Auxiliary Particle Filtering with Variational Inference for Jump Markov Systems with Unknown Measurement Noise Covariance

This paper studies an auxiliary particle filter with variational inference for jointly estimating the system mode, the state and the measurement noise covariance matrix of jump Markov systems. The joint posterior distribution of the system mode, the state and the noise covariance matrix is marginalized out with respect to the system mode. The marginalized posterior distribution of the mode is then approximated by using an auxiliary particle filter, and the state and noise covariance matrix conditionally on each particle of the mode variable are updated using variational Bayesian inference. A simulation study is conducted to compare the proposed method with state-of-the-art approaches for a target tracking scenario.