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


Proceedings of the 2015 7th IEEE International Conference on Cybernetics and Intelligent Systems (CIS) And Robotics, Automation and Mechatronics (RAM), Angkor Wat, Cambodia, 15 - 17 July 2015, pp.65-70 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/iccis.2015.7274549
  • City: Angkor Wat
  • Country: Cambodia
  • Page Numbers: pp.65-70
  • Keywords: system identification, power spectrum, frequency domain, subspace method, nuclear norm, regularization, reweighted nuclear norm, positive real, POWER SPECTRA, SYSTEM-IDENTIFICATION, SPACED MEASUREMENTS, RANK MINIMIZATION, NORM MINIMIZATION, APPROXIMATION, MATRICES
  • Anadolu University Affiliated: Yes


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.