Operational performances of a MUSIC algorithm robust to outliers

In operational systems (Radar, communication, sonar,‥), for practical considerations the MUSIC pseudo spectrum optimization must be conducted after removing the outliers. When the number of sources is known, this work considers the influence of the statistical rejection of dominating outliers. Strictly speaking, we calculate, in presence of modeling errors, the MUSIC performances (bias and variance) conditionally to the fact that, in the pseudo spectrum, outliers are not dominating the true DOAs. We also provide the probability that dominating outliers occur. These theoretical investigations lead us to propose a outliers-robust MUSIC based on pseudo-spectrum thresholding to remove outliers. We then calculate the performances of the proposed algorithm. These performances prediction is a key tool for operational system design.