A Progressive Bayesian Filtering Framework for Nonlinear Systems With Heavy-Tailed Noises

This article studies the Bayesian filtering problem for nonlinear systems with heavy-tailed noises. Because of the nonlinearity and heavy tail characteristics, the Gaussian distribution or particle sets may fail to express the posterior probability density distribution; thus, the progressive Bayesian filtering framework is proposed. With the filtering framework, the measurement update is divided into several steps, and the intermediate posterior distributions are chosen as the importance proposal distributions to improve the approximation of posterior probability density distributions. Moreover, termination conditions for the progressive measurement update are also proposed to improve the robustness of the progressive Bayesian filter against outliers. Finally, a simulation example is exploited to illustrate the effectiveness and superiority of the proposed filtering framework.