Subspace-based spectrum estimation by reweighted and regularized nuclear norm minimization in frequency-domain

Abstract

In this paper, we study model order choice in subspace-based identification algorithms using nonuniformly spaced spectrum measurements. A critical step in these methods is splitting of two invariant subspaces associated with causal and non-causal eigenvalues of some structured matrices built from spectrum measurements via singular-value decomposition in order to determine model error. Mirror image symmetry with respect to the unit circle between the eigenvalue sets of the two invariant spaces required by the subspace algorithms is lost due to noise and insufficient amount of data. Recently, a robust model order selection scheme based on the regularized nuclear norm optimization in combination with a subspace-based spectrum estimation algorithm was proposed. We propose a reweighted version of this scheme. A numerical example shows that the reweighted nuclear norm minimization makes model order selection easier and results in more accurate models compared to unweighted nuclear norm minimization, in particular at high signal-to-noise ratios.