Spectrum estimation in frequency-domain by subspace and regularization-based algorithms: A survey

In this survey article, we study methods to identify multi-input/multi-output, discrete-time, linear time-invariant systems from power spectrum measurements. First, we examine subspace-based identification algorithms. A hindrance to these methods is splitting of two invariant spaces generated by causal and anti-causal eigenvalues in order to determine model order. Next, we study model order selection criteria based on the regularized nuclear norm and the regularized and reweighted nuclear norm heuristics. The latter heuristic, formulated in a different way, is used to ensure positivity of the spectrum estimate delivered by subspace identification algorithms. A numerical example illustrates properties of the regularized and reweighted nuclear norm heuristic.