access icon free Hybrid extended-cubature Kalman filters for non-linear continuous-time fractional-order systems involving uncorrelated and correlated noises using fractional-order average derivative

© The Institution of Engineering and Technology
Received 25/09/2019, Accepted 13/01/2020, Revised 13/12/2019, Published 18/05/2020

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.

Inspec keywords: state estimation; Kalman filters; nonlinear control systems; difference equations; continuous time systems; nonlinear filters

Other keywords: cubature points; Grunwald–Letnikov difference method; HECKFs; difference equation; EKF method; nonlinear function; uncorrelated-correlated noises; nonlinear continuous-time fractional-order systems; third-degree spherical-radical rule; state estimation; first-order Taylor expansion; fractional-order average derivative method; hybrid extended-cubature Kalman filters

Subjects: Differential equations (numerical analysis); Signal processing theory; Simulation, modelling and identification; Differential equations (numerical analysis); Nonlinear control systems; Filtering methods in signal processing

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