Estimation of time-varying autoregressive symmetric alpha stable processes by particle filters

In the last decade alpha-stable distributions have become a standard model for impulsive data. Especially the linear symmetric alpha-stable processes have found applications in various fields. When the process parameters are time-invariant, various techniques are available for estimation. However, time-invariance is an important restriction given that in many communications applications channels are time-varying. For such processes, we propose a relatively new technique, based on particle filters which obtained great success in tracking applications involving non-Gaussian signals and nonlinear systems. Since particle filtering is a sequential method, it enables us to track the time-varying autoregression coefficients of the alpha-stable processes. The method is tested both for abruptly and slowly changing autoregressive parameters of signals, where the driving noises are symmetric-alpha-stable processes and is observed to perform very well. Moreover, the method can easily be extended to skewed alpha-stable distributions.