{"id":"https://openalex.org/W2794369236","doi":"https://doi.org/10.3390/s18030778","title":"Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint","display_name":"Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint","publication_year":2018,"publication_date":"2018-03-04","ids":{"openalex":"https://openalex.org/W2794369236","doi":"https://doi.org/10.3390/s18030778","mag":"2794369236","pmid":"https://pubmed.ncbi.nlm.nih.gov/29510539"},"language":"en","primary_location":{"id":"doi:10.3390/s18030778","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18030778","pdf_url":"https://www.mdpi.com/1424-8220/18/3/778/pdf?version=1520161456","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1424-8220/18/3/778/pdf?version=1520161456","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013833731","display_name":"Bonan Jin","orcid":"https://orcid.org/0000-0002-4635-3106"},"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":false,"raw_author_name":"Bonan Jin","raw_affiliation_strings":["Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"],"raw_orcid":"https://orcid.org/0000-0002-4635-3106","affiliations":[{"raw_affiliation_string":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074042000","display_name":"Xiaosu Xu","orcid":"https://orcid.org/0000-0002-5165-0981"},"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":"Xiaosu Xu","raw_affiliation_strings":["Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"],"raw_orcid":"https://orcid.org/0000-0002-5165-0981","affiliations":[{"raw_affiliation_string":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100375754","display_name":"Tao Zhang","orcid":"https://orcid.org/0000-0001-9955-3905"},"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":false,"raw_author_name":"Tao Zhang","raw_affiliation_strings":["Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"],"raw_orcid":"https://orcid.org/0000-0001-9955-3905","affiliations":[{"raw_affiliation_string":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074042000"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2598},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2598},"fwci":4.9741,"has_fulltext":true,"cited_by_count":69,"citation_normalized_percentile":{"value":0.95713676,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"18","issue":"3","first_page":"778","last_page":"778"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":1.0,"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":1.0,"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.998199999332428,"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/T10655","display_name":"GNSS positioning and interference","score":0.9937000274658203,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multilateration","display_name":"Multilateration","score":0.6334159970283508},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4930584132671356},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.47050946950912476},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4346396327018738},{"id":"https://openalex.org/keywords/tangent-cone","display_name":"Tangent cone","score":0.4282560646533966},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.42163902521133423},{"id":"https://openalex.org/keywords/cram\u00e9r\u2013rao-bound","display_name":"Cram\u00e9r\u2013Rao bound","score":0.4206479489803314},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.41502779722213745},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38899898529052734},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.3731262683868408},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3044890761375427}],"concepts":[{"id":"https://openalex.org/C104037064","wikidata":"https://www.wikidata.org/wiki/Q1640884","display_name":"Multilateration","level":3,"score":0.6334159970283508},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4930584132671356},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.47050946950912476},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4346396327018738},{"id":"https://openalex.org/C149944404","wikidata":"https://www.wikidata.org/wiki/Q2392464","display_name":"Tangent cone","level":3,"score":0.4282560646533966},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.42163902521133423},{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.4206479489803314},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.41502779722213745},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38899898529052734},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3731262683868408},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3044890761375427},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C159737794","wikidata":"https://www.wikidata.org/wiki/Q124274","display_name":"Azimuth","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/s18030778","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18030778","pdf_url":"https://www.mdpi.com/1424-8220/18/3/778/pdf?version=1520161456","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},{"id":"pmid:29510539","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29510539","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":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:bce79b5e09354637a6a3277c1f167c56","is_oa":true,"landing_page_url":"https://doaj.org/article/bce79b5e09354637a6a3277c1f167c56","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 