Accession Number:

ADA149192

Title:

Relative-Entropy Minimization with Uncertain Constraints--Theory and Application to Spectrum Analysis.

Descriptive Note:

Memorandum rept.,

Corporate Author:

NAVAL RESEARCH LAB WASHINGTON DC

Personal Author(s):

Report Date:

1984-12-31

Pagination or Media Count:

16.0

Abstract:

The relative-entropy principle principle of minimum cross entropy is a provably optimal information theoretic method for inferring a probability density from an initial prior estimate together with constraint information that confines the density to a specified convex set. Typically the constraint information takes the form of linear equations that specify the expectation values of given functions. This paper discusses the effect of replacing such linear-equality constraints with quadratic constraints that require linear constraints to hold approximately, to within a specified error bound. The results are applied to the derivation of a new multisignal spectrum-analysis method that simultaneously estimates a number of power spectra given 1 an initial estimate of each 2 imprecise values of the autocorrelation function of their sum 3 estimates of the error in measurement of the autocorrelation values. One application is to separate estimation of the spectra of a signal and independent additive noise, based on imprecise measurements of the autocorrelations of the signal plus noise. The new method is an extension of multisignal relative-entropy spectrum analysis with exact auto-correlations. The two methods are compared, and connections with previous related work are indicated. Mathematical properties of the new method are discussed, and an illustrative numerical example is presented. Originator-supplied keywords include Maximum entropy, cross entropy, Relative entropy, Information theory, Prior estimates, and Initial estimates.

Subject Categories:

  • Statistics and Probability
  • Cybernetics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE