A novel robust Student's t-based Gaussian approximate filter with one-step randomly delayed measurements

In this paper, a novel robust Student's t-based Gaussian approximate filter (RSTGAF) is proposed to solve the filtering problem of the nonlinear system with one-step randomly delayed measurements (ORDM) and heavy-tailed measurement noise. The conditional likelihood function is transformed into an exponential multiplication form after using state augmentation approach and introducing a Bernoulli random variable, and then the augmentation state vector, the auxiliary random variables and the Bernoulli random variable are jointly estimated based on the variational Bayesian (VB) approach. The simulation results demonstrate the superiority of the proposed filter, as compared with the existing filters, to address the ORDM and heavy-tailed measurement noise.