{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T14:44:35Z","timestamp":1775745875175,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61571131; 61401188"],"award-info":[{"award-number":["61571131; 61401188"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a novel parallel factor (PARAFAC) model for processing the nested vector-sensor array is proposed. It is first shown that a nested vector-sensor array can be divided into multiple nested scalar-sensor subarrays. By means of the autocorrelation matrices of the measurements of these subarrays and the cross-correlation matrices among them, it is then demonstrated that these subarrays can be transformed into virtual scalar-sensor uniform linear arrays (ULAs). When the measurement matrices of these scalar-sensor ULAs are combined to form a third-order tensor, a novel PARAFAC model is obtained, which corresponds to a longer vector-sensor ULA and includes all of the measurements of the difference co-array constructed from the original nested vector-sensor array. Analyses show that the proposed PARAFAC model can fully use all of the measurements of the difference co-array, instead of its partial measurements as the reported models do in literature. It implies that all of the measurements of the difference co-array can be fully exploited to do the 2-D direction of arrival (DOA) and polarization parameter estimation effectively by a PARAFAC decomposition method so that both the better estimation performance and slightly improved identifiability are achieved. Simulation results confirm the efficiency of the proposed model.<\/jats:p>","DOI":"10.3390\/s18113708","type":"journal-article","created":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T11:55:41Z","timestamp":1540986941000},"page":"3708","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Novel PARAFAC Model for Processing the Nested Vector-Sensor Array"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5738-0759","authenticated-orcid":false,"given":"Wei","family":"Rao","sequence":"first","affiliation":[{"name":"Key Laboratory for Information Science of Electromagnetic Waves (MoE), School of Information Science and Technology, Fudan University, Shanghai 200433, China"},{"name":"Nanchang Institute of Technology, Nanchang 330099, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dan","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory for Information Science of Electromagnetic Waves (MoE), School of Information Science and Technology, Fudan University, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian Qiu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory for Information Science of Electromagnetic Waves (MoE), School of Information Science and Technology, Fudan University, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2481","DOI":"10.1109\/78.317869","article-title":"Acoustic vector-sensor array-processing","volume":"42","author":"Nehorai","year":"1994","journal-title":"IEEE Trans. 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