Outlier-resistant adaptive filtering based on sparse Bayesian learning

In adaptive processing applications, the design of the adaptive filter requires estimation of the unknown interference-plus-noise covariance matrix from secondary training data. The presence of outliers in the training data can severely degrade the performance of adaptive processing. By exploiting the sparse prior of the outliers, a Bayesian framework to develop a computationally efficient outlier-resistant adaptive filter based on sparse Bayesian learning (SBL) is proposed. The expectation-maximisation (EM) algorithm is used therein to obtain a maximum a posteriori (MAP) estimate of the interference-plus-noise covariance matrix. Numerical simulations demonstrate the superiority of the proposed method over existing methods.