Robust Adaptive Filters and Smoothers for Linear Systems With Heavy-Tailed Multiplicative/Additive Noises

This article studies robust adaptive Kalman filtering and smoothing problems for the linear state-space model with heavy-tailed multiplicative (measurement) noise and additive (process and measurement) noises. First, to model the heavy-tailed noises, the state transition and measurement likelihood densities are modeled as two generalized
t
distributions. Then, the unknown covariance matrices of process and measurement additive noises are modeled as inverse Wishart distributions, and the multiplicative noise covariance is modeled as an inverse Gamma distribution. To further improve the estimation performance and robustness to outliers, a one-step smoothing strategy is employed. Finally, robust adaptive Kalman filters with corresponding smoothers are proposed using variational Bayesian inference. A target tracking example is provided to verify the effectiveness and robustness of the proposed filters and smoothers.