Fractional-order Kalman filters for continuous-time linear and nonlinear fractional-order systems using Tustin generating function

2017 ◽  
Vol 92 (5) ◽  
pp. 960-974 ◽  
Author(s):  
Zhe Gao
Keyword(s):  
Fractional Order ◽  
Generating Function ◽  
Continuous Time ◽  
Kalman Filters ◽  
Fractional Order Systems ◽  
Linear And Nonlinear ◽  
Time Linear

Fractional-order Kalman filters for continuous-time fractional-order systems involving correlated and uncorrelated process and measurement noises

2018 ◽  
Vol 41 (7) ◽  
pp. 1933-1947 ◽  
Author(s):  
Fanghui Liu ◽  
Zhe Gao ◽  
Chao Yang ◽  
Ruicheng Ma
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
Equation Model ◽  
Order System ◽  
Fractional Order Systems ◽  
Derivative Method ◽  
Measurement Noises ◽  
Computation Load ◽  
Average Derivative

This paper presents fractional-order Kalman filters using the fractional-order average derivative method for linear fractional-order systems involving process and measurement noises. By using the fractional-order average derivative method, a difference equation model is obtained by discretizing the investigated continuous-time fractional-order system, and the accuracy of state estimation is improved. Meanwhile, compared with the Tustin generating function, the fractional-order average derivative method proposed in this paper can reduce computation load and save calculation time. Two kinds of fractional-order Kalman filters are given, for the correlated and uncorrelated cases, in terms of the process and measurement noises for linear fractional-order systems, respectively. Finally, simulation results are illustrated to verify the effectiveness of the proposed Kalman filters using the fractional-order average derivative method.

Hybrid extended-unscented Kalman filters for continuous-time nonlinear fractional-order systems involving process and measurement noises

2020 ◽  
Vol 42 (9) ◽  
pp. 1618-1631
Author(s):  
Xiaojiao Chen ◽  
Zhe Gao ◽  
Ruicheng Ma ◽  
Xiaomin Huang
Keyword(s):  
Kalman Filter ◽  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
Unscented Kalman Filter ◽  
Nonlinear Function ◽  
Fractional Order Systems ◽  
Error Matrix ◽  
Current Time ◽  
Measurement Noises

Hybrid extended-unscented Kalman filters (HEUKFs) for continuous-time nonlinear fractional-order systems with process and measurement noises are investigated in this paper. The Grünwald-Letnikov difference and the fractional-order average derivative (FOAD) method are adopted to discretize the investigated nonlinear fractional-order system, and the nonlinear functions in the system description are coped with the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The first-order Taylor expansion used in the EKF method is performed for the nonlinear function at the current time. Meanwhile, the unscented transformation used in the UKF is also concerned for the nonlinear function at the previous time. By using the HEUKF designed in this paper, the third-order approximations for the nonlinear function can be achieved to enhance the accuracy of state estimation and estimation error matrix. Finally, numerical examples are provided to illustrate the effectiveness of the proposed HEUKF for nonlinear fractional-order systems.

scholarly journals Design of unknown input fractional-order observers for fractional-order systems

2013 ◽  
Vol 23 (3) ◽  
pp. 491-500 ◽  
Author(s):  
Ibrahima N’Doye ◽  
Mohamed Darouach ◽  
Holger Voos ◽  
Michel Zasadzinski
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Order Error ◽  
Error System ◽  
Time Linear

Abstract This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1≤α<2 and 0<α≤1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.

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