一種基于多尺度核學(xué)習(xí)的仿射投影濾波算法

李群生; 趙剡; 寇磊; 王進達

doi:10.11999/JEIT190023

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

李群生^{1, 2, ,},
趙剡¹,
寇磊³,
王進達²

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
2.
中國空空導(dǎo)彈研究院洛陽 471009
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

基金項目: 國家自然科學(xué)基金(61233005)，航空基金(20160812004, 20160112002, 2016ZA12002)

詳細(xì)信息

作者簡介:
李群生：男，1977年生，博士，研究方向為濾波信號處理，組合導(dǎo)航技術(shù)

趙剡：男，1956年生，教授，研究方向為慣性技術(shù)，信號處理技術(shù)

寇磊：女，1971年生，高級工程師，研究方向為慣性技術(shù)

王進達：男，1989年生，博士，研究方向為濾波信號處理，組合導(dǎo)航技術(shù)

通訊作者:
李群生　570658391@qq.com

中圖分類號: TN911.7, TP391
計量
- 文章訪問數(shù): 2027
- HTML全文瀏覽量: 964
- PDF下載量: 81
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2019-01-09
- 修回日期: 2019-07-30
- 網(wǎng)絡(luò)出版日期: 2020-01-11
- 刊出日期: 2020-06-04

An Affine Projection Algorithm with Multi-scale Kernels Learning

Qunsheng LI^{1, 2
, ,},
Yan ZHAO¹,
Lei KOU³,
Jinda WANG²

1.
School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China
2.
Air-to-Air Missile Research Institute, Luoyang 471009, China
3.
National Key Laboratory on Flight Vehicle Control Integrated Technology, Xi’an 710065, China

Funds: The National Natural Science Foundation of China (61233005), The Aviation Science Fund (20160812004, 20160112002, 2016ZA12002)

摘要

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。
- 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.
- Adaptive filters /
- Kernel learning /
- Variable kernel bandwidth /
- Affine projection with multi-kernels /
- Surprise criterion

HTML全文

圖 1 濾波器除噪原理

下載: 全尺寸圖片幻燈片

圖 2 噪聲分布

下載: 全尺寸圖片幻燈片

圖 3 對數(shù)條件下MSE的學(xué)習(xí)曲線

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圖 4 對數(shù)條件下MSE的學(xué)習(xí)曲線

下載: 全尺寸圖片幻燈片

圖 5 MG時間序列的預(yù)測學(xué)習(xí)曲線

下載: 全尺寸圖片幻燈片

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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