{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T15:26:56Z","timestamp":1767626816796,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T00:00:00Z","timestamp":1631145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Beidou Navigation In-orbit Support System","award":["JKBDZGDH01"],"award-info":[{"award-number":["JKBDZGDH01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Detection of faults at the incipient stage is critical to improving the availability and continuity of satellite services. The application of a local optimum projection vector and the Kullback\u2013Leibler (KL) divergence can improve the detection rate of incipient faults. However, this suffers from the problem of high time complexity. We propose decomposing the KL divergence in the original optimization model and applying the property of the generalized Rayleigh quotient to reduce time complexity. Additionally, we establish two distribution models for subfunctions F1(w) and F3(w) to detect the slight anomalous behavior of the mean and covariance. The effectiveness of the proposed method was verified through a numerical simulation case and a real satellite fault case. The results demonstrate the advantages of low computational complexity and high sensitivity to incipient faults.<\/jats:p>","DOI":"10.3390\/e23091194","type":"journal-article","created":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T12:20:37Z","timestamp":1631190037000},"page":"1194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Satellite Incipient Fault Detection Method Based on Decomposed Kullback\u2013Leibler Divergence"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7127-9940","authenticated-orcid":false,"given":"Ge","family":"Zhang","sequence":"first","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS, Shanghai 201203, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiong","family":"Yang","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS, Shanghai 201203, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guotong","family":"Li","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS, Shanghai 201203, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaxing","family":"Leng","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS, Shanghai 201203, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mubiao","family":"Yan","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS, Shanghai 201203, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s43020-019-0006-0","article-title":"Basic performance and future developments of BeiDou global navigation satellite system","volume":"1","author":"Yang","year":"2020","journal-title":"Satell. 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