Identification of power spectra by reweighted and regularized nuclear norm minimization

In this paper, we study model order choice in subspace identification algorithms using uniformly spaced spectrum measurements. In these algorithms, model order is determined by singular-value decomposition of a structured matrix constructed from spectrum measurements. This process requires splitting of the two invariant subspaces associated with the causal and the non-causal system poles presumed to be mirror image symmetric with respect to the unit circle. Due to noise, undermodelling, and insufficient amount of data, this symmetry is lost. Recently, a robust model order selection procedure based on the regularized nuclear norm optimization was proposed. We propose a reweighted version of this scheme. Numerical and real-life examples in this paper show that the reweighted nuclear norm minimization makes model order selection easier and results in more accurate models compared to the subspace approaches and the unweighted nuclear norm minimization, in particular at high signal-to-noise ratios.