Bayesian filtering for nonlinear state-space models in symmetric alpha-stable measurment noise

Abstract

Bayesian ltering appears in many signal processing problems,reason why it attracted the attention of many researchers to develop efficient algorithms, yet computationally a ordable. 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 ltering problem, what leads to a robust method against both outliers and a weak knowledge of the system.