Adaptive filtering in the presence of outliers

Adaptive filters aimed at detecting a signal of interest in the presence of noise undergo a significant degradation in terms of the output signal to interference and noise ratio when the training samples contain signal-like components. It is thus crucial to take into account this contamination when estimating the noise covariance matrix which is used to compute the adaptive filter. In this paper, we consider a covariance matrix estimation scheme which takes into account the possible presence of outliers, without censoring any training sample. A Bayesian model is formulated where the amplitude of the signal component of each training sample is assumed to follow a Bernoulli-Gaussian distribution. Additionally, the noise covariance matrix is assigned some non informative prior distribution, namely a maximum entropy distribution. The posterior distributions of these variables are derived and an efficient Markov Chain Monte Carlo method is presented to obtain the minimum mean-square error estimates. The new scheme is shown to outperform robust schemes based on diagonal loading.