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Kalman Filters for Continuous-time Fractional-order Systems Involving Fractional-order Colored Noises Using Tustin Generating Function

Zhe Gao
International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp.1049-1059, 2018

Abstract : "This study presents fractional-order Kalman filers for linear fractional-order systems with colored noises using Tustin generating function. A continuous-time fractional-order system with the fractional-order colored process noise is discretized by Tustin generating function. The augmented vector consists of the state and the colored noise is offered to construct an augmented system based on the discretized state equation of a fractional-order system and the colored process noise. The Tustin fractional-order Kalman filter is designed based on the augmented system to obtain the state estimation, effectively. Besides, the colored noise involved in the measurement of a continuous-time fractional-order system is also discussed, and the corresponding Tustin fractional-order Kalman filter is provided in this study. Two illustrative examples are given to verify the effectiveness of Tustin fractionalorder Kalman filters for the colored process and measurement noises.d separately by solving a set of LMIs and then used to estimate the unmeasured states, sensor and actuator"

Keyword : Colored noise, fractional-order systems, Kalman filters, state estimation, Tustin generating function.

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