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.

中文翻译：

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基于误差估计时变界法的集合成员 LMS 自适应算法

为了降低计算复杂度，提高收敛速度，本文提出了基于误差估计时变界法的集合成员最小均方自适应算法。边界由前一次迭代的估计误差和时变误差调整因子构成。集合成员（SM）方法利用当前迭代的估计误差和边界来确定是否更新权向量。当估计误差大于界限时，更新权向量；否则，不需要更新。然后，利用步长和估计误差之间的非线性函数，修改步长以进一步提高收敛速度。与传统的集合成员归一化最小均方算法相比，