Gauss-Newton based adaptive subspace estimation

An adaptive approach for estimating all (or some) of the orthogonal eigenvectors of the data covariance matrix (of a time series consisting of real narrowband signals in additive white noise) is presented. The inflation approach is used to estimate each of these vectors as minimum eigenvectors (eigenvectors corresponding to the minimum eigenvalue) of appropriately constructed symmetric positive definite matrices. This reformulation of the problem is made possible by the fact that the problem of estimating the minimum eigenvector of a symmetric positive definite matrix can be restated as the unconstrained minimization of an appropriately constructed nonlinear nonconvex cost function. The modular nature of the algorithm that results from this reformation makes the proposed approach highly parallel, resulting in a high-speed adaptive approach for subspace estimation