Adaptive Factor Analysis for Direction Finding in Colored Disturbance

The methodology of factor analysis is extended to cases where primary and secondary measurements in a multi-sensor array bring information about the covariance matrices in a multivariate normal model. The new methodology is termed adaptive factor analysis. The primary channel contains measurements that may carry a low-dimensional subspace signal plus noise, in which case the covariance matrix for the measurements consists of a low-rank matrix plus a positive-definite matrix. The secondary channel contains measurements that carry only noise, in which case the covariance matrix consists only of a positive definite matrix, identical to the positive definite covariance matrix in the primary channel. Neither the low-rank nor positive definite covariance matrix is known. The results of this paper return rank-shaping estimators of the low-rank and positive definite components of covariance, and automatically identify the signal subspace. These estimators are then used to build up MUSIC-like direction finding algorithms.