In this paper, we propose a novel reduced-rank adaptive filtering algorithm exploiting the Krylov subspace associated with estimates of certain statistics of input and output signals. We point out that, when the estimated statistics are erroneous (e.g., due to sudden changes of environments), the existing Krylov-subspace-based reduced-rank methods compute the point that minimizes a wrong mean-square error (MSE) in the subspace. The proposed algorithm exploits the set-theoretic adaptive filtering framework for tracking efficiently the optimal point in the sense of minimizing the true MSE in the subspace. Therefore, compared with the existing methods, the proposed algorithm is more suited to adaptive filtering applications. A convergence analysis of the algorithm is performed by extending the adaptive projected subgradient method (APSM). Numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for system identification problems.
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