Rayleigh estimates: performing like SVD

Abstract

This paper describes the structure of the so- called Rayleigh estimates and the features they share with indirect SVD like procedures. The problem of finding procedures of high resolution in spectral estimation is faced under the framework of non-linear estimates of the autocorrelation matrix and the low rank approximation to the frequency estimation problem. It is shown the existing relations hip between the proposed estimates and the principal component analysis. The main advantages of the procedure is that the performance of the spectral estimates reported herein is almost equal to SVD techniques, yet preserving a good asymptotic convergence to the actual power spectral density. Also, the procedure could be viewed under variotional concepts revealing its potential under adaptive schemes and data adaptive windowing for spectral estimation. In summary, the work shows how classical constrained Wiener filtering with data adaptive windowing can enhance the performance of SVD met hods with very low complexity.