{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:14:36Z","timestamp":1774624476277,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T00:00:00Z","timestamp":1671753600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Research and Development Program of Shaanxi","award":["2022GY-240"],"award-info":[{"award-number":["2022GY-240"]}]},{"name":"Key Research and Development Program of Shaanxi","award":["51909217"],"award-info":[{"award-number":["51909217"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022GY-240"],"award-info":[{"award-number":["2022GY-240"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51909217"],"award-info":[{"award-number":["51909217"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In addition to various estimation algorithms, the target localization accuracy in wireless sensor networks (WSNs) can also be improved from the perspective of geometry optimization. Note that existing placement strategies are mainly aimed at unconstrained deployment regions, i.e., the positions of sensors are arbitrary. In this paper, considering factors such as terrain, communication, and security, the optimal range-based sensor geometries under circular deployment region and minimum safety distance constraints are proposed. The geometry optimization problem is modeled as a constrained optimization problem, with a D-optimality-based (maximizing the determinant of FIM matrix) scalar function as the objective function and the irregular feasible deployment regions as the constraints. We transform the constrained optimization problem into an equivalent form using the introduced maximum feasible angle and separation angle, and discuss the optimal geometries based on the relationship between the minimum safety distance and the maximum feasible angle. We first consider optimal geometries for two and three sensors in the localization system, and then use their findings to extend the study to scenarios with arbitrary numbers of sensors and arbitrarily shaped feasible regions. Numerical simulation results are included to verify the theoretical conclusions.<\/jats:p>","DOI":"10.3390\/e25010032","type":"journal-article","created":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T04:40:39Z","timestamp":1672116039000},"page":"32","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Improving Localization Accuracy under Constrained Regions in Wireless Sensor Networks through Geometry Optimization"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9134-7039","authenticated-orcid":false,"given":"Xinpeng","family":"Fang","sequence":"first","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhihao","family":"He","sequence":"additional","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shouxu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junbing","family":"Li","sequence":"additional","affiliation":[{"name":"Aeronautical and Astronautical Engineering Collage, Air Force Engineering University, Xi\u2019an 710043, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ranjun","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s11235-021-00804-y","article-title":"A parallel compact sine cosine algorithm for TDOA localization of wireless sensor network","volume":"78","author":"Zhang","year":"2021","journal-title":"Telecommun. 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