Nonlinear Kalman Filter Design for the Fractional Order Nonlinear Stochastic Systems with Student's t measurement Noise

This paper presents a fractional order Kalman filter for the stochastic nonlinear fractional order systems where the measurement noise is assumed to have Student’s t distribution. Modeling of the system and measurement noises in the state space representation, for target tracking problems, often carried out by additive Gaussian noise, but Gaussian distribution is not enough robust to the outliers, in the other words, Gaussian distribution has much less robustness against outliers than Student's t distribution, so if the tracking system affected by noises that have outliers, modeling of theses noises by the Gaussian distribution, may cause large estimation error or divergence of filter in the filtering and estimation problems. In this paper, after defining the stochastic fractional order systems, by comparing the performance of two Student’s t and Gaussian distributions in the modeling of noises that have outliers, try to design a nonlinear Kalman filter for fractional order systems using variational Bayesian inference method. Finally by comparing the simulation results of proposed filter in this paper and a fractional extended Kalman filer in the presence of Gaussian and Student’s t noises, the effectiveness of the proposed filter in estimation of states of the fractional order systems is demonestrated.