A novel variational Bayesian adaptive Kalman filter for systems with unknown state-dependent noise covariance matrices

We consider state estimation for a dynamical system that has unknown state-dependent dynamic process and measurement noise covariance matrices. When the noise covari-ances are state-dependent the typical Kalman filter (KF) fails to accurately estimate the states of the system. To estimate the states of such a system, we model the covariance matrices via the Wishart process and propose a novel variational Bayesian adaptive Kalman filter (VB-AKF). The proposed VB-AKF combines the variational Bayesian inference of the Wishart process with the KF. The resulting VB-AKF can estimate the states of the system together with the state-dependent dynamic process and measurement noise covariances. Through simulations, we show that the developed VB-AKF is effective and achieves satisfactory performance.