一種基于多尺度核學(xué)習(xí)的仿射投影濾波算法
doi: 10.11999/JEIT190023
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1.
北京航空航天大學(xué)儀器科學(xué)與光電工程學(xué)院 北京 100191
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2.
中國空空導(dǎo)彈研究院 洛陽 471009
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3.
中航工業(yè)自控所飛行器控制一體化重點實驗室 西安 710065
An Affine Projection Algorithm with Multi-scale Kernels Learning
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1.
School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China
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2.
Air-to-Air Missile Research Institute, Luoyang 471009, China
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3.
National Key Laboratory on Flight Vehicle Control Integrated Technology, Xi’an 710065, China
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摘要:
為了提高強非線性信號的噪聲消除和信道均衡能力,在核學(xué)習(xí)自適應(yīng)濾波方法的基礎(chǔ)上,該文提出一種基于驚奇準(zhǔn)則的多尺度核學(xué)習(xí)仿射投影濾波方法(SC-MKAPA)。在核仿射投影濾波算法的基礎(chǔ)上,對核組合函數(shù)結(jié)構(gòu)進行改進,將多個不同高斯核帶寬作為可變參數(shù),與加權(quán)系數(shù)共同參與濾波器的更新;利用驚奇準(zhǔn)則將計算結(jié)果稀疏化,根據(jù)仿射投影算法的約束條件對驚奇測度進行改進,簡化其方差項,降低了計算的復(fù)雜度。將該算法應(yīng)用于噪聲消除、信道均衡以及MG時間序列預(yù)測中,與多種自適應(yīng)濾波算法及核學(xué)習(xí)自適應(yīng)濾波算法進行仿真結(jié)果的對比分析,驗證了該算法的優(yōu)越性。
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關(guān)鍵詞:
- 自適應(yīng)濾波 /
- 核學(xué)習(xí) /
- 可變核帶寬 /
- 多核仿射投影 /
- 驚奇準(zhǔn)則
Abstract:In order to improve the ability of noise elimination and channel equalization of strong non-linear signals, a Multi-scale Kernels learning Affine Projection filtering Algorithm based on Surprise Criterion (SC-MKAPA) is proposed on the basis of kernel learning adaptive filtering method. Based on the kernel affine projection filtering algorithm, the structure of the kernel combination function is improved, and the bandwidths of several different Gaussian kernels are taken as variable parameters to participate in the update of the filter together with the weighted coefficients.The calculation results are sparsed by using the surprise criterion, and the surprise measure is improved according to the constraints of the affine projection algorithm, which simplifies the variance term and reduces the calculation complexity. The algorithm is applied to noise cancellation, channel equalization, and Mackey Glass (MG) time series prediction. The simulation results are compared with the traditional adaptive filtering algorithm and the kernel learning adaptive filtering algorithm, it proves the superiority of the proposed algorithm.
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表 1 算法參數(shù)
算法 核帶寬 收斂因子 正則化參數(shù)$\delta $ SC-MKAPA ${\eta _1} = 1.0$, ${\eta _{\rm{2}}} = {\rm{0}}{\rm{.5}}$, ${\eta _{\rm{3}}} = 1{\rm{0}}$ $\mu = 0.2$, $\Delta t = 0.01$ 5.0×10–3 NC-MKAPA ${\eta _1} = 1.0$, ${\eta _{\rm{2}}} = {\rm{0}}{\rm{.5}}$, ${\eta _{\rm{3}}} = 1{\rm{0}}$ $\mu = 0.2$ 5.0×10–3 NC-KAPA ${\eta _1} = 1.0$ $\mu = 0.2$ 5.0×10–3 KLMS ${\eta _1} = 1.0$ $\mu = 0.2$ 5.0×10–3 LMS ${\eta _1} = 1.0$ $\mu = 0.2$ 5.0×10–3 下載: 導(dǎo)出CSV
表 2 不同高次項下5種方法MMSE(dB)
高次項$N$ SC-MKAPA NC-MKAPA NC-KAPA KLMS LMS 2 –71.2 –62.8 –67.2 –32.7 –25.6 3 –62.1 –56.9 –60.6 –24.4 –19.3 6 –33.9 –29.3 –30.2 –21.5 –17.8 7 –18.3 –16.3 –15.2 –13.3 –12.9 下載: 導(dǎo)出CSV
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