State Estimation for Nonlinear Discrete–time Fractional Systems: A Bayesian Perspective

Abstract In this paper, the state estimation issue for fractional dynamic systems is addressed. First, based on the Bayesian formula, a recursive Bayesian filter is derived from a probability density perspective. Then for a nonlinear fractional Gaussian system, a general fractional Gaussian filtering framework is investigated. Under this framework, the fractional particle filter is investigated systematically, and the working mechanism, time complexity and estimation accuracy of four suboptimal fractional filters are analyzed. Finally, several simulation examples verify the effectiveness of four suboptimal filters.