Multisignal minimum-cross-entropy spectrum analysis with weighted initial estimates

This paper presents a generalization of multisignal minimum-cross-entropy spectrum analysis (multisignal relative-entropy spectrum analysis, multisignal RESA), a method for simultaneously estimating a number of power spectra when an initial ("prior") estimate of each is available and new information is obtained in the form of values of the sum of their autocorrelation functions. The generalization involves attaching to each initial spectrum estimate a possibly frequency-dependent weighting parameter that indicates its relative reliability, i.e., the relative "degree of belief" associated with the initial estimate. Mathematical properties of the generalized method are discussed, and illustrative numerical examples are given.