Abstract
This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems.
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Torabi, H., Pariz, N. & Karimpour, A. Kalman filters for fractional discrete-time stochastic systems along with time-delay in the observation signal. Eur. Phys. J. Spec. Top. 225, 107–118 (2016). https://doi.org/10.1140/epjst/e2016-02619-6
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DOI: https://doi.org/10.1140/epjst/e2016-02619-6