A Variable Step-Size Robust Saturation Algorithm Against Impulsive Noises

This brief proposes a new approach for deriving a robust saturation algorithm against impulsive noises. The proposed approach presents the saturation algorithm by using the Lagrange multiplier approach to obtain an analytically exact solution to the problem of optimizing the cost function: the ℓ
₁
norm of a posteriori error with the ℓ
₂
norm constraint on the update distance of weight vectors. In addition, a variable step size is designed by mean-square-deviation (MSD) analysis. The various simulation results show that the proposed algorithm has faster convergence rate and lower steady-state error than the existing algorithms in both impulsive and free-impulsive noises environments.