{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T10:54:33Z","timestamp":1773572073741,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T00:00:00Z","timestamp":1665705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Special Fund Project for Technology Innovation of Shanghai Institute of Technical Physics, Chinese Academy of Scicences","award":["CX-212"],"award-info":[{"award-number":["CX-212"]}]},{"name":"Special Fund Project for Technology Innovation of Shanghai Institute of Technical Physics, Chinese Academy of Scicences","award":["CXJJ-20S030"],"award-info":[{"award-number":["CXJJ-20S030"]}]},{"name":"Special Fund Project of Chinese Academy of Scicences \u201cStudy on the infrared characteristics of chaotic medium response to the disturbance\u201d","award":["CX-212"],"award-info":[{"award-number":["CX-212"]}]},{"name":"Special Fund Project of Chinese Academy of Scicences \u201cStudy on the infrared characteristics of chaotic medium response to the disturbance\u201d","award":["CXJJ-20S030"],"award-info":[{"award-number":["CXJJ-20S030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Under the too short arc scenario, the evolutionary-based algorithm has more potential than traditional methods in initial orbit determination. However, the underlying multimodal phenomenon in initial orbit determination is ignored by current works. In this paper, we propose a new enhanced differential evolution (DE) algorithm with multimodal property to study the angle-only IOD problem. Specifically, a coarse-to-fine convergence detector is implemented, based on the Boltzmann Entropy, to determine the evolutionary phase of the population, which lays the basis of the balance between the exploration and exploitation ability. A two-layer niching technique clusters the individuals to form promising niches after each convergence detected. The candidate optima from resulting niches are saved as supporting individuals into an external archive for diversifying the population, and a local search within the archive is performed to refine the solutions. In terms of performance validation, the proposed multimodal differential evolution algorithm is evaluated on the CEC2013 multimodal benchmark problems, and it achieved competitive results compared to 11 state-of-the-art algorithms, which present its capability of multimodal optimization. Moreover, several IOD experiments and analyses are carried out on three simulated scenarios of space-based observation. The findings show that, compared to traditional IOD approaches and EA-based IOD algorithms, the proposed algorithm is more successful at finding plausible solutions while improving IOD accuracy.<\/jats:p>","DOI":"10.3390\/rs14205140","type":"journal-article","created":{"date-parts":[[2022,10,17]],"date-time":"2022-10-17T03:43:58Z","timestamp":1665978238000},"page":"5140","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Multimodal Differential Evolution Algorithm in Initial Orbit Determination for a Space-Based Too Short Arc"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7873-9399","authenticated-orcid":false,"given":"Hui","family":"Xie","sequence":"first","affiliation":[{"name":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Intelligent Infrared Perception, Chinese Academy of Sciences, Shanghai 200083, China"}]},{"given":"Shengli","family":"Sun","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"Key Laboratory of Intelligent Infrared Perception, Chinese Academy of Sciences, Shanghai 200083, China"}]},{"given":"Tianru","family":"Xue","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Wenjun","family":"Xu","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"Key Laboratory of Intelligent Infrared Perception, Chinese Academy of Sciences, Shanghai 200083, China"}]},{"given":"Huikai","family":"Liu","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Intelligent Infrared Perception, Chinese Academy of Sciences, Shanghai 200083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8467-1634","authenticated-orcid":false,"given":"Linjian","family":"Lei","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Intelligent Infrared Perception, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}]},{"given":"Yue","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Intelligent Infrared Perception, Chinese Academy of Sciences, Shanghai 200083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s10569-004-6593-5","article-title":"Orbit determination with very short arcs. 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