On-line Bayesian estimation of signals in symmetric α-stable noise

In this paper, we describe on-line Bayesian filtering methods for time series models with heavy-tailed α-stable noise. The filtering methodology is based on a scale mixtures of normals (SMiN) representation of the α-stable distribution, which reexpresses the intractable stable distribution in a conditionally Gaussian form. We describe how the method can be used for estimation of time-varying autoregressive signals buried in symmetric α-stable noise, efficiently implemented using an adaptation to an existing Rao-Blackwellized particle filter. The methodology is shown to work well with both simulated and real corrupted audio data, for which the α-stable noise distribution is found to fit the noise data better than other more standard heavy-tailed distributions.