{"id":"https://openalex.org/W2108704185","doi":"https://doi.org/10.1109/tnnls.2015.2388782","title":"Performance Bounds of Quaternion Estimators","display_name":"Performance Bounds of Quaternion Estimators","publication_year":2015,"publication_date":"2015-01-26","ids":{"openalex":"https://openalex.org/W2108704185","doi":"https://doi.org/10.1109/tnnls.2015.2388782","mag":"2108704185","pmid":"https://pubmed.ncbi.nlm.nih.gov/25643416"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2015.2388782","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2388782","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yili Xia","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, China","School of Information Science and Engineering, Southeast University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, China","institution_ids":[]},{"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/A5028505296","display_name":"Cyrus Jahanchahi","orcid":null},"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":"Cyrus Jahanchahi","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/A5008618142","display_name":"Tohru Nitta","orcid":"https://orcid.org/0000-0001-9628-7920"},"institutions":[{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tohru Nitta","raw_affiliation_strings":["Mathematical Neuroinformatics Group, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan"],"affiliations":[{"raw_affiliation_string":"Mathematical Neuroinformatics Group, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan","institution_ids":["https://openalex.org/I73613424"]}]},{"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"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5005242197"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":3.5512,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.93280766,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"12","first_page":"3287","last_page":"3292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11325","display_name":"Inertial Sensor and Navigation","score":0.9994000196456909,"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":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.9324853420257568},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.8356815576553345},{"id":"https://openalex.org/keywords/generality","display_name":"Generality","score":0.7439497709274292},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.6949827671051025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6148564219474792},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5712740421295166},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.45721909403800964},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41028687357902527},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39968740940093994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.361590176820755},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20628318190574646},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0788731575012207}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.9324853420257568},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8356815576553345},{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.7439497709274292},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.6949827671051025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6148564219474792},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5712740421295166},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.45721909403800964},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41028687357902527},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39968740940093994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.361590176820755},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20628318190574646},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0788731575012207},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2015.2388782","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2388782","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:25643416","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25643416","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3589703592","display_name":null,"funder_award_id":"61401094","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5876015803","display_name":"Novel Adaptive Filtering Techniques for Multidimensional Signals","funder_award_id":"EP/H026266/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G756866442","display_name":null,"funder_award_id":"EP/H026266/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7616653276","display_name":null,"funder_award_id":"BK20140645","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W81722178","https://openalex.org/W142384176","https://openalex.org/W639989723","https://openalex.org/W1965914766","https://openalex.org/W2002714615","https://openalex.org/W2010961394","https://openalex.org/W2040575700","https://openalex.org/W2043978450","https://openalex.org/W2062144489","https://openalex.org/W2065144261","https://openalex.org/W2067009792","https://openalex.org/W2067489830","https://openalex.org/W2069222481","https://openalex.org/W2080375618","https://openalex.org/W2098918476","https://openalex.org/W2099057098","https://openalex.org/W2114765937","https://openalex.org/W2118369318","https://openalex.org/W2130071409","https://openalex.org/W2136580750","https://openalex.org/W2144472563","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/W2294288691","https://openalex.org/W2476841360","https://openalex.org/W2492889297","https://openalex.org/W2962854822","https://openalex.org/W4211251910","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2045049461","https://openalex.org/W4381094582","https://openalex.org/W1978893398","https://openalex.org/W1977906818","https://openalex.org/W2369625323","https://openalex.org/W2896838204","https://openalex.org/W3125536267","https://openalex.org/W2274645452","https://openalex.org/W1999706086","https://openalex.org/W2521753262"],"abstract_inverted_index":{"The":[0,115],"quaternion":[1,18,72],"widely":[2],"linear":[3,39],"(WL)":[4],"estimator":[5],"has":[6],"been":[7],"recently":[8],"introduced":[9],"for":[10,48,68,76],"optimal":[11,119],"second-order":[12,21,25],"modeling":[13],"of":[14,17,31,71,99,104],"the":[15,36,44,62,69,86,97,105,112,118,125,128],"generality":[16],"data,":[19],"both":[20],"circular":[22],"(proper)":[23],"and":[24,54,78],"noncircular":[26],"(improper).":[27],"Experimental":[28],"evidence":[29],"exists":[30],"its":[32],"performance":[33,56,100],"advantage":[34],"over":[35],"conventional":[37],"strictly":[38],"(SL)":[40],"as":[41,43],"well":[42],"semi-WL":[45],"(SWL)":[46],"estimators":[47],"improper":[49],"data.":[50,80],"However,":[51],"rigorous":[52,92],"theoretical":[53],"practical":[55],"bounds":[57],"are":[58,131],"still":[59],"missing":[60],"in":[61,102],"literature,":[63],"yet":[64],"this":[65,82],"is":[66],"crucial":[67],"development":[70],"valued":[73],"learning":[74],"systems":[75],"3-D":[77],"4-D":[79],"To":[81],"end,":[83],"based":[84],"on":[85],"orthogonality":[87],"principle,":[88],"we":[89],"introduce":[90],"a":[91],"closed-form":[93],"solution":[94],"to":[95],"quantify":[96],"degree":[98],"benefits,":[101],"terms":[103],"mean":[106],"square":[107],"error,":[108],"obtained":[109],"when":[110,117],"using":[111],"WL":[113,120],"models.":[114],"cases":[116],"estimation":[121,130],"can":[122],"simplify":[123],"into":[124],"SWL":[126],"or":[127],"SL":[129],"also":[132],"discussed.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}