A QR decomposition based subspace algorithm for adaptive superresolution spectral estimate

Abstract

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.<>