核集员双归一化最小平均p范数算法

Kernel Set-membership Bi-normalized Least Mean p–norm Algorithm

针对α稳定分布噪声中核集员归一化(KSM-NLMS)算法性能下降问题,提出了核集员归一化最小平均p范数(KSM-NLMP)算法和核集员双归一化最小平均p范数(KSM-BNLMP)算法。首先,将输入信号映射到再生核希尔伯特空间,在此空间基于集员滤波理论和最小p范数准则构造算法的代价函数。其次,根据最优解、误差方程和集员滤波约束条件,推导得到滤波器权向量的更新迭代公式。最后,利用核技巧得到滤波器输出和算法的迭代公式。非线性信道均衡的仿真结果表明,KSM-NLMP和KSM-BNLMP算法比KSM-NLMS算法具有更好的均衡效果。

Aiming at the performance degradation of KSM-NLMS algorithm in αstable distribution noise,kernel set-membership normalized least mean p-norm（KSM-NLMP） algorithm and kernel set-membership bi-normalized least mean p-norm（KSM-BNLMP） algorithm are proposed.Firstly,the input data is mapped into RKHS（Reproducing Kernel Hilbert Space）,and in this space,based on set-membership theory and the least p–norm criterion,the cost function of algorithm is constructed.Then,according to the optimal solution,error equation and set-membership filter restrictions;the iterative updating formula of the filter weight vector is deduced.Finally,the output of the filter and the iterative formula of the algorithm are obtained by using kernel technique.The simulation results of nonlinear channel equalization indicate that the KSM-NLMP and KSM-BNLMP algorithms both have better equalization performance than the KSM-NLMS algorithm.