Kalman Filter for Fractional Order Singular Systems

In this paper, a Kalman filter for fractional order singular systems has been proposed. To design the Kalman filter, the fractional order singular system is decomposed into two sub-systems by using several transformations. The first sub-system is a dynamic system with fractional order non-singular state equations and the second sub-system is a static system in which the output is a combination of fractional derivatives of its input. Then, the Kalman filter has been elaborated for the system with an index 1 and 2. In the case of index 2, the identification method should be used due to the existence of color noise. At the end, two examples are used to demonstrate efficiency of the proposed method.