A Kernel Normalization Decorrelated Affine Projection P-norm Algorithm Based on Gaussian Kernel Explicit Mapping
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摘要:
为了降低核仿射投影P范数(KAPP)算法的计算量和存储容量，提高在输入信号强相关时KAPP算法的收敛速度和稳态性能，该文提出基于高斯核显性映射的核归一化解相关APP(KNDAPP-GKEM)算法。该算法利用归一化解相关方法预先解除输入信号的相关性；利用高斯核显式映射方法近似得到显式核函数，消除了对历史数据的依赖，解决了KAPP算法因结构不断生长导致的计算量和存储容量过大的问题。α稳定分布噪声背景下的非线性系统辨识仿真结果表明，在输入信号强相关时KNDAPP-GKEM算法收敛速度快，非线性系统辨识稳态均方误差小，训练所需时间呈线性缓慢增长，有利于实际非线性系统辨识的应用。
Abstract:In order to reduce the computation complexity and storage capacity of the Kernel Affine Projection P-norm (KAPP) algorithm, and improve the convergence rate and steady-state performance of the algorithm when the input signal is strongly correlated, a Kernel Normalization Decorrelated Affine Projection P-norm algorithm based on Gaussian Kernel Explicit Mapping (KNDAPP-GKEM) is proposed. The correlation of the input signal is eliminated in advance by the normalized correlation method. The explicit kernel function is approximated by Gaussian kernel explicit mapping method, which eliminates the dependence on historical data and solves the problem that the computation and storage capacity of the KAPP algorithm are too high due to the continuous growth of structure. The simulation results of nonlinear system identification under α-stable distribution noise environment show that when the training data scale is large, the KNDAPP-GKEM algorithm still maintains a fast convergence rate and the low identification mean square error of nonlinear system. Moreover, its training time is linearly and slowly increased, which is more conducive to the practical application of nonlinear system identification.
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表 1 KNDAPP-GKEM算法在n时刻的计算复杂度
迭代步骤 乘法运算次数 加法运算次数 计算复杂度 映射得到$\varphi ({{x}}(n)$ DL+D DL–D O(1) 归一化计算${{{Z}}_{\rm{N}}}(n)$ 2K3+3DK2+2D2K 3DK2+2D2K+2K3–D2–2DK–3K2 O(K3) 计算y(n), e(n)和ep(n) DK +K DK O(K) 更新权重${{w}}{\rm{(}}n{\rm{)}}$ DK+D+1 DK O(K) 
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