Variational Adaptive Kalman Filter With Gaussian-Inverse-Wishart Mixture Distribution

In this article, a new variational adaptive Kalman filter with Gaussian-inverse-Wishart mixture distribution is proposed for a class of linear systems with both partially unknown state and measurement noise covariance matrices. The state transition and measurement likelihood probability density functions are described by a Gaussian-inverse-Wishart mixture distribution and a Gaussian-inverse-Wishart distribution, respectively. The system state vector together with the state noise covariance matrix and the measurement noise covariance matrix are jointly estimated based on the derived hierarchical Gaussian model. Examples are provided to demonstrate the effectiveness and potential of the developed new filtering design techniques.