Robust Kalman Filters With Unknown Covariance of Multiplicative Noise

In this article, the joint estimation of state and noise covariance for linear systems with unknown covariance of multiplicative noise is considered. The measurement likelihood is modeled as a mixture of two Gaussian distributions and a Student's
t
distribution, respectively. The unknown covariance of multiplicative noise is modeled as an inverse Gamma/Wishart distribution and the initial condition is formulated as the nominal covariance. By using robust design and choosing hierarchical priors, two variational Bayesian-based robust Kalman filters are proposed. The stability and convergence of the proposed filters and the covariance parameters are analyzed. The lower and upper bounds are also provided to guarantee the performance of the proposed filters. A target tracking simulation is provided to validate the effectiveness of the proposed filters.