{"id":"https://openalex.org/W1990956097","doi":"https://doi.org/10.1137/070699020","title":"The Large Equal Radius Conditions and Time of Arrival Geolocation Algorithms","display_name":"The Large Equal Radius Conditions and Time of Arrival Geolocation Algorithms","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1990956097","doi":"https://doi.org/10.1137/070699020","mag":"1990956097"},"language":"en","primary_location":{"id":"doi:10.1137/070699020","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070699020","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5109530391","display_name":"Louis A. Romero","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Louis A. Romero","raw_affiliation_strings":["lromero@sandia.gov and dmday@sandia.gov#TAB#"],"affiliations":[{"raw_affiliation_string":"lromero@sandia.gov and dmday@sandia.gov#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063920966","display_name":"J. Jeff Mason","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jeff Mason","raw_affiliation_strings":["jjmason@sandia.gov#TAB#"],"affiliations":[{"raw_affiliation_string":"jjmason@sandia.gov#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109329785","display_name":"David Day","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David M. Day","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109530391"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2314,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.54138612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"1","first_page":"254","last_page":"272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12004","display_name":"Advanced Frequency and Time Standards","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12004","display_name":"Advanced Frequency and Time Standards","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9853000044822693,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.635826826095581},{"id":"https://openalex.org/keywords/geolocation","display_name":"Geolocation","score":0.6096616983413696},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5922647714614868},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5362754464149475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.533616304397583},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5196208357810974},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5086656212806702},{"id":"https://openalex.org/keywords/arrival-time","display_name":"Arrival time","score":0.42700326442718506},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.400043249130249},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3692438006401062},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34086090326309204},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2809050381183624}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.635826826095581},{"id":"https://openalex.org/C22041718","wikidata":"https://www.wikidata.org/wiki/Q638949","display_name":"Geolocation","level":2,"score":0.6096616983413696},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5922647714614868},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5362754464149475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.533616304397583},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5196208357810974},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5086656212806702},{"id":"https://openalex.org/C3017552255","wikidata":"https://www.wikidata.org/wiki/Q4135208","display_name":"Arrival time","level":2,"score":0.42700326442718506},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.400043249130249},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3692438006401062},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34086090326309204},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2809050381183624},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C22212356","wikidata":"https://www.wikidata.org/wiki/Q775325","display_name":"Transport engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070699020","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070699020","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1971972151","https://openalex.org/W2029716185","https://openalex.org/W2061446664","https://openalex.org/W2077503693","https://openalex.org/W2083839214","https://openalex.org/W2104264645","https://openalex.org/W2114681990","https://openalex.org/W2120204404","https://openalex.org/W2120450738","https://openalex.org/W2150802260","https://openalex.org/W2164238332","https://openalex.org/W2164571208","https://openalex.org/W2803921418"],"related_works":["https://openalex.org/W2163194970","https://openalex.org/W3105229732","https://openalex.org/W2799094075","https://openalex.org/W2945387931","https://openalex.org/W2187946387","https://openalex.org/W2892370851","https://openalex.org/W2052024186","https://openalex.org/W2939141610","https://openalex.org/W4310429133","https://openalex.org/W2380692702"],"abstract_inverted_index":{"We":[0,109],"show":[1,32,50,111],"that":[2,33,51,75,112,119],"several":[3],"methods":[4],"for":[5,64],"solving":[6],"time":[7],"of":[8,81],"arrival":[9],"(TOA)":[10],"geolocation":[11],"problems":[12,104],"depend":[13],"crucially":[14],"on":[15],"what":[16],"we":[17,27,49,120],"call":[18,121],"the":[19,38,52,60,78,82,94,122,130],"large":[20],"equal":[21],"radius":[22],"(LER)":[23],"conditions.":[24],"For":[25],"example,":[26],"analyze":[28],"Bancroft's":[29],"method":[30,53,71,87,118,127],"and":[31,56],"it":[34],"works":[35],"well":[36,92],"assuming":[37],"LER":[39,95,131],"conditions":[40,46,96,132],"are":[41,47,97,107,133],"satisfied.":[42,108,134],"However,":[43],"when":[44,93,105,129],"these":[45],"violated,":[48],"significantly":[54],"deteriorates":[55,128],"does":[57],"not":[58,98],"achieve":[59],"minimum":[61],"possible":[62],"variance":[63],"a":[65,113],"least":[66,83,124],"squares":[67,84,125],"solution.":[68],"A":[69],"direct":[70],"is":[72,88],"also":[73,110],"presented":[74],"finds":[76],"all":[77],"critical":[79],"points":[80],"functional.":[85],"The":[86],"found":[89],"to":[90],"perform":[91],"satisfied":[99],"but":[100,115],"suffers":[101],"from":[102],"conditioning":[103],"they":[106],"simple":[114],"statistically":[116],"inferior":[117],"reduced":[123],"(RLS)":[126]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
