Improved Adaptive Kalman Filter with Unknown Process Noise Covariance

This paper considers the joint recursive estimation of the dynamic state and the time-varying process noise covariance for a linear state space model. The conjugate prior on the process noise covariance, the inverse Wishart distribution, provides a latent variable. A variational Bayesian inference framework is then adopted to iteratively estimate the posterior density functions of the dynamic state, process noise covariance and the introduced latent variable. The performance of the algorithm is demonstrated with simulated data in a target tracking application.