Regularized Nuclear Norm Spectrum Estimation in Frequency Domain

Abstract

Subspace-based methods have been effectively used to estimate multi-input/multi-output, discrete-time, linear-time invariant systems from spectrum samples. A critical step in these methods is the splitting of causal and noncausal invariant subspaces of a Hankel matrix built from spectrum measurements via singular-value decomposition in order to determine the model order. Quite often, in particular when signal-to-noise ratio is low, unmodelled dynamics is present, and when the number of measurements is small, this step is not conclusive since the assumed mirror image symmetry with respect to the unit circle between the eigenvalues of the invariant spaces is lost. In this paper, we propose a robust model order selection scheme based on the regularized nuclear norm optimization in combination with a particular subspace method. By a numerical example, efficacy of the proposed scheme is shown for a broad range of signal-to-noise ratio and short data records. Then, in a real-life example, the proposed scheme, integrated into a recently developed subspace-based algorithm, is used to estimate cross-power spectra of induction motors from sound data collected by a microphone array in a test rig.