{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:14:54Z","timestamp":1761581694968,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T00:00:00Z","timestamp":1525737600000},"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":["61771488","61671473","61631020"],"award-info":[{"award-number":["61771488","61671473","61631020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation for Distinguished Young Scholars of Jiangsu Province","award":["BK20160034"],"award-info":[{"award-number":["BK20160034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The problem of distributed power allocation in wireless sensor network (WSN) localization systems is investigated in this paper, using the game theoretic approach. Existing research focuses on the minimization of the localization errors of individual agent nodes over all anchor nodes subject to power budgets. When the service area and the distribution of target nodes are considered, finding the optimal trade-off between localization accuracy and power consumption is a new critical task. To cope with this issue, we propose a power allocation game where each anchor node minimizes the square position error bound (SPEB) of the service area penalized by its individual power. Meanwhile, it is proven that the power allocation game is an exact potential game which has one pure Nash equilibrium (NE) at least. In addition, we also prove the existence of an   \u03f5   -equilibrium point, which is a refinement of NE and the better response dynamic approach can reach the end solution. Analytical and simulation results demonstrate that: (i) when prior distribution information is available, the proposed strategies have better localization accuracy than the uniform strategies; (ii) when prior distribution information is unknown, the performance of the proposed strategies outperforms power management strategies based on the second-order cone program (SOCP) for particular agent nodes after obtaining the estimated distribution of agent nodes. In addition, proposed strategies also provide an instructional trade-off between power consumption and localization accuracy.<\/jats:p>","DOI":"10.3390\/s18051480","type":"journal-article","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T12:15:03Z","timestamp":1525781703000},"page":"1480","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Distributed Power Allocation for Wireless Sensor Network Localization: A Potential Game Approach"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3037-5324","authenticated-orcid":false,"given":"Mingxing","family":"Ke","sequence":"first","affiliation":[{"name":"The College of Communications Engineering, PLA Army Engineering University, Nanjing 210007, China"},{"name":"Science and Technology on Communication Networks Laboratory, Shijiazhuang 050002, China"}]},{"given":"Ding","family":"Li","sequence":"additional","affiliation":[{"name":"Modern Educational and Technological Center, Agricultural University of South China, Guangzhou 510642, China"}]},{"given":"Shiwei","family":"Tian","sequence":"additional","affiliation":[{"name":"The College of Communications Engineering, PLA Army Engineering University, Nanjing 210007, China"}]},{"given":"Yuli","family":"Zhang","sequence":"additional","affiliation":[{"name":"The College of Communications Engineering, PLA Army Engineering University, Nanjing 210007, China"},{"name":"Science and Technology on Communication Networks Laboratory, Shijiazhuang 050002, China"}]},{"given":"Kaixiang","family":"Tong","sequence":"additional","affiliation":[{"name":"The College of Communications Engineering, PLA Army Engineering University, Nanjing 210007, China"}]},{"given":"Yuhua","family":"Xu","sequence":"additional","affiliation":[{"name":"The College of Communications Engineering, PLA Army Engineering University, Nanjing 210007, China"},{"name":"Science and Technology on Communication Networks Laboratory, Shijiazhuang 050002, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2220","DOI":"10.1109\/COMST.2016.2544751","article-title":"A survey on mobile anchor node assisted localization in wireless sensor networks","volume":"18","author":"Han","year":"2016","journal-title":"IEEE Commun. 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