Approximative Covariance Interpolation

When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power spectra consistent with such an estimate and in applications, such as identification, we want to single out the most representative spectrum. We choose a prior spectral density to represent a priori information, and the spectrum closest to it in a given quasi-distance is determined. However, if the estimates are based on few data, or the model class considered is not consistent with the process considered, it may be necessary to use an approximative covariance interpolation. Two different types of regularizations are considered in this paper that can be applied on many covariance interpolation based estimation methods.