A modified Kalman filter algorithm for fractional system under Lévy noises

• Published in: Journal of the Franklin Institute 2015-05, Vol.352 (5), p.1963-1978
• Main Authors: Wu, Xiaopeng, Sun, Yonghui, Lu, Zigang, Wei, Zhinong, Ni, Ming, Yu, Wenjie
• Format: Article
• Language: English
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2015.02.008

This paper considers the filter designing problem for discrete linear fractional order systems with non-Gaussian noises. Taking both the system noise and the measurement noise as Lévy noises instead of Gaussian white noises, through the approximating transformation for Lévy noises, a modified Kalman filter algorithm is proposed for discrete linear fractional order system. The developed results can be used to estimate the system states for discrete linear fractional order system under non-Gaussian Lévy noises with satisfactory accuracy, which are more general than some existing results. Finally, simulation results are provided to verify and illustrate the effectiveness of the obtained results. •Considering the filter designing problem for discrete linear fractional order systems with non-Gaussian noises.•Proposing a novel Kalman filter algorithm for discrete linear fractional order system with Levy noises.•Estimating the system states for the discrete linear fractional order system under non-Gaussian Lévy noises with a satisfactory accuracy.