Numerically stable method of signal subspace estimation based on multistage Wiener filter

In this paper, a numerically stable method of signal subspace estimation based on Householder multistage Wiener filter (HMSWF) is proposed. Numerical stability of the method lies on the fact that the Householder matrix in HMSWF ensures the unitary blocking operation and significantly strengthens the orthogonality of basis vectors, especially in the finite-precision implementation. In the following, we analyze the numerical stability of HMSWF and MSWF based on the correlation subtractive structure (CSS-MSWF) by establishing the equivalence between the forward recursion of MSWF and the Arnoldi algorithm in numerical linear algebra. Besides, the equivalence between HMSWF and the Householder QR decomposition (QRD) on the Krylov matrix underlying in MSWF is directly established. Based on the relationship, two theoretical upper bounds of the orthogonality error of basis vectors in signal subspace are obtained and it is demonstrated that the orthogonality of basis vectors based on HMSWF is perfectly preserved by the numerically well-behaved Householder matrix, and the corresponding signal subspace estimation is much more numerically stable than that based on CSS-MSWF. Simulations show the numerical stability of the proposed method of signal subspace estimation by HMSWF.