Modeling of non-stationary autoregressive alpha-stable processes by particle filters

Gencaga D, Ertuzun A, Kuruoglu E E

Alpha-stable distributions  Non-stationary processes  Particle filtering  Sequential Monte Carlo  Bayesian estimation  Impulsive processes  Skewed processes 

In the literature, impulsive signals are mostly modeled by symmetric alpha-stable processes. To represent their temporal dependencies, usually autoregressive models with time-invariant coefficients are utilized. We propose a general sequential Bayesian odeling methodology where both unknown autoregressive coefficients and distribution parameters can be estimated successfully, even when they are time-varying. In contrast to most work in the literature on signal processing with alpha-stable distributions, our work is general and models also skewed alpha-stable processes. Successful performance of our method is demonstrated by computer simulations. We support our empirical results by providing posterior Cramer-Rao lower bounds. The proposed method is also tested on a practical application where seismic data events are modeled.

Source: DIGITAL SIGNAL PROCESSING, vol. 18 (issue 3), pp. 465-478

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