A Robust Generalized $t$ Distribution-Based Kalman Filter

Since the Gaussian-inverse Wishart hierarchical form has similar properties to Student’s
$t$
distribution, we name it generalized
$t$
distribution in this article. Based on this, a robust generalized
$t$
distribution-based Kalman filter (GTKF) is proposed for state-space models that are eroded by state and measurement outliers. Different from the existing algorithms, the state transition and measurement likelihood densities are directly modeled as generalized
$t$
distributions by employing the one-step smoothing strategy.An analytical closed-form solution can be obtained through the variational inference approach. Moreover, two variants of the proposed GTKF are also presented to apply to different engineering scenarios. Simulation and experimental examples demonstrate that the proposed GTKFs yield improved robustness over the existing algorithms.