A Maximum Entropy Enhancement for a Family of High-Resolution Spectral Estimators

Structured covariances occurring in spectral analysis, filtering and identification need to be estimated from a finite observation record. The corresponding sample covariance usually fails to possess the required structure. This is the case, for instance, in the Byrnes–Georgiou–Lindquist THREE-like tunable, high-resolution spectral estimators. There, the output covariance S of a linear filter is needed to initialize the spectral estimation technique. The sample covariance estimate Ss, however, is usually not compatible with the constraints imposed by the filter. In this paper, we present a new, systematic way to overcome this difficulty. The new estimate S_0 is obtained by solving an ancillary problem with an entropic-type criterion. Extensive scalar and multivariate simulation shows that this new approach consistently leads to a significant improvement of the spectral estimators performances.