Robust Constrained Affine-Projection-Like Adaptive Filtering Algorithms Using the Modified Huber Function

In this brief, two robust constrained affine-projection-like M-estimate (CAPLM) adaptive filtering algorithms are proposed, which solve the problem that the traditional constrained affine projection (CAP) algorithm is not robust to impulsive interference, and realize unbiased output in some applications where the desired signal is unavailable or unnecessary. Specifically, a modified Huber function (MHF) based robust AP-like (APL) minimization problem with constraints is defined and can be transformed into two different unconstrained optimization problems by using Lipschitz continuity and two different methods, and then CAPLM-I and CAPLM-II algorithms are obtained respectively. Both CAPLM algorithms can avoid a certain amount of computational complexity caused by the inversion of the input signal matrix in classical AP algorithm, and realize the robustness to impulsive interference. In addition, the mean square stabilities of them are analyzed, and the corresponding stable step size ranges are also given. Simulation results show that the proposed CAPLM-I and CAPLM-II algorithms perform well in system identification and beamforming applications in impulsive noise environment, and provide lower steady-state error and faster convergence speed than other compared algorithms.