A new enabling variational inference model for approximating measurement likelihood in filtering nonlinear system

This article considers the filtering problem with nonlinear measurements. We propose a new enabling variational inference model for approximating measurement likelihood, which is constructed by a linear Gaussian regression process. The resulting filter is referred to as the new enabling variational inference filter (NEVIF). In variational inference framework, the NEVIF obtains the variational posterior of state by minimizing the Kullback–Leibler divergence between the variational distribution and the true posterior. Then, the accuracy improvement and robustness of the NEVIF compared with the traditional methods are analyzed. Furthermore, an evaluation rule called the filtering evidence lower bound is developed to analyze the estimation accuracy performance of filters. Finally, the efficiency and superiority of the proposed filters compared with some existing filters are shown in numerical simulations.