CEEMD结合改进小波阈值的激光雷达信号去噪算法

doi:10.12305/j.issn.1001-506X.2023.01.12

摘要/Abstract

摘要：

激光雷达远距离回波信号受噪声影响, 严重失真。为了有效去除信号的噪声, 提高回波信号信噪比, 提出一种互补集合经验模态分解(complementary ensemble empirical mode decomposition, CEEMD)结合改进小波阈值的去噪算法。CEEMD可以自适应地分解非线性和非平稳信号, 改进小波阈值函数具有高阶可导特性, 能够克服硬阈值、软阈值函数各自存在的问题。两种方法结合, 可以更有效地去除噪声。首先, 对回波信号进行CEEMD分解, 得到若干固有模态函数(intrinsic mode function, IMF)。其次, 通过相关系数法计算IMF分量与信号的相关系数, 确定相关分量和不相关分量。最后, 对不相关分量使用小波改进阈值法进行去噪, 对相关分量使用粗糙惩罚法进行平滑, 再重构信号。基于实测数据的实验结果表明, 所提算法比CEEMD去噪法和CEEMD结合原改进阈值去噪法, 信噪比分别提升了2.65 dB和0.58 dB。

关键词: 激光雷达, 信号处理, 互补集合经验模态分解, 小波阈值去噪

Abstract:

The long-distance echo signal of laser radar is affected by noise and is seriously distorted. In order to effectively remove the noise of the signal and improve the signal-to-noise ratio of the echo signal, a denoising algorithm combining complementary ensemble empirical mode decomposition (CEEMD) with an improved wavelet threshold is proposed. CEEMD can adaptively decompose nonlinear and non-stationary signals, and the improved wavelet threshold function has high-order differentiability characteristics, which can overcome the problems of hard threshold and soft threshold functions. The combination of the two methods can remove noise more effectively. Firstly, the echo signal is decomposed by CEEMD to obtain several intrinsic mode function (IMF) components. Secondly, the correlation coefficient between the IMF components and the signal is calculated by the correlation coefficient method. And the relevant and uncorrelated components are determined. Finally, the wavelet improved threshold method is used to denoise the uncorrelated components, and the rough penalty method is used to smooth the correlated components, and then the signal is reconstructed. Experimental results based on measured data show that the proposed algorithm has improved the signal-to-noise ratio by 2.65 dB and 0.58 dB compared with the CEEMD denoising method and CEEMD combined with the original improved threshold denoising method.

Key words: laser radar, signal processing, complementary ensemble empirical mode decomposition (CEEMD), wavelet threshold denoising

中图分类号:

TP212

马愈昭, 刘逵, 张岩峰, 冯帅, 熊兴隆. CEEMD结合改进小波阈值的激光雷达信号去噪算法[J]. 系统工程与电子技术, 2023, 45(1): 93-100.

Yuzhao MA, Kui LIU, Yanfeng ZHANG, Shuai FENG, Xinglong XIONG. Laser radar signal denoising algorithm based on CEEMD combined with improved wavelet threshold[J]. Systems Engineering and Electronics, 2023, 45(1): 93-100.

