A robust constrained set-membership affine-projection adaptive-filtering algorithm

A robust constrained set-membership (SM) affine-projection adaptive-filtering algorithm is proposed that works with two error bounds. One of the error bounds works during transience and the other works during steady state and in this way a faster convergence and significantly reduced steady-state misalignment can be achieved relative to what can be achieved with the constrained normalized least mean-squares (CNLMS), the constrained affine-projection (CAP), and the constrained set-membership affine-projection (CSMAP) algorithms. The proposed algorithm achieves in addition robust performance with respect to impulsive noise and yields good tracking performance compared to the CNLMS, CAP, and CSMAP algorithms. These features of the proposed CSMAP algorithm are demonstrated in system identification, sinusoid-filtering, and interference suppression applications.