A maximum entropy enhancement for a family of high-resolution spectral estimators

Abstract—Structured covariances occurring in spectral analysis, filtering and identification need to be estimated from a finite obser-vation 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-reso-lution spectral estimators. There, the output covariance of a linear filter is needed to initialize the spectral estimation technique. The sample covariance estimate , however, is usually not compat-ible with the filter. In this paper, we present a new, systematic way to overcome this difficulty. The new estimate is obtained by solving an ancillary problem with an entropic-type criterion. Ex-tensive scalar and multivariate simulation shows that this new ap-proach consistently leads to a significant improvement of the spec-tral estimators performances. Index Terms—Convex optimization, covariance extension, max-imum entropy, multivariable spectral estimation. I