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

ABSTRACT

This paper presents the fractional-order Kalman filters using Tustin generating function for linear and nonlinear fractional-order systems involving process noise and measurement noise. By using the Tustin generating function, the differential equation model is obtained by discretising the investigated continuous-time fractional-order system. The two kinds of fractional-order Kalman filters are given for the correlated and uncorrelated cases in terms of the process noise and measurement noise for linear fractional-order system, respectively. In addition, based on the first-order Taylor expansion formula, the extended fractional-order Kalman filter using Tustin generating function is proposed to improve the accuracy of state estimation. Finally, three examples are illustrated to verify the effectiveness of the Tustion fractional-order Kalman filters for linear and nonlinear fractional-order systems.

KEYWORDS:

• Fractional-order systems
• Kalman filter
• Gaussian white noise
• state estimation
• Tustin generating function

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61304094]; the Scientific Research Fund of Liaoning Provincial Education Department, China [grant number L2015194].