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

• By introducing a Bernoulli random variable and using state augmentation approach, the conditional likelihood function is transformed into an exponential multiplication form. • The augmentation state vector together with the auxiliary random variables and the Bernoulli random variable are inferred based on variational Bayesian approach. • The superiority of the proposed filter as compared with the existing filters is demonstrated in a target tracking simulation. 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. [ABSTRACT FROM AUTHOR]