Design of the robust fractional Bayesian filter with randomly delayed measurements

Facing the state estimation problem for nonlinear fractional-order dynamical systems with measurement stochastic delays, a robust fractional Bayesian filtering strategy is presented in this paper. The measurement equation is first reconstructed using two variables that portray the stochastic delay. One random variable follows a Bernoulli distribution to describe whether the measurement delay occurs at a certain time. The other obeys a geometric distribution to characterize the number of delay steps. This way, it is no longer bound to a fixed number of delay steps and is more in line with engineering practice. The robust fractional Bayesian filter is then implemented based on Bayesian theory in three iterative steps of state prediction, measurement correction and estimation update. In addition an explicit implementation based on first-order Stirling polynomial interpolation is provided. Finally, the effectiveness of the proposed method is verified by numerical simulation, and two important probability parameters in the algorithm are fully analyzed.