Accurate subspace tracking algorithms based on cross-space properties

In this paper, we analyse the issue of efficiently using Givens rotations to perform a more accurate SVD-based subspace tracking. We propose an alternative type of decomposition which allows a more versatile use of Givens rotations. We also show the direct effect of the latter on the tracking error, and develop a cross-terms cancellation concept which leads to a class of high performance algorithms with very low complexity: O(N²) if signal and noise subspaces are tracked, O(Nr) if only the signal subspace is tracked, where N is the data vector dimension, and r the number of sources. Comparative simulation experiments support the theoretical work