A Natural Rank-selection Criterion for Krylov-subspace-based Filtering Techniques

摘要

We propose a novel rank-selection criterion for the Krylov-subspace-based filtering techniques such as the well-known multistage Wiener filter. We provide two necessary and sufficient conditions for the low-dimensional Krylov subspace to contain the optimal filter. The first is that the subspace is invariant under the transformation by the autocorrelation matrix associated with the subspace itself, and the second is its reverse inclusion. We derive two criteria based on the conditions; the criterion based on the first condition coincides with the conventional, and the one based on the second is the proposed. Simulation results indicate that the proposed criterion has more natural relations, compared with the conventional one, between (i) the threshold for each of the proposed and conventional criteria and (ii) the selected rank averaged over 300 experiments. Specifically, the curves for the proposed criterion decrease monotonically in a smooth-slope shape, whereas those for the conventional one decrease monotonically in a terrace shape. This suggests that the use of the proposed criterion should lead to adequate rank-selection, therefore it is expected to improve the filtering performance.