Set-Membership NLMS Algorithm With Robust Error Bound

A new robust error bound for the set-membership normalized least mean square (SMNLMS-REB) is proposed in this brief. The new robust set-membership error bound leads to improved robustness against impulsive noise and steady-state misalignment relative to those achieved in the set-membership normalized least mean square (SMNLMS) algorithm. Stability analysis shows that the proposed algorithm is stable. Using the individual weight error variance (IWV) analysis method, new expressions for the steady-state mean square deviation (MSD) of the SMNLMS-REB are also obtained. Simulation results on system identification show that the robustness and probability of the update (PU) of the proposed SMNLMS-REB considerably outperform the traditional SMNLMS and other robust set-membership NLMS algorithms in the presence of impulsive noise.