Affine-Projection-Like M-Estimate Adaptive Filter for Robust Filtering in Impulse Noise

In this brief, an affine-projection-like M-estimate (APLM) algorithm is proposed for robust adaptive filtering. To eliminate the adverse effects of impulsive noise in case of the impulse interference environment on the filter weight updates. The proposed APLM algorithm uses a robust cost function based on M-estimate and is derived by using the unconstrained minimization method. More importantly, the APLM algorithm has lower computational complexity than the M-estimate affine projection algorithm, since the direct or indirect inversion of the input signal matrix does not need to be calculated. In order to further improve the performance of the APLM algorithm, namely convergence speed and steady-state misalignment, the convex combination of the APLM (C-APLM) algorithm is presented. Simulation results verify that the proposed APLM and C-APLM algorithms are effective in system identification and echo cancellation scenarios. It also demonstrates that the C-APLM algorithm improves the filter performance in terms of the convergence speed and the normalized mean squared deviation in the presence of impulse noise.