{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:07:54Z","timestamp":1760242074170,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T00:00:00Z","timestamp":1543363200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC 61871414"],"award-info":[{"award-number":["NSFC 61871414"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Angle estimation methods in two-dimensional co-prime planar arrays have been discussed mainly based on peak searching and sparse recovery. Peak searching methods suffer from heavy computational complexity and sparse recovery methods face some problems in selecting the regularization parameters. In this paper, we propose an improved trilinear model-based method for angle estimation for co-prime planar arrays in the view of trilinear decomposition, namely parallel factor analysis. Due to the principle of trilinear decomposition, our method does not require peak searching and can conduct auto-pairing easily, which can reduce the computational loads and avoid parameter selection problems. Furthermore, we exploit the virtual array concept of the whole co-prime planar array through the cross-correlation matrix obtained from the received signal data and present a matrix reconstruction method using the Khatri\u2013Rao product to tackle the matrix rank deficiency problem in the virtual array condition. The simulation results show that our proposed method can not only achieve high estimation accuracy with low complexity compared to other similar approaches, but also utilize limited sensor number to implement the angle estimation tasks.<\/jats:p>","DOI":"10.3390\/s18124180","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T11:43:44Z","timestamp":1543405424000},"page":"4180","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Improved Trilinear Model-Based Angle Estimation Method for Co-Prime Planar Arrays"],"prefix":"10.3390","volume":"18","author":[{"given":"Chenxi","family":"Guo","sequence":"first","affiliation":[{"name":"National Key Laboratory of Mechatronic Engineering and Control, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6448-4839","authenticated-orcid":false,"given":"Xinhong","family":"Hao","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Mechatronic Engineering and Control, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Li","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Mechatronic Engineering and Control, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research: The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. 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