The classical sign algorithm (SA) has attracted much attention in many applications because of its low computational complexity and robustness against impulsive noise. However, its steady-state mean-square derivation (MSD) is large when a large step-size is used to guarantee a relatively fast convergence rate. To address this problem, the dual sign algorithm (DSA) was developed by using a piecewise cost function in the literature. In this paper a family of normalized DSAs (NDSAs) is proposed to further improve the performance of the DSA in terms of MSD. Specifically, two sparse NDSAs are firstly developed, by using the ${\ell }_1$-norm and ${\ell }_0$-norm constraints, respectively; on this basis, some variable step-size algorithms are then proposed based on mean-square a posteriori error minimization. Finally, simulation results are provided to show the superior performance of our proposed algorithms.

经典符号算法（SA）由于其低的计算复杂度和对脉冲噪声的鲁棒性而在许多应用中引起了广泛的关注。但是，当使用大步长来保证相对快的收敛速度时，其稳态均方差（MSD）很大。为了解决这个问题，文献中使用分段成本函数开发了双符号算法（DSA）。本文提出了一系列标准化的DSA（NDSA），以进一步提高MSA方面的DSA性能。具体来说，首先开发了两个稀疏的NDSA，方法是使用${\ell }_{\mathrm{1个}}$-规范和 ${\ell }_0$-规范约束；在此基础上，提出了基于均方后验误差最小化的可变步长算法。最后，仿真结果表明了我们提出的算法的优越性能。