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 for the sensitivity to noise of the affine projection algorithm (APA). The proposed adaptive algorithm is computationally efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces that are highly expected to contain the unknown system to be identified and is free from the computational load of solving a system of linear equations. The numerical examples show that the proposed adaptive filtering scheme realizes dramatically fast and stable convergence for highly colored excited speech like input signals in severe noise situations.