图/表 13

图1

图2

图3

表1

图4

图5

图6

图7

表2

表3

表4

图8

表5

参考文献 30

1	熊兴隆, 李永东, 冯帅, 等. PM2.5质量浓度廓线的激光雷达反演研究[J]. 光子学报, 2020, 49 (4): 43- 52.
	XIONG X L , LI Y D , FENG S , et al. Research on lidar retrieval of PM2.5 mass concentration profile[J]. Acta Photonica Sinica, 2020, 49 (4): 43- 52.
2	马愈昭, 刘嘉琪, 王强强, 等. 基于Fernald-PSO法反演气溶胶激光雷达比及其对斜程能见度的影响[J]. 光子学报, 2019, 48 (3): 201- 210.
	MA Y Z , LIU J Q , WANG Q Q , et al. Retrieving the aerosol lidar ratio based on the Fernald-PSO method and its influence on slope visibility[J]. Acta Photonica Sinica, 2019, 48 (3): 201- 210.
3	VISHNU R , KUMAR Y B , NAIR A K M . An investigation of the elevated aerosol layer using a polarization lidar over a tropical rural site in India[J]. Boundary-Layer Meteorology, 2021, 178 (2): 323- 340. doi: 10.1007/s10546-020-00573-2
4	LIU Z R , WEN J X , HE T . Application of wavelet threshold de-noising technique in the gearbox vibration signal processing[J]. Modern Manufacturing Engineering, 2010, 4, 75- 78.
5	XI X G , WU H , LUO Z Z . De-noising method of the SEMG based on EMD autocorrelation[J]. Chinese Journal of Scientific Instrument, 2014, 35 (11): 2494- 2500.
6	HUANG N E , SHEN Z , LONG S R , et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1998, 454 (1971): 903- 995. doi: 10.1098/rspa.1998.0193
7	SUN Z Y , XI X G , YUAN C M , et al. Surface electromyography signal denoising via EEMD and improved wavelet thresholds[J]. Mathematical Biosciences and Engineering, 2020, 17 (6): 6945- 6962. doi: 10.3934/mbe.2020359
8	XIE S L, ZHANG W M, LU Y J, et al. Denoising method for bearing vibration signal based on EEMD and wavelet packet transform[C]//Proc. of the 10th IEEE Institute of Electrical and Electronics Engineers International Conference on Cyber Technology in Automation, Control, and Intelligent Systems, 2020: 277-282.
9	原磊明, 关瑞, 石国栋, 等. 基于EEMD与小波阈值去噪的单相接地故障选线方法[J]. 煤炭工程, 2020, 52 (12): 137- 140.
	YUAN L M , GUAN R , SHI G D , et al. Single-phase grounding fault line selection method based on EEMD and wavelet threshold denoising[J]. Coal Engineering, 2020, 52 (12): 137- 140.
10	WU Z , HUANG N E . Ensemble empirical mode decomposition: a noise-assisted data analysis method[J]. Advances in Adaptive Data Analysis, 2009, 1 (1): 1- 41. doi: 10.1142/S1793536909000047
11	YEH J R , SHIEH J S , HUANG N E . Complementary ensemble empirical mode decomposition: a novel noise enhanced data analysis method[J]. Advances in Adaptive Data Analysis, 2010, 2 (2): 135- 156. doi: 10.1142/S1793536910000422
12	朱玲嬿, 常建华, 李红旭, 等. 改进的激光雷达回波信号去噪方法[J]. 电子测量与仪器学报, 2017, 31 (10): 1608- 1613.
	ZHU L Y , CHANG J H , LI H X , et al. Improved lidar echo signal denoising method[J]. Journal of Electronic Measurement and Instrument, 2017, 31 (10): 1608- 1613.
13	WANG J , LI Z C , WANG D Y . A method for wavelet threshold denoising of seismic data based on CEEMD[J]. Geophysical Prospecting for Petroleum, 2014, 53 (2): 164- 172.
14	RONG H X , GAO Y B , GUAN L W , et al. GAM-based mooring alignment for SINS based on an improved CEEMD denoising method[J]. Sensors, 2019, 19 (16): 3564. doi: 10.3390/s19163564
15	LI J , LIU C , ZENG Z F , et al. GPR signal denoising and target extraction with the CEEMD method[J]. IEEE Geoscience and Remote Sensing Letters, 2015, 12 (8): 1615- 1619. doi: 10.1109/LGRS.2015.2415736
16	HOU S Z , GUO W . Optimal denoising and feature extraction methods using modified CEEMD combined with duffing system and their applications in fault line selection of non-solid-earthed network[J]. Symmetry, 2020, 12 (4): 536.
17	SUN M M , LI Z C , LI Z N , et al. A noise attenuation method for weak seismic signals based on compressed sensing and CEEMD[J]. IEEE Access, 2020, 8, 71951- 71964.
18	DUAN Y B , SONG C T . Relevant modes selection method based on Spearman correlation coefficient for laser signal denoising using empirical mode decomposition[J]. Optical Review, 2016, 23 (6): 936- 949.
19	ZHANG S Y, LIU Y Y, YANG G L. EMD interval thresholding denoising based on correlation coefficient to select relevant modes[C]//Proc. of the IEEE 34th Chinese Control Confer-ence, 2015: 4801-4806.
20	WANG E J , ZHANG J W , MA X W , et al. A new threshold denoising algorithm for partial discharge based on CEEMD- EEMD[J]. Power System Protection and Control, 2016, 44 (15): 93- 98.
21	JIANG L Y, WANG S Y, CUI J G, et al. Research on gear signal denoising method based on CEEMD and SSA[C]//Proc. of the IEEE Chinese Control and Decision Conference, 2019: 2751-2756.
22	ZHANG M , ZENG Q J , SUI X , et al. Denoising method of MEMS gyro of an underwater vehicle based on CEEMD[J]. Journal of Sensing Technology, 2014, 12 (27): 1622- 1626.
23	LI Z J , ZHANG H P , WANG Y N , et al. Wavelet threshold denoising harmonic detection method based on permutation entropy-CEEMD decomposition[J]. Electric Machines & Control, 2020, 24 (12): 120- 129.
24	孙文军, 芮国胜, 张驰, 等. 机械故障的级联共振和EMD联合参数辨识方法[J]. 电子测量与仪器学报, 2016, 30 (3): 352- 360.
	SUN W J , RUI G S , ZHANG C , et al. Joint parameter identification method of cascade resonance and EMD for mechanical faults[J]. Journal of Electronic Measurement and Instrument, 2016, 30 (3): 352- 360.
25	关山, 王龙山. 小波阈值去噪技术研究及其在信号处理中的应用[J]. 计算机工程与设计, 2008, 29 (22): 5857- 5859.
	GUAN S , WANG L S . Research on wavelet threshold denoising and its application in signals' processing[J]. Computer Engineering and Design, 2008, 29 (22): 5857- 5859.
26	ZHAO R M, CUI H. Improved threshold denoising method based on wavelet transform[C]// Proc. of the 7th IEEE International Conference on Modelling, Identification and Control, 2015.
27	GONG J. A study on wavelet selection in power signal denoising[C]//Proc. of the IOP Conference Series: Earth and Environmental Science, 2021, 675(1): 012104.
28	刘厚通, 陈良富, 苏林. Fernald前向积分用于机载激光雷达气溶胶后向散射系数反演的理论研究[J]. 物理学报, 2011, 60 (6): 310- 318.
	LIU H T , CHEN L F , SU L . Theoretical study of Fernald forward integration for the inversion of airborne lidar aerosol backscattering coefficients[J]. Acta Physica Sinica, 2011, 60 (6): 310- 318.
29	AMINUDDIN J, AMINUDDIN I, TURSILOWATI L, et al. Continuous lidar observation of near surface aerosol using optical and sampling data from ground-based instruments[C]//Proc. of the EPJ Web of Conferences on EDP Sciences, 2020.
30	ATTO A M , PASTOR D , MERCIER G . Wavelet shrinkage: unification of basic thresholding functions and thresholds[J]. Signal, Image and Video Processing, 2011, 5 (1): 11- 28.

