org/W2069222481","https://openalex.org/W2090550497","https://openalex.org/W2091366315","https://openalex.org/W2091669036","https://openalex.org/W2098918476","https://openalex.org/W2099057098","https://openalex.org/W2108704185","https://openalex.org/W2110728483","https://openalex.org/W2114765937","https://openalex.org/W2118369318","https://openalex.org/W2130071409","https://openalex.org/W2136580750","https://openalex.org/W2155973954","https://openalex.org/W2157910179","https://openalex.org/W2161397505","https://openalex.org/W2161872204","https://openalex.org/W2170400088","https://openalex.org/W2170646498","https://openalex.org/W2344336171","https://openalex.org/W2407528929","https://openalex.org/W2476841360","https://openalex.org/W2525110762","https://openalex.org/W2553809626","https://openalex.org/W2761069238","https://openalex.org/W2770517446","https://openalex.org/W2775180954","https://openalex.org/W2780762438","https://openalex.org/W2887329810","https://openalex.org/W2962810704","https://openalex.org/W2963982127","https://openalex.org/W4211251910","https://openalex.org/W4213332888","https://openalex.org/W4229748564","https://openalex.org/W639989723"],"related_works":["https://openalex.org/W4225472102","https://openalex.org/W3127350447","https://openalex.org/W3125536267","https://openalex.org/W3108700312","https://openalex.org/W2949310342","https://openalex.org/W2907746047","https://openalex.org/W2887325221","https://openalex.org/W2382948573","https://openalex.org/W2274645452","https://openalex.org/W2075897667"],"abstract_inverted_index":{"Novel":[0],"physical":[1],"insights":[2],"are":[3],"provided":[4],"into":[5],"the":[6,24,51,59,62,65,80,85,99,106,137,144,149],"mean":[7,40],"square":[8,41],"performance":[9],"bounds":[10,63],"of":[11,26,38,44,54,61,64,71,79,92,98,108,118],"quaternion-valued":[12,27],"widely":[13],"linear":[14,17,21],"(WL),":[15],"semi-widely":[16],"(SWL),":[18],"and":[19,47,84],"strictly":[20],"estimators":[22,46,72,109],"for":[23,94,105,110,123],"generality":[25],"Gaussian":[28],"data.":[29],"This":[30],"is":[31,113,131],"achieved":[32],"by":[33,48,68],"first":[34],"defining":[35],"three":[36],"kinds":[37],"complementary":[39],"errors":[42],"(CMSEs)":[43],"these":[45,69],"further":[49],"exploiting":[50],"corresponding":[52],"degrees":[53,91],"'Hi-improperness":[55],"(second-order":[56],"noncircularity).":[57],"Next,":[58],"investigation":[60],"attainable":[66],"CMSEs":[67],"classes":[70],"shows":[73],"that":[74],"only":[75],"a":[76,95],"joint":[77],"consideration":[78],"proposed":[81],"CMSE":[82],"analysis":[83,88,107,140],"standard":[86,138],"MSE":[87,100,139],"provides":[89],"enough":[90],"freedom":[93],"detailed":[96],"account":[97],"performance.":[101],"The":[102],"so-established":[103],"framework":[104],"'Hi-improper":[111],"data":[112,125],"shown":[114],"to":[115,134],"be":[116],"capable":[117],"measuring":[119],"error":[120],"power":[121],"distribution":[122],"each":[124],"channel,":[126],"an":[127],"important":[128],"finding,":[129],"which":[130],"not":[132],"possible":[133],"obtain":[135],"through":[136],"only.":[141],"Simulations":[142],"in":[143],"system":[145],"identification":[146],"setting":[147],"support":[148],"analysis.":[150]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2955958653","counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3}],"updated_date":"2025-03-17T18:40:27.636571","created_date":"2019-07-12"}