A finite step adaptive implementation of the Pisarenko's harmonic retrieval method in colored noise

Abstract

An adaptive spectral analysis technique is presented for estimating complex frequencies in colored noise. It is assumed that the noise covariance matrix of the colored noise is known. The method presented in this paper is similar to Thompson's technique of an on line estimation of the eigenvector of the covariance matrix corresponding to the minimum eigenvalue, without explicitly evaluating the covariance matrix. The method of conjugate gradient has been utilized to obtain the eigenvector corresponding to the minimum eigenvalue. The advantages of this technique over the method of steepest descent is that it is a finite step iterative method and secondly there is no arbitrary constants in the expression which dictates the overall rate of convergence. In the proposed method, the spread of the eigenvalues has no significant effect on the overall rate of convergence. The disadvantage of this technique is that one has to store a matrix of data instead of one row only, as is conventionally done. The proposed method however yields unbiased estimates for the frequencies in colored noise.