Factor Analysis and Estimation of Covariance Matrix

Abstract

Factor Analysis is a general method of computation whose purpose consists of reconstructing the random pattern of a set of Gaussian variables, whose covariance matrix has been empirically evaluated. This paper discusses a method for building a new matrix from vector samples of random process as “close” as possible to the former one with the desired features; signals matrix plus noise matrix; the noises are uncorrelated and have different variances or powers on each sensor. The theoritical foundation of the method is to assume that the random process is zero-mean multivariate Gaussian, and to find the maximum-likelihood covariance matrix that has the specified structure.

A major contribution of this paper is an iterative algorithm that estimates the number of impinging signals, noise diagonal matrix and source-location angle. Applications in underwater acoustics of our method are, of course, in reconstructing from simulated data and signals recorded at sea, the shape of narrow-band waves impinging a set of linear equal spaced sensors. We have studied the statistic performances of our method and the Cramer-Rao bounds.

This work was supported by Department of Defense and administrated through DRET PARIS under contract No. 86–015–015.