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Bayesian filtering for nonlinear state-space models in symmetric α-stable measurement noise

Bayesian filtering appears in many signal processing problems, reason why it attracted the attention of many researchers to develop efficient algorithms, yet computationally affordable. In many real systems, it is appropriate to consider α-stable noise distributions to model possible outliers or impulsive behavior in the measurements. In this paper, we consider a nonlinear state-space model with Gaussian process noise and symmetric α-stable measurement noise. To obtain a robust estimation framework we consider that both process and measurement noise statistics are unknown. Using the product property of α-stable distributions we rewrite the measurement noise in a conditionally Gaussian form. Within this framework, we propose an hybrid sigma-point/Monte Carlo approach to solve the Bayesian filtering problem, what leads to a robust method against both outliers and a weak knowledge of the system.