Fast approximated sub-space algorithms

In this paper, fast techniques for invariant subspace separation with applications to the direction of arrival (DOA) and the harmonic retrieval problems are presented. The main feature of these techniques is that they are computationally efficient as they can be implemented in parallel and can be transformed into matrix inverse-free algorithms. The basic operations used are the QR factorization and matrix multiplication. Specifically, two types of methods are developed. The first method uses Newton-like iteration, and is quadratically convergent. The second method can be developed to have convergence of any prescribed order. Applying these approximations to the DOA and the harmonic retrieval problems, the minimum norm solution for the projection of least squares weight on to the signal subspace of the data is obtained simply, without performing any singular value decomposition (SVD). Some of the developed methods are also examined on several test problems.