Set-Membership LMS Adaptive Algorithms Based on an Error-Estimation Time-Varying Bound Method

To reduce the computational complexity and enhance the convergence rate, this article presents set-membership least mean square adaptive algorithms based on an error-estimation time-varying bound method. The bound is constituted by the estimation error for the previous iteration and a time-varying error adjustment factor. The set-membership (SM) method utilizes the estimation error for the current iteration and the bound to determine whether to update the weight vector. When the estimation error is larger than the bound, the weight vector is updated; otherwise, no updating is required. Then, by utilizing a nonlinear function between the step size and the estimation error, the step size is modified to further enhance the convergence rate. Compared to the traditional set-membership normalized least mean square algorithms, the simulation results show that the proposed algorithms have the following advantages: (1) fast convergence with low computational costs, (2) maintaining low, steady-state mean square error, (3) enhancing noise resistance in low-SNR environments and (4) estimating the SM bound in noisy environments without requiring noise power estimation.