Single vector approaches to eigenstructure analysis for harmonic retrieval

In recent years, there has been considerable renewed interest in the analysis of eigenstructure of the estimated signal covariance matrix for spectrum estimation or, equivalently, beam forming. The computational task involved is generally very large. In this paper, we report on two methods developed for improving the computational efficiency after the eigenvectors are known. These two methods both rely on the use of a single vector rather than the entire set of all the eigenvectors. In other words, the Simplified Formula (SF) method, the single vector is the sum of the autocorrelation function vector of all the noise eigenvectors. In the other method, the Minimizing Magnitude (MM) method, the single vector is the autocorrelation function vector of a weighted combination of all the noise eigenvectors. Simulations show that both methods yield good results with a decrease in computational effect proportional to the number of noise eigenvectors.