Nonlinear Bayesian filtering in the Gaussian scale mixture context

In many real-life Bayesian estimation problems, it is appropriate to consider non-Gaussian noise distributions to model possible outliers or impulsive behaviors in the measurements. In this paper, we considered a nonlinear Bayesian filtering problem with a Gaussian process noise and a Gaussian scale mixture (GSM) distributed measurement noise. Both processes' statistics parameters are assumed unknown. Within this framework, we present a filtering method based on a sigma-point core that exploits GSM's product property and accounts for such heavier distribution tail and parameter uncertainty. Numerical results exhibit enhanced robustness against both outliers and a weak knowledge of the system with respect to state-of-the-art nonlinear Bayesian filters based on the Gaussian assumption, requiring much less computational load than standard Sequential Monte-Carlo methods and approaching theoretical bounds of performance.