{"id":"https://openalex.org/W7123348883","doi":"https://doi.org/10.1109/taes.2026.3652032","title":"Numerical Techniques for the Maximum Likelihood Toeplitz Covariance Matrix Estimation: Part II\u2014Hermitian Toeplitz Matrices","display_name":"Numerical Techniques for the Maximum Likelihood Toeplitz Covariance Matrix Estimation: Part II\u2014Hermitian Toeplitz Matrices","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7123348883","doi":"https://doi.org/10.1109/taes.2026.3652032"},"language":null,"primary_location":{"id":"doi:10.1109/taes.2026.3652032","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2026.3652032","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/A5122882298","display_name":"Yuri Abramovich","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yuri Abramovich","raw_affiliation_strings":["WR Systems, Ltd., Fairfax, VA, USA"],"affiliations":[{"raw_affiliation_string":"WR Systems, Ltd., Fairfax, VA, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Victor Abramovich","orcid":"https://orcid.org/0000-0003-1155-8512"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Victor Abramovich","raw_affiliation_strings":["WR Systems, Ltd., Fairfax, VA, USA"],"affiliations":[{"raw_affiliation_string":"WR Systems, Ltd., Fairfax, VA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5122873951","display_name":"Tanit Pongsiri","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tanit Pongsiri","raw_affiliation_strings":["WR Systems, Ltd., Fairfax, VA, USA"],"affiliations":[{"raw_affiliation_string":"WR Systems, Ltd., Fairfax, VA, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5122882298"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12629054,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"62","issue":null,"first_page":"3971","last_page":"3990"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.2305999994277954,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.2305999994277954,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11716","display_name":"Random Matrices and Applications","score":0.1387999951839447,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.0997999981045723,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9243000149726868},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6959999799728394},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.6553000211715698},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.6273000240325928},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.578000009059906},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.5425999760627747},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.448199987411499},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.44119998812675476},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.42649999260902405}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9243000149726868},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6959999799728394},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6553000211715698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6514000296592712},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6273000240325928},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.578000009059906},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.5425999760627747},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5174000263214111},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.44119998812675476},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.4108000099658966},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3749000132083893},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36079999804496765},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C129759605","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance mapping","level":5,"score":0.33079999685287476},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3212999999523163},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.31690001487731934},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.3091999888420105},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.30000001192092896},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.2939999997615814},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.28929999470710754},{"id":"https://openalex.org/C2777701225","wikidata":"https://www.wikidata.org/wiki/Q5241941","display_name":"Waviness","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C88271906","wikidata":"https://www.wikidata.org/wiki/Q786973","display_name":"Autocovariance","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2517000138759613}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/taes.2026.3652032","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2026.3652032","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1659823078","https://openalex.org/W1988969747","https://openalex.org/W1999640431","https://openalex.org/W2006269597","https://openalex.org/W2045867863","https://openalex.org/W2049514806","https://openalex.org/W2055576793","https://openalex.org/W2061303336","https://openalex.org/W2062239955","https://openalex.org/W2068135051","https://openalex.org/W2068207164","https://openalex.org/W2080686531","https://openalex.org/W2096852244","https://openalex.org/W2097820992","https://openalex.org/W2105502962","https://openalex.org/W2108696776","https://openalex.org/W2110106967","https://openalex.org/W2136274821","https://openalex.org/W2136606783","https://openalex.org/W2140014273","https://openalex.org/W2150629312","https://openalex.org/W2157921975","https://openalex.org/W2299769372","https://openalex.org/W2539904871","https://openalex.org/W3021961868","https://openalex.org/W3047830053","https://openalex.org/W3162471214","https://openalex.org/W4213251304","https://openalex.org/W4234502143","https://openalex.org/W4235706696","https://openalex.org/W4394616891","https://openalex.org/W4415914118"],"related_works":[],"abstract_inverted_index":{"Independence":[0],"of":[1,43,91],"the":[2,10,13,24,32,44,50,62,71,75,79,89,92,97],"normalized":[3],"likelihood":[4,45],"functions":[5],"(likelihood":[6],"ratios,":[7],"LR)":[8],"with":[9],"argument":[11],"being":[12],"true":[14,39],"Toeplitz":[15],"covariance":[16,40],"matrix":[17],"creates":[18],"a":[19,57],"statistical":[20],"lower":[21],"bound":[22],"for":[23,56],"optimized":[25,63],"maximum":[26,82,100],"likelihood,":[27],"since":[28],"in":[29,74,101],"this":[30,38],"case":[31],"pdf":[33],"does":[34],"not":[35],"depend":[36],"on":[37],"matrix.":[41],"Analysis":[42],"ratio":[46],"maximization":[47],"results":[48],"using":[49],"MATLAB":[51],"fmincon":[52,93],"routine":[53,94],"demonstrated":[54],"that":[55],"large":[58],"enough":[59],"sample":[60],"volume,":[61],"solution":[64],"is":[65],"either":[66],"unacceptable,":[67],"mainly":[68],"due":[69],"to":[70,87,95],"negative":[72],"eigenvalues":[73],"solution,":[76],"or":[77],"meets":[78],"global":[80,98],"LR":[81,99],"criteria.":[83],"The":[84],"method":[85],"proposed":[86],"modify":[88],"initialization":[90],"achieve":[96],"every":[102],"trial.":[103]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2026-01-14T00:00:00"}