噪声强度/dB	自适应阈值	启发式阈值	固定阈值	极大极小阈值
10	17.26	17.86	16.13	19.61
15 20	21.97 26.91	22.50 27.40	22.25 27.23	23.65 27.84

指标	本文算法	CEEMD去噪	CEEMD+小波阈值去噪	CEEMD+原改进阈值去噪	EEMD+本文改进小波阈值去噪
SNR/dB	20.60	5.68	19.43	19.45	20.19
RMSE(×10^-7)	1.27	7.11	1.46	1.43	1.33

噪声强度/dB	本文算法	CEEMD去噪	CEEMD+小波阈值去噪	CEEMD+原改进阈值去噪	EEMD+本文改进小波阈值去噪
10	15.47	3.50	12.77	14.91	15.31
15 20	21.86 28.01	3.38 3.42	17.78 23.50	21.52 23.50	21.72 27.79

C值	本文算法	CEEMD去噪	CEEMD+小波阈值去噪	CEEMD+原改进阈值去噪	EEMD+本文改进小波阈值去噪
0.75 0.80	25.90 16.57	3.47 5.75	23.45 15.65	24.70 16.02	25.18 14.62

算法	本文算法	CEEMD去噪	CEEMD+小波阈值去噪	CEEMD+原改进阈值去噪	EEMD+本文改进小波阈值去噪
去噪效果指标	6.63	3.98	6.46	6.05	6.61