{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T10:46:29Z","timestamp":1767091589567,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,22]],"date-time":"2023-07-22T00:00:00Z","timestamp":1689984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62003261","61702410","62073258","61871318","2020JQ-645","2020JQ-650","2021JQ-487","2023-CX-TD-01"],"award-info":[{"award-number":["62003261","61702410","62073258","61871318","2020JQ-645","2020JQ-650","2021JQ-487","2023-CX-TD-01"]}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["62003261","61702410","62073258","61871318","2020JQ-645","2020JQ-650","2021JQ-487","2023-CX-TD-01"],"award-info":[{"award-number":["62003261","61702410","62073258","61871318","2020JQ-645","2020JQ-650","2021JQ-487","2023-CX-TD-01"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["62003261","61702410","62073258","61871318","2020JQ-645","2020JQ-650","2021JQ-487","2023-CX-TD-01"],"award-info":[{"award-number":["62003261","61702410","62073258","61871318","2020JQ-645","2020JQ-650","2021JQ-487","2023-CX-TD-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Although the cost-reference particle filter (CRPF) has a good advantage in solving the state estimation problem with unknown noise statistical characteristics, its estimation accuracy is still affected by the lack of particle diversity and sensitivity to the particles\u2019 initial value. In order to solve these problems of the CRPF, this paper proposed an intelligent cost-reference particle filter algorithm based on multi-population cooperation. A multi-population cooperative resampling strategy based on ring structure was designed. The particles were divided into multiple independent populations upon initialization, and each population generated particles with a different initial distribution. The particles in each population were divided into three different particle sets with high, medium and low weights by the golden section ratio according to the weight. The particle sets with high and medium weights were retained. Then, a cooperative strategy based on Gaussian mutation was designed to resample the low-weight particle set of each population. The high-weight particles of the previous population in the ring structure were randomly selected for Gaussian mutation to replace the low-weight particles in the current population. The low-weight particles of all populations were resampled in turn. The simulation results show that the intelligent CRPF based on multi-population cooperation proposed in this paper can reduce the sensitivity of the CRPF to the particles\u2019 initial value and improve the particle diversity in resampling. Compared with the general CRPF and intelligent CRPF with adaptive MH resampling (MH-CRPF), the RMSE and MAE of the proposed method are lower.<\/jats:p>","DOI":"10.3390\/s23146603","type":"journal-article","created":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T03:03:25Z","timestamp":1690167805000},"page":"6603","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Intelligent Cost-Reference Particle Filter with Resampling of Multi-Population Cooperation"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9518-4644","authenticated-orcid":false,"given":"Xinyu","family":"Zhang","sequence":"first","affiliation":[{"name":"Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Faculty of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}]},{"given":"Mengjiao","family":"Ren","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Faculty of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}]},{"given":"Jiemin","family":"Duan","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Faculty of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}]},{"given":"Yingmin","family":"Yi","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Faculty of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}]},{"given":"Biyu","family":"Lei","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Faculty of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}]},{"given":"Shuyue","family":"Wu","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Faculty of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"8831","DOI":"10.1109\/TIM.2020.2996004","article-title":"Remaining useful life prediction of lithium-ion batteries based on conditional vibrational auto encoders-particle filter","volume":"69","author":"Jiao","year":"2020","journal-title":"IEEE Trans. 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