A QR decomposition based subspace algorithm for adaptive superresolution spectral estimate

Eigenstructure based subspace technique is known for good performance, but it requires intensive computations. To overcome this difficulty, the authors present a QR decomposition (QRD) based subspace algorithm for direction of arrival (DOA) estimate. The proposed method takes advantage of the noise-free property of the ideal cross-covariance matrix to generate valid subspace estimate. The columns of the orthogonal matrix Q span the same subspace as the eigenvectors of the auto-covariance matrix. Further, by invariant subspace technique, the authors present a QR-ESPRIT algorithm, which can transform the M-dimension eigenproblem to a k-dimension one. An adaptive version of the proposed QR method is also derived to deal with adaptive spectral estimate, which uses the rank-one update of the last QRD. Required operations are much simpler compared with common QRD procedure