18, Iss 3, p 778 (2018)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:4796742","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5876713","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:mdpi.com:/1424-8220/18/3/778/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/s18030778","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors; Volume 18; Issue 3; Pages: 778","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s18030778","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18030778","pdf_url":"https://www.mdpi.com/1424-8220/18/3/778/pdf?version=1520161456","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5430905184","display_name":null,"funder_award_id":"61473085","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5874086168","display_name":null,"funder_award_id":"51375088","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G817174545","display_name":null,"funder_award_id":"51775110","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2794369236.pdf","grobid_xml":"https://content.openalex.org/works/W2794369236.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1975107695","https://openalex.org/W1977356379","https://openalex.org/W1979537916","https://openalex.org/W1982494121","https://openalex.org/W2028073198","https://openalex.org/W2038301993","https://openalex.org/W2059673153","https://openalex.org/W2112950808","https://openalex.org/W2116950968","https://openalex.org/W2120350100","https://openalex.org/W2142947066","https://openalex.org/W2146845212","https://openalex.org/W2149310890","https://openalex.org/W2218603760","https://openalex.org/W2293189367","https://openalex.org/W2343970396","https://openalex.org/W2345238027","https://openalex.org/W2412202319","https://openalex.org/W2721893673","https://openalex.org/W2963634839","https://openalex.org/W3104427658","https://openalex.org/W6704487870"],"related_works":["https://openalex.org/W123898865","https://openalex.org/W3092288791","https://openalex.org/W2391887161","https://openalex.org/W2185042433","https://openalex.org/W2381565014","https://openalex.org/W2353074735","https://openalex.org/W2328485329","https://openalex.org/W1671552943","https://openalex.org/W2384343431","https://openalex.org/W1966593065"],"abstract_inverted_index":{"Finding":[0],"the":[1,29,33,70,74,77,82,85,92,105,116,119,122,129,142,146,150,155,161,165,193,198,201],"position":[2,94],"of":[3,35,47,54,213],"a":[4,51,100,126,169,173,183],"radiative":[5],"source":[6,78,120,152,215],"based":[7],"on":[8,154,200],"time-difference-of-arrival":[9],"(TDOA)":[10],"measurements":[11],"from":[12,69,135,164],"spatially":[13],"separated":[14],"receivers":[15],"has":[16],"been":[17],"widely":[18],"applied":[19],"in":[20,32,73,87,225],"sonar,":[21],"radar,":[22],"mobile":[23],"communications":[24],"and":[25,39,66,121,148,172,191,208,217,236],"sensor":[26,124,144],"networks.":[27],"For":[28],"nonlinear":[30],"model":[31],"process":[34],"positioning,":[36],"Taylor":[37],"series":[38],"other":[40,136],"novel":[41],"methods":[42],"are":[43,67],"proposed.":[44],"The":[45,113,176,203,228],"idea":[46],"cone":[48,106,137,174,177],"constraint":[49,109,171,178],"provides":[50],"new":[52],"way":[53],"solving":[55],"this":[56,139,232],"problem.":[57],"However,":[58],"these":[59,226],"approaches":[60],"do":[61],"not":[62],"always":[63],"perform":[64],"well":[65],"away":[68],"Cramer-Rao-Lower-Bound":[71],"(CRLB)":[72],"situations":[75],"when":[76],"is":[79,89,95,132,158,180,234],"set":[80],"at":[81],"array":[83],"edge,":[84],"noise":[86],"measurement":[88,166],"loud,":[90],"or":[91],"initial":[93],"biased.":[96],"This":[97,186],"paper":[98,140],"presents":[99],"weighted-least-squares":[101],"(WLS)":[102],"algorithm":[103,205,233],"with":[104],"tangent":[107,184,194],"plane":[108,167],"for":[110,160],"hyperbolic":[111],"positioning.":[112],"method":[114,187],"adds":[115],"range":[117],"between":[118],"reference":[123,143],"as":[125,145],"dimension.":[127],"So,":[128],"space-range":[130],"frame":[131],"established.":[133],"Different":[134],"theories,":[138],"sets":[141],"apex":[147],"finds":[149],"optimal":[151,162],"estimation":[153],"cone.":[156,202],"WLS":[157],"used":[159],"result":[163],"equations,":[168],"vertical":[170],"constraint.":[175],"equation":[179],"linearized":[181],"by":[182],"plane.":[185],"iterates":[188],"through":[189],"loops":[190],"updates":[192],"plane,":[195],"which":[196],"approximates":[197],"truth-value":[199],"proposed":[204],"was":[206],"simulated":[207],"verified":[209],"under":[210,238],"various":[211],"conditions":[212],"different":[214],"positions":[216],"noises.":[218],"Besides,":[219],"some":[220],"state-of-the-art":[221],"algorithms":[222],"were":[223],"compared":[224],"simulations.":[227],"results":[229],"show":[230],"that":[231],"accurate":[235],"robust":[237],"poor":[239],"external":[240],"environment.":[241]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
