A novel progressive Gaussian approximate filter with variable step size based on a variational Bayesian approach

The selection of step sizes in the progressive Gaussian ap- proximate filter (PGAF) is important, and it is difficult to se- lect optimal values in practical applications. Furthermore, in the PGAF, significant integral approximation errors are gener- ated by the repeated approximate calculations of the Gaussian weighted integrals, which results in an inaccurate measure- ment noise covariance matrix (MNCM). To solve these prob- lems, in this paper, the step sizes and the MNCM are jointly estimated based on the variational Bayesian (VB) approach. By incorporating the adaptive estimates of step sizes and the MNCM into the PGAF framework, a novel PGAF with vari- able step size is proposed. Simulation results illustrate that the proposed filter has higher estimation accuracy than exist- ing state-of-the-art nonlinear Gaussian approximate filters.