This paper presents a novel robust adaptive filtering scheme based on the interactive use of statistical noise information and the ideas developed originally for efficient algorithmic solutions to the convex feasibility problems. The statistical noise information is quantitatively formulated as stochastic property closed convex sets by the simple design formulae developed in this paper. A simple set-theoretic inspection also leads to an important statistical reason of the sensitiveness of the affine projection algorithm (APA). The proposed adaptive algorithm is computationaly efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces highly expected to contain the unknown system to be identified. The numerical examples show that the proposed adaptive filtering scheme realizes dramatically fast and stable convergence even for highly colored excited speech like input signals in severe noise situations, which is bard task even for the RLS because RLS suffers from certain model mismatch problem causing serious degradation of the learning performance.
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