核递归最小平均P范数算法

摘要

在强脉冲噪声干扰背景中,核递归最小二乘(Kernel Recursive Least Square,KRLS)算法和核递归最大相关熵(Kernel Recursive Maximum Correntropy,KRMC)算法对非线性信号预测性能严重退化,对此提出一种核递归最小平均P范数(Kernel Recursive Least Mean P-norm,KRLMP)算法.首先运用核方法将输入数据映射到再生核希尔伯特空间(Reproducing Kernnel Hilbert Space,RKHS).其次基于最小P范数准则和正则化方法,推导得到自适应滤波器的最佳权向量,其降低了非高斯脉冲和样本量少的影响.然后利用矩阵求逆理论,推导得到矩阵的递归公式.最后利用核技巧得到在输入空间高效计算的滤波器输出和算法的迭代公式.α稳定分布噪声背景下Mackey-Glass时间序列预测的仿真结果表明:KRLMP算法与KRLS算法和KRMC算法相比,抗脉冲噪声能力强,鲁棒性好.%In worse impulsive noise environment,the performance of the nonlinear signal prediction of the kernel recursive least square (KRLS) algorithm and kernel recursive maxmum correntropy (KRMC) algorithm is degraded in nonlinear systems.So,the kernel recursive least mean P-norm (KRLMP) algorithm is proposed.Firstly,using kernel method,the input data is mapped to reproducing kernel Hilbert space (RKHS).Secondly,based the least P-norm criterion and regularization method,the optimal weight vector of the adaptive filter is deduced,which reduces the influence of non-Gaussian pulse and the small sample size.Then,using the matrix inversion theory,the recursion formula of the matrix is obtained.Finally,the kernel method is used to calculating the filter output efficiently in the input space and the algorithm is obtained.The simulation results of prediction of a Mackey-Glass time series in α-stable distribution noise show that compared with KRLS algorithm and KRMC algorithm,KRLMP has a strong impulsive noise rejection capability and good robustness.