基于高斯核顯性映射的核歸一化解相關(guān)仿射投影P范數(shù)算法
doi: 10.11999/JEIT190602 cstr: 32379.14.JEIT190602
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杭州電子科技大學(xué)通信工程學(xué)院 杭州 310018
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中國電子科技集團(tuán)第36研究所通信系統(tǒng)信息控制技術(shù)國家級(jí)重點(diǎn)實(shí)驗(yàn)室 嘉興 314001
A Kernel Normalization Decorrelated Affine Projection P-norm Algorithm Based on Gaussian Kernel Explicit Mapping
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School of Communication Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
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State Key Laboratory of Information Control Technology in Communication System, The 36th Research Institute of China Electronics Technology Group Corporation, Jiaxing 314001, China
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摘要:
為了降低核仿射投影P范數(shù)(KAPP)算法的計(jì)算量和存儲(chǔ)容量，提高在輸入信號(hào)強(qiáng)相關(guān)時(shí)KAPP算法的收斂速度和穩(wěn)態(tài)性能，該文提出基于高斯核顯性映射的核歸一化解相關(guān)APP(KNDAPP-GKEM)算法。該算法利用歸一化解相關(guān)方法預(yù)先解除輸入信號(hào)的相關(guān)性；利用高斯核顯式映射方法近似得到顯式核函數(shù)，消除了對(duì)歷史數(shù)據(jù)的依賴，解決了KAPP算法因結(jié)構(gòu)不斷生長導(dǎo)致的計(jì)算量和存儲(chǔ)容量過大的問題。α穩(wěn)定分布噪聲背景下的非線性系統(tǒng)辨識(shí)仿真結(jié)果表明，在輸入信號(hào)強(qiáng)相關(guān)時(shí)KNDAPP-GKEM算法收斂速度快，非線性系統(tǒng)辨識(shí)穩(wěn)態(tài)均方誤差小，訓(xùn)練所需時(shí)間呈線性緩慢增長，有利于實(shí)際非線性系統(tǒng)辨識(shí)的應(yīng)用。
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關(guān)鍵詞:
- 信號(hào)處理 /
- 核仿射投影P范數(shù) /
- 相關(guān)性 /
- 高斯核顯性映射 /
- α穩(wěn)定分布 /
- 非線性系統(tǒng)辨識(shí)
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時(shí)刻的計(jì)算復(fù)雜度
迭代步驟 乘法運(yùn)算次數(shù) 加法運(yùn)算次數(shù) 計(jì)算復(fù)雜度 映射得到$\varphi ({{x}}(n)$ DL+D DL–D O(1) 歸一化計(jì)算${{{Z}}_{\rm{N}}}(n)$ 2K3+3DK2+2D2K 3DK2+2D2K+2K3–D2–2DK–3K2 O(K3) 計(jì)算y(n), e(n)和ep(n) DK +K DK O(K) 更新權(quán)重${{w}}{\rm{(}}n{\rm{)}}$ DK+D+1 DK O(K) 
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