Open AccessHybrid extended‐cubature Kalman filters for non‐linear continuous‐time fractional‐order systems involving uncorrelated and correlated noises using fractional‐order average derivative
Author(s) -
Yang Chuang,
Gao Zhe,
Huang Xiaomin,
Kan Tao
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.1121
Subject(s) - mathematics , kalman filter , extended kalman filter , control theory (sociology) , fractional calculus , uncorrelated , taylor series , linear system , filter (signal processing) , function (biology) , mathematical analysis , computer science , statistics , control (management) , artificial intelligence , evolutionary biology , computer vision , biology
In this study, hybrid extended‐cubature Kalman filters (HECKFs) for non‐linear continuous‐time fractional‐order systems with uncorrelated and correlated noises are investigated. A non‐linear continuous‐time fractional‐order system using the fractional‐order average derivative is discretised to gain a difference equation. The fractional‐order average derivative method can achieve more accurate state estimation compared with the Grünwald–Letnikov difference method and the non‐linear functions in the system description are dealt with the extended Kalman filter (EKF) and cubature Kalman filter (CKF). The first‐order Taylor expansion used in the EKF method is implemented for a non‐linear function at the current time. Meanwhile, by using the third‐degree spherical‐radical rule, the functions in the state equation and output equation are performed by the cubature points. Based on these cubature points, the CKFs for uncorrelated and correlated noises are presented to achieve the effective state estimation. Besides, the simulation results are offered to validate the effectiveness of the HECKF proposed in this study.