Estimation of Covariance Matrix in Signal Processing When the Noise Covariance Matrix is Arbitrary

An estimator of the covariance matrix in signal processing is derived when the noise covariance matrix is arbitrary based on the method of maximum likelihood estimation. The estimator is a continuous function of the eigenvalues and eigenvectors of the matrix (Sigma) over cap (1) -1/2 S* (Sigma) over cap (1) -1/2, where S* is the sample covariance matrix of observations consisting of both noise and signals and ($) over cap (1) is the estimator of covariance matrix based on observations consisting of noise only. Strong consistency and asymptotic normality of the estimator are briefly discussed.