Spectrum estimation with missing values: A regularized nuclear norm minimization approach

In this paper, we consider estimation of a power spectrum from noise corrupted spectrum samples on uniform grids of frequencies with missing values. We propose two schemes based on the regularized nuclear norm minimization in combination with a recent subspace identification algorithm. The proposed schemes estimate the model order and the missing spectrum values in one step and are robust to large amplitude noise over short data records. Although this estimation problem can be cast as a spectrum estimation problem from nonuniformly spaced measurements and the algorithms developed for this type of data can be used, the identification example of this paper shows that the incomplete data formulation yields more accurate results. The properties of one of the proposed schemes are illustrated in an application example concerned with low-pass modeling of transformer current.