On updating signal subspaces

The authors develop an algorithm for adaptively estimating the noise subspace of a data matrix, as is required in signal processing applications employing the `signal subspace´ approach. The noise subspace is estimated using a rank-revealing QR factorization instead of the more expensive singular value or eigenvalue decompositions. Using incremental condition estimation to monitor the smallest singular values of triangular matrices, the authors can update the rank-revealing triangular factorization inexpensively when new rows are added and old rows are deleted. Experiments demonstrate that the new approach usually requires O(n²) work to update an n×n matrix, and that it accurately tracks the noise subspace