{"id":"https://openalex.org/W3114373765","doi":"https://doi.org/10.1109/taes.2020.3046080","title":"A Practical Diophantine Approximation for Sparse Linear Array Direction Finding","display_name":"A Practical Diophantine Approximation for Sparse Linear Array Direction Finding","publication_year":2020,"publication_date":"2020-12-21","ids":{"openalex":"https://openalex.org/W3114373765","doi":"https://doi.org/10.1109/taes.2020.3046080","mag":"3114373765"},"language":"en","primary_location":{"id":"doi:10.1109/taes.2020.3046080","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2020.3046080","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","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/A5089816970","display_name":"Songsri Sirianunpiboon","orcid":"https://orcid.org/0000-0001-5479-2435"},"institutions":[{"id":"https://openalex.org/I1303474014","display_name":"Defence Science and Technology Group","ror":"https://ror.org/05ddrvt52","country_code":"AU","type":"funder","lineage":["https://openalex.org/I1303474014","https://openalex.org/I2801453606","https://openalex.org/I3139952251"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Songsri Sirianunpiboon","raw_affiliation_strings":["Defence Science and Technology Group, Edinburgh, SA, Australia"],"affiliations":[{"raw_affiliation_string":"Defence Science and Technology Group, Edinburgh, SA, Australia","institution_ids":["https://openalex.org/I1303474014"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047215762","display_name":"Peter Q. C. Ly","orcid":"https://orcid.org/0000-0003-4352-5715"},"institutions":[{"id":"https://openalex.org/I1303474014","display_name":"Defence Science and Technology Group","ror":"https://ror.org/05ddrvt52","country_code":"AU","type":"funder","lineage":["https://openalex.org/I1303474014","https://openalex.org/I2801453606","https://openalex.org/I3139952251"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Peter Q. C. Ly","raw_affiliation_strings":["Defence Science and Technology Group, Edinburgh, SA, Australia"],"affiliations":[{"raw_affiliation_string":"Defence Science and Technology Group, Edinburgh, SA, Australia","institution_ids":["https://openalex.org/I1303474014"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084334435","display_name":"Stephen D. Elton","orcid":null},"institutions":[{"id":"https://openalex.org/I1303474014","display_name":"Defence Science and Technology Group","ror":"https://ror.org/05ddrvt52","country_code":"AU","type":"funder","lineage":["https://openalex.org/I1303474014","https://openalex.org/I2801453606","https://openalex.org/I3139952251"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Stephen D. Elton","raw_affiliation_strings":["Defence Science and Technology Group, Edinburgh, SA, Australia"],"affiliations":[{"raw_affiliation_string":"Defence Science and Technology Group, Edinburgh, SA, Australia","institution_ids":["https://openalex.org/I1303474014"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089816970"],"corresponding_institution_ids":["https://openalex.org/I1303474014"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.15806452,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"57","issue":"3","first_page":"1405","last_page":"1412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10860","display_name":"Speech and Audio Processing","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9896000027656555,"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/algorithm","display_name":"Algorithm","score":0.6959187388420105},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.6691799163818359},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5455023050308228},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5142540335655212},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4755639433860779},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4688454866409302},{"id":"https://openalex.org/keywords/direction-of-arrival","display_name":"Direction of arrival","score":0.45678457617759705},{"id":"https://openalex.org/keywords/antenna-array","display_name":"Antenna array","score":0.4368467926979065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43509453535079956},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.4349656403064728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43436241149902344},{"id":"https://openalex.org/keywords/sparse-array","display_name":"Sparse array","score":0.41917189955711365},{"id":"https://openalex.org/keywords/antenna","display_name":"Antenna (radio)","score":0.14181077480316162},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13112452626228333}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6959187388420105},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.6691799163818359},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5455023050308228},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5142540335655212},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4755639433860779},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4688454866409302},{"id":"https://openalex.org/C172051844","wikidata":"https://www.wikidata.org/wiki/Q5280438","display_name":"Direction of arrival","level":3,"score":0.45678457617759705},{"id":"https://openalex.org/C62191587","wikidata":"https://www.wikidata.org/wiki/Q4771249","display_name":"Antenna array","level":3,"score":0.4368467926979065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43509453535079956},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.4349656403064728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43436241149902344},{"id":"https://openalex.org/C145177509","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse array","level":2,"score":0.41917189955711365},{"id":"https://openalex.org/C21822782","wikidata":"https://www.wikidata.org/wiki/Q131214","display_name":"Antenna (radio)","level":2,"score":0.14181077480316162},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13112452626228333},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/taes.2020.3046080","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2020.3046080","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W263992175","https://openalex.org/W1499739822","https://openalex.org/W1499886568","https://openalex.org/W1827663536","https://openalex.org/W2007343403","https://openalex.org/W2033208766","https://openalex.org/W2041401149","https://openalex.org/W2043204079","https://openalex.org/W2057669171","https://openalex.org/W2114675012","https://openalex.org/W2201571739","https://openalex.org/W2332984834","https://openalex.org/W2424924930","https://openalex.org/W2597651523","https://openalex.org/W2781926993","https://openalex.org/W2782306098","https://openalex.org/W2808237721","https://openalex.org/W3183879652","https://openalex.org/W6752232773","https://openalex.org/W6798444507"],"related_works":["https://openalex.org/W1502194460","https://openalex.org/W2172110403","https://openalex.org/W1972262469","https://openalex.org/W4376608380","https://openalex.org/W2348704334","https://openalex.org/W2130116177","https://openalex.org/W2074954788","https://openalex.org/W2517787832","https://openalex.org/W2344357198","https://openalex.org/W4317795331"],"abstract_inverted_index":{"This":[0],"article":[1],"presents":[2],"a":[3,16,23,61,103,149],"computationally":[4],"efficient,":[5],"fixed":[6,95],"complexity":[7],"algorithm":[8,66,85,92,137],"for":[9,32,56,81],"estimating":[10],"the":[11,33,57,64,84,91,110,124,130,133],"angle":[12],"of":[13,15,27,49,52,75,79,83,106,132,144],"arrival":[14],"radio":[17],"frequency":[18],"signal":[19],"that":[20,143],"impinges":[21],"on":[22],"sparse":[24],"linear":[25],"array":[26,107,111],"sensors.":[28],"The":[29,77,98,126],"likelihood":[30],"function":[31],"bearing":[34,135],"estimation":[35,118,136],"problem":[36,44],"is":[37],"reduced":[38,151],"to":[39,63,93,102,113,116,122,138,142],"an":[40,46,69],"inhomogeneous":[41],"Diophantine":[42],"approximation":[43],"involving":[45],"unknown":[47],"set":[48],"integer":[50],"multiples":[51],"2\u03c0.":[53],"In":[54],"solving":[55],"integers,":[58],"we":[59],"propose":[60],"modification":[62],"Cassels":[65],"and":[67],"generate":[68],"approximate":[70],"linearized":[71],"maximum-likelihood":[72],"(ML)":[73],"estimate":[74],"bearing.":[76],"number":[78],"iterations":[80],"convergence":[82],"can":[86],"be":[87,114,139],"precomputed,":[88],"which":[89],"allows":[90],"have":[94],"computational":[96,152],"complexity.":[97],"proposed":[99,134],"technique":[100],"applies":[101],"large":[104],"class":[105],"configurations,":[108],"allowing":[109],"configuration":[112],"chosen":[115],"optimize":[117],"performance":[119,131],"rather":[120],"than":[121],"suit":[123],"algorithm.":[125],"simulation":[127],"results":[128],"show":[129],"very":[140],"close":[141],"ML":[145],"estimation,":[146],"but":[147],"with":[148],"significantly":[150],"overhead.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
