{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T05:14:36Z","timestamp":1780463676048,"version":"3.54.1"},"reference-count":22,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:00:00Z","timestamp":1630368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"[03] key project of National Natural Science Foundation of China (No. 61933013): intelligent diagnosis, prediction and maintenance of abnormal working conditions of large petrochemical units","award":["No.61933013"],"award-info":[{"award-number":["No.61933013"]}]},{"name":"[02] key project of National Natural Science Foundation of China and Zhejiang joint fund for integration of industrialization and industrialization (No. u1509203), life cycle fault prediction, and intelligent health management of large ship power system o","award":["No.U1509203"],"award-info":[{"award-number":["No.U1509203"]}]},{"name":"[01] key project of National Natural Science Foundation of China (No. 61751304), extraction and deep learning of optimal decision rules in an uncertain small sample environment","award":["No.61751304"],"award-info":[{"award-number":["No.61751304"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes one new design method for a higher order extended Kalman filter based on combining maximum correlation entropy with a Taylor network system to create a nonlinear random dynamic system with modeling errors and unknown statistical properties. Firstly, the transfer function and measurement function are transformed into a nonlinear random dynamic model with a polynomial form via system identification through the multidimensional Taylor network. Secondly, the higher order polynomials in the transformed state model and measurement model are defined as implicit variables of the system. At the same time, the state model and the measurement model are equivalent to the pseudolinear model based on the combination of the original variable and the hidden variable. Thirdly, higher order hidden variables are treated as additive parameters of the system; then, we establish an extended dimensional linear state model and a measurement model combining state and parameters via the previously used random dynamic model. Finally, as we only know the results of the limited sampling of the random modeling error, we use the combination of the maximum correlation estimator and the Kalman filter to establish a new higher order extended Kalman filter. The effectiveness of the new filter is verified by digital simulation.<\/jats:p>","DOI":"10.3390\/s21175864","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T22:58:15Z","timestamp":1630450695000},"page":"5864","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Design Method for a Higher Order Extended Kalman Filter Based on Maximum Correlation Entropy and a Taylor Network System"],"prefix":"10.3390","volume":"21","author":[{"given":"Qiupeng","family":"Wang","sequence":"first","affiliation":[{"name":"School of HDU-ITMO, Joint Institute, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaohui","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenglin","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problems. actions of the","volume":"82","author":"Kalman","year":"1960","journal-title":"Trans. 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