Variational Bayesian Auxiliary Particle Filter for Jump Markov Systems with Unknown Measurement Noises

The jump Markov system estimation problem involves estimating the state and system mode based on a sequence of noisy measurements. In some practical applications， changes in sensor conditions and external random interferences can lead to variations in measurement noise. This variability can render the jump Markov system model inaccurate， resulting in degraded estimates of the state and system mode. To account for these changing conditions， the measurement noise covariance matrix of jump Markov systems is modeled as a discrete stochastic process， with its prior probability distribution assigned as an inverse Wishart distribution. Additionally， dynamic equations for the hyperparameters of the measurement noise covariance matrix are defined. A new variational Bayesian auxiliary particle filter is proposed to sequentially approximate the joint posterior probability distribution associated with the system mode， state， and measurement noise covariance matrix. The joint posterior distribution of the system mode， state， and noise covariance matrix is marginalized with respect to the system mode. The marginalized posterior distribution of the mode is then approximated using an auxiliary particle filter， and the state and noise covariance matrix， conditioned on each particle of the mode variable， are updated using variational Bayesian inference， with conjugacy for the state and noise covariance matrix preserved at all times. A simulation study is conducted to compare the proposed method with state-of-the-art approaches in the context of radar target tracking. The simulation results show that the estimation accuracy for the state and noise covariance matrix can be effectively improved， ensuring system mode identification accuracy at the cost of higher computational complexity.