Minimum relative entropy spectral estimation with uncertainties in the autocorrelation measurements

A technique to estimate a spectrum when errors in the autocorrelation function values are present is discussed. The principle of minimum relative entropy is used to derive the spectral estimation technique. It is assumed that some statistics of the noise corrupting the autocorrelation measurements are known; this provides the constraint equations subject to which the relative entropy functional is minimized. Often in practice, the variance of the noise is known (or calculatable) in which case the constraint equation is a mean squared error. An iterative algorithm that utilizes the ability to include a priori guess in the minimum relative entropy principle is derived. Examples using the proposed technique to obtain spectral estimates from noisy autocorrelation data are presented. The spectral estimates are shown to be superior to classical and entropy-based techniques that incorrectly assume the autocorrelation values to be exact. The method is not limited to a white Gaussian noise environment and can be applied to utilize the knowledge of any statistics for any type of noise that is corrupting the autocorrelation function