α稳定分布噪声下的核最小平均P范数算法

Kernel least mean P-norm algorithm in α stable distribution noise

在α稳定分布噪声环境下,最小平均P范数算法(LMP)的鲁棒性显著强于最小均方算法(LMS),但是在非线性系统中LMP算法性能严重退化。运用核方法可将输入数据映射到再生核希尔伯特空间(RKHS),再对变换后数据选用合适的线性方法,能有效地处理多种非线性问题。将核方法引入LMP算法,推导得到核最小平均P范数算法(KLMP)。α稳定分布噪声背景下的Mackey-Glass时间序列预测的计算机仿真结果表明,在非线性、非高斯系统中,KLMP算法的性能显著优于LMS、LMP、加权平均LMP和KLMS算法,抗脉冲噪声能力强。

In α-stable distribution noise environment, the robustness of least mean P-norm algorithm （LMP） is significantly stronger than that of the least mean square algorithm（LMS）. But the performance of LMP is seriously degraded in nonlinear systems. By using kernel method, this paper mapped the input data to reproducing kernel Hilbert space （RKHS） , and subse-quently applied appropriate linear methods to the transformed data to effectively handle a variety of nonlinear problems. It applied the kernel method to LMP and deduced the kernel least mean P-norm algorithm （KLMP）. The computer simulation results of prediction of a Mackey-Glass time series in α-stable distribution noise show that KLMP is obviously superior to LMS, LMP, weighted average LMP and KLMS in nonlinear and non-Gaussian systems. KLMP has a good impulsive noise rejection capability.