Improved consistent estimation on Krylov subspaces

An improved construction of the optimum minimum variance unbiased estimator on a reduced-dimensional subspace is proposed that uniquely relies on the sample estimate of the observation covariance matrix. Unlike traditional subspace realizations based on directly replacing the true covariance matrix with the sample covariance matrix, the proposed implementation is based on an estimation of the Krylov subspace that is consistent under a limited number of samples per observation dimension. By allowing for arbitrarily large-dimensional samples, our approach not only generalizes the conventional subspace estimator but also models appropriately finite sample-size situations, in which it is shown to present a significantly superior performance.