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On-line Subspace Estimation Using A Generalized Schur Method

A new method is presented for estimating the column space (signal subspace) of a low rank data matrix distorted by additive noise. It is based on a tangible expression for the set of all matrices of minimal rank that are ε-close to the data matrix in matrix 2-norm. The usual truncated SVD approximant is contained in this set. Features of the algorithm are (1) it has the same computational structure and complexity as a QR factorization of the data matrix, (2) it yields an on-line scheme, amenable to parallel (systolic) implementation, (3) updating and downdating is straightforward, (4) a rank decision (to detect the number of signals) is automatic, for a given thresholdε. It is shown in simulations on a typical direction finding application that the algorithm exhibits similar performance as SVD-based methods, at a fraction of the computational cost.