A variational Bayesian marginalized particle filter for jump Markov nonlinear systems with unknown measurement noise parameters

Abstract

This paper studies a new variational Bayesian marginalized particle filter for estimating the state vector of a jump Markov nonlinear system (JMNLS) with unknown measurement noise parameters. Conjugate priors are assigned to the variables indicating the system mode of the JMNLS and the measurement noise parameters, which are regarded as unknown parameters. According to the marginalized particle filter, the unknown parameters are marginalized from the joint posterior distribution of the state and the unknown parameters of the JMNLS. The posterior distribution of the state is then approximated by using an appropriate particle filter, and the posterior distributions of the system mode and the measurement noise parameters conditionally on each state particle are calculated by using variational Bayesian inference. A simulation study is conducted to compare the proposed method with state-of-the-art approaches in the context of a modified nonlinear benchmark model and radar target tracking.