An efficient parallel variable-metric projection algorithm based on set-theoretic and Krylov-proportionate adaptive filtering techniques

We blend two adaptive filtering techniques for further efficiency: the set-theoretic adaptive filter (STAF, Yamada et al. 2002) and the Krylov-proportionate adaptive filter (KPAF, Yukawa 2009). Although the ideas behind these techniques are quite different from each other, there is a way to blend them together by noticing that KPAF can be seen as a sort of 'variable-metric' projection algorithm. We propose a blended algorithm named set-theoretic Krylov-proportionate adaptive filter (SKAF), which features iterative parallel variable-metric projection onto well-designed closed convex sets. We present comparisons in complexity and mean square error (MSE) performance, showing significant advantages of the proposed algorithm over the existing algorithms.