Robust estimation of structured covariance matrices

In the context of the narrowband array processing problem, robust methods for accurately estimating the spatial correlation matrix using a priori information about the matrix structure are developed. By minimizing the worse case asymptotic variance, robust, structured, maximum-likelihood-type estimates of the spatial correlation matrix in the presence of noises with probability density functions in the ∈-contamination and Kolmogorov classes are obtained. These estimates are robust against variations in the noise´s amplitude distribution. The Kolmogorov class is demonstrated to be the natural class to use for array processing applications, and a technique is developed to determine exactly the size of this class. Performance of bearing estimation algorithms improves substantially when the robust estimates are used, especially when nonGaussian noise is present. A parametric structured estimate of the spatial correlation matrix that allows direct estimation of the arrival angles is also demonstrated