Fractional-order Kalman filters for continuous-time linear and nonlinear fractional-order systems using Tustin generating function |
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Authors: | Zhe Gao |
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Affiliation: | Department of Electrical Engineering and Automation, College of Light Industry, Liaoning University , Shenyang, P. R. China |
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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. |
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Keywords: | Fractional-order systems Kalman filter Gaussian white noise state estimation Tustin generating function |
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