Subspace estimation using unitary Schur-type methods

This paper presents efficient Schur-type algorithms for estimating the column space (signal subspace) of a low rank data matrix corrupted by additive noise. Its computational structure and complexity are similar to that of an LQ-decomposition, except for the fact that plane and hyperbolic rotations are used. Therefore, they are well suited for a parallel (systolic) implementation. The required rank decision, i.e., an estimate of the number of signals, is automatic, and updating as well as downdating are straightforward. The new scheme computes a matrix of minimal rank which is γ-close to the data matrix in the matrix 2-norm, where γ is a threshold that can be determined from the noise level. Since the resulting approximation error is not minimized, critical scenarios lead to a certain loss of accuracy compared to SVD-based methods. This loss of accuracy is compensated by using Unitary ESPRIT in conjunction with the Schur-type subspace estimation scheme. Unitary ESPRIT represents a simple way to constrain the estimate