Fractional central difference Kalman filter with unknown prior information

Publication Type:
Journal Article
Signal Processing, 2019, 154 pp. 294 - 303
Issue Date:
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© 2018 In this paper, a generalized fractional central difference Kalman filter for nonlinear discrete fractional dynamic systems is proposed. Based on the Stirling interpolation formula, the presented algorithm can be implemented as no derivatives are needed. Besides, in order to estimate the state with unknown prior information, a maximum a posteriori principle based adaptive fractional central difference Kalman filter is derived. The adaptive algorithm can estimate the noise statistics and system state simultaneously. The unbiasedness of the proposed algorithm is analyzed. Several numerical examples demonstrate the accuracy and effectiveness of the two Kalman filters.
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