Open AccessKalman filters for linear continuous‐time fractional‐order systems involving coloured noises using fractional‐order average derivative
Author(s) -
Yang Chao,
Gao Zhe,
Liu Fanghui
Publication year - 2018
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.2017.0817
Subject(s) - kalman filter , noise (video) , control theory (sociology) , fractional calculus , mathematics , correctness , filter (signal processing) , linear system , algorithm , computer science , mathematical analysis , statistics , artificial intelligence , control (management) , image (mathematics) , computer vision
In this study, Kalman filters for continuous‐time linear fractional‐order systems are studied with fractional‐order coloured process and measurement noise, respectively. By fractional‐order average derivative, linear fractional‐order systems with coloured fractional‐order process or measurement noise are discretised. To deal with coloured noises, the authors construct an augmented system with respect to the state, the process noise and the measurement noise. Furthermore, fractional‐order Kalman filter using the fractional‐order average derivative is proposed. This filter improves the accuracy of the state estimation and the filtering effect for coloured process and measurement noises. Finally, they give two examples to verify the correctness and validity of the proposed algorithm.