﻿ 基于希尔伯特黄变换的雷达信号滤波

# 基于希尔伯特黄变换的雷达信号滤波Filtering of Radar Signal Based on Hilbert Huang Transform

Abstract: A method of radar signal filtering based on Hilbert Huang transform (HHT) is explored. Through handling the radar signal by empirical mode decomposition (EMD), the intrinsic mode function (IMF) components are obtained, and the spectrum and Hilbert spectrum of the IMF component are obtained by frequency analysis. According to the distribution law of time-frequency characteristics, the signal-to-noise ratio of the filtered signal and the echo signal energy contained in the signal component are estimated to determine the component used to reconstruct the filtered signal. The filtering effect is tested by comparing the simulated filtered signal with the measured radar signal. The results show that the filtering algorithm based on HHT has a good effect on the filtering of radar signal.

1. 引言

20世纪末，美国物理学家黄愕首次提出了一种非常适合于分析非稳定或非线性信号的希尔伯特黄变换(Hilbert-Huang Transformation, HHT)算法。HHT已在地震预测、地球勘探 [1]、建筑结构隐患侦测 [2]、雷达滤波 [3] [4] 等研究领域得到有效应用。本文结合雷达信号的特性与HHT变换的特点，提出了基于HHT的雷达信号滤波方法，并与设备上现有的滤波结果进行对比，检验HHT滤波方法对雷达信号的滤波效果。

2. 希尔伯特黄变换及其滤波原理

2.1. 希尔伯特–黄变换

$x\left(t\right)=\underset{i=1}{\overset{n}{\sum }}{c}_{i}\left(t\right)+{r}_{n}\left(t\right)$ (1)

$x\left(t\right)=\mathrm{Re}\left[\underset{i=1}{\overset{n}{\sum }}{a}_{i}\left(t\right){e}^{j\int {\omega }_{i}\left(t\right)dt}\right]$ (2)

2.2. HHT滤波的基本原理

HHT滤波是将信号通过EMD分解得到频率由高到低的IMF分量，然后用原信号减去包含噪声的分量，得到滤波信号；或是对包含原信号的分量进行去噪后再重构，得到滤波信号，达到对原信号滤波的目的。IMF的频率成分是由原信号的频率特性决定的，频率的高低也是相对的，没有特定的频率数值来区分高频或低频分量，HHT是根据信号自身特性分解信号，自适应性强，非常适合于非平稳信号滤波。

3. 雷达信号分析

Figure 1. The IF signal waveform of a signal radar

Figure 2. (a) Spectrum analysis of clutter signal; (b) Spectrum analysis of signal with high imitation echo

Figure 3. Signal with high imitation echo EMD decomposition result

Figure 4. The IMF component of the signal with high imitation echo spectrum analysis

Figure 5. The Hilbert spectrum of signal with high imitation echo

4. 信号滤波处理

Table 1. Signal to noise ratio of reconstructed signal and estimation of echo energy in components

Figure 6. (a) Filtered signal waveform, (b) Filtered signal spectrum analysis

Figure 7. (a) Waveform of amplified and frequency scaled original signal, (b) The measured third IF signal waveform, (c) Waveform of amplified and frequency scaled filtered signal

5. 小结

[1] 周海军, 李磊. 地震波形的HHT特征提取和GMM识别研究[J]. 黑龙江工业学院学报(综合版), 2018(4): 69-73.

[2] 周彪. 基于改进HHT的桥梁结构震后损伤识别[D]: [硕士学位论文]. 成都: 西南交通大学, 2017.

[3] 王超, 沈斐敏. 一维HHT变换在探地雷达数据处理中的应用[J]. 工程地质学报, 2015, 23(2): 328-334.

[4] 王陶. HHT与压缩传感在雷达回波分析中的应用研究[D]: [硕士学位论文]. 成都: 电子科技大学, 2012.

[5] Huang, N.E., Zheng, S., Steven, R., et al. (1998) The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis. Proceedings of the Royal Society of London, 454, 903-993.
https://doi.org/10.1098/rspa.1998.0193

[6] 郑君里, 应启珩, 杨为理. 信号与系统[M]. 北京: 高等教育出版社, 2000.

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