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In this article, a novel normal-skew mixture (NSM) distribution is presented to model the normal and/or heavy-tailed and/or skew nonstationary distributed noises. The NSM distribution can be formulated as a hierarchically Gaussian presentation by leveraging a Bernoulli distributed random variable. Based on this, a novel robust Kalman filtering framework can be developed utilizing the variational Bayesian method, where the one-step prediction and measurement-likelihood densities are modeled as NSM distributions. For implementation, several exemplary robust Kalman filters (KFs) are derived based on some specific cases of NSM distribution. The relationships between some existing robust KFs and the presented framework are also revealed. The superiority of the proposed robust Kalman filtering framework is validated by a target tracking simulation example. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]