Keywords: Affine projection sign algorithm; robust adaptive algorithm; errror scalar matrix.Abstract. Proposed is an affine projection sign algorithm with a nonlinear error scalar matrix to improve the robustness and the tracking performance against non-Gaussian impulsive interferences. The error scalar matrix scalars down the errors of some projection directions in the presence of impulsive noise. The major contribution of the letter is that variable error nonlinearity methods used in normalized least mean square (NLMS) can be applied to the scalar matrix with a little modification. An ideal scalar matrix is presented in the simulation environment of the two component Gaussian mixture noise model. Although a closed-form solution of the ideal matrix cannot be obtained in practice, it provides us a heuristic consideration about how to design the scalar matrix and theoretically best learning curves that the proposed method can achieve. We also discuss a practical method to approximate the optimal learning curve. Improved performance of the proposed algorithm is demonstrated in a system identification scenario.
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