Minimum Cross Entropy and Informational Approaches for Spectrum Estimation

Abstract

Abstract In this paper, we present the methods to estimate spectra based upon the principle of minimum cross entropy. First, we review briefly the principle of minimum cross entropy and introduce the spectral estimation method by Shore and Johnson. Next we present an extension of their work in case of partial correlation data obtained uncertainly. Furthermore, by the principle of minimum cross entropy, we show a direct extension of Burg's continuous spectral estimation method which has been developed based on the principle of maximum entropy. The extension work is achieved by applying the spectral expression of cross entropy (Kullback Leibler's information measure of discrimination) between two zero mean Gaussian stationary time series, where a prior spectrum is assumed as the one generated by autoregressive (AR) model. Two numerical examples are included for verifying our proposed spectral estimation methods based on the principle of minimum cross entropy.