Particle filtering with alpha-stable distributions

In this paper we introduce a novel sequential Monte Carlo technique, which is based on the family of symmetric alphastable (SalphaS) distributions. Sequential Bayesian estimation generally involves recursive estimation of filtering and predictive distributions of unobserved signals from their noisy measurements. In our proposed algorithm, the relevant density functions are approximated by particles drawn from stable distributions. We call this novel technique SalphaS particle filtering (SalphaSPF). We assess the performance of the SalphaSPF in comparison with the Gaussian sum particle filter (GSPF) and a standard (non-parametric) particle filter (PF). Results obtained using highly nonlinear models with simulated data show that the SalphaSPF outperforms the GSPF and compares very favorably with the PF