A new Gaussian approximate filter with colored non-stationary heavy-tailed measurement noise

The filtering issue of a nonlinear system with colored non-stationary heavy-tailed measurement noise (CNSHMN) is addressed in this study via designing a new Gaussian approximate filter. By utilizing the state expansion method and the measurement difference method, the nonlinear filtering problem with the one-step delayed state and the white non-stationary heavy-tailed measurement noise (NSHMN) after the difference is turned into the traditional nonlinear filtering problem with NSHMN. A Gaussian student t-mixed distribution (GSTM) with Bernoulli random variable is utilized to describe the differenced measurement noise. The state vector, intermediate random variables (IRV), mixed probability and Bernoulli random variable (BRV) are simultaneously inferred by introducing variational Bayesian (VB) technique. Target tracking simulation examples reveal that the proposed filter is superior to the existing methods in the nonlinear filtering issue of CNSHMN.