Variational Bayesian learning for robust AR modeling with the presence of sparse impulse noise

A single distribution is typically used to model the innovations of an autoregressive (AR) model. However, sparse impulses may exist within the innovations which may cause outliers in the observations. These impulses cannot be modeled by a single distribution and may potentially degrade the estimation. In this study, the innovation of an AR model is modeled by using both a Gaussian noise component and a sparse impulse noise model in order to obtain robust estimation and estimation of the impulses simultaneously. The Gaussian distribution models the normal noise and the sparse impulse noise model models the sparse abnormal innovation impulses. A hierarchal Bayesian model is built for the proposed model. Automatic relevance determination (ARD) priors are set for both the coefficients and the sparse impulses. A Variational Bayesian (VB) learning algorithm is given to estimate the parameters of the model. Experimental results show that the proposed model with the learning algorithm is valid for AR models with outliers caused by sparse innovation impulses, the coefficient estimation accuracy is better than other methods, and the sparse impulses can be estimated simultaneously.