The Applicability of Minimum-Relative-Entropy Spectral Estimation: An Analysis and Critique.
Abstract
The principle of minimizing the relative entropy of the posterior spectral estimate with respect to the prior has been given a good theoretical foundation for stationary gaussian random processes. It is not as firm as one might like however, and its real value thus lies in how accurately it can determine spectra and how much computing is involved. The question remains open as to which applications are suitable for relative-entropy methods, which are not, and why. It can best be answered by trying out this technique along with others on a wide variety of waveforms. Multiple-signal minimum-relative-entropy spectral estimation (MRESE) has been applied to the sum of a signal plus noise to obtain improved estimates of the spectra of both, and provision has been made for weighting their prior estimates. The limit is here investigated as the weight assigned to the prior signal-spectrum estimate approaches zero while the total signal power is required to have a given value. In this limit the prior signal spectrum is found to have no effect on the posterior noise spectrum of signal spectrum. The latter becomes a line at the frequency where the difference between the reciprocals of the posterior and prior estimates of the noise spectral density is least. In addition, a method is found for estimating unknown scaling of the prior spectral estimates. Some aspects of MRESE still in need of investigation are pointed out and possible approaches are suggested for several of them. Keywords: Spectral estimation, Spectral analysis, Maximum-entropy methods, Signal detection and estimation, Signal processing, Relative entropy.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 21, 1987
- Accession Number
- ADA177452
Entities
People
- Nelson M. Blachman
Organizations
- United States Naval Research Laboratory