相關(guān)熵與循環(huán)相關(guān)熵信號處理研究進展

邱天爽

doi:10.11999/JEIT190646

Development in Signal Processing Based on Correntropy and Cyclic Correntropy

Tianshuang QIU^,

Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China

Funds: The National Natural Science Foundation of China (61671105, 61172108, 61139001, 81241059)

摘要

摘要:
在無線電監(jiān)測和目標定位等應(yīng)用中，接收信號經(jīng)常會受到脈沖噪聲和同頻帶干擾等復雜電磁環(huán)境的影響，傳統(tǒng)的基于2階統(tǒng)計量的信號處理方法往往不能正常工作，基于分數(shù)低階統(tǒng)計量的信號處理方法也由于對信號噪聲統(tǒng)計先驗知識的依賴性而遇到困難。近年來提出并受到信號處理領(lǐng)域普遍關(guān)注的相關(guān)熵和循環(huán)相關(guān)熵信號處理理論與方法，是解決復雜電磁環(huán)境下信號分析處理、參數(shù)估計、目標定位和其他應(yīng)用問題的有效技術(shù)手段，有力促進了非高斯、非平穩(wěn)信號處理理論方法和應(yīng)用的發(fā)展。該文系統(tǒng)性地綜述了相關(guān)熵和循環(huán)相關(guān)熵信號處理的基本理論和基本方法，包括相關(guān)熵與循環(huán)相關(guān)熵的起源背景、定義概念、性質(zhì)特點，以及所包含的數(shù)學物理意義。該文還介紹了相關(guān)熵與循環(huán)相關(guān)熵信號處理在多個領(lǐng)域的應(yīng)用問題，希望對非高斯、非平穩(wěn)統(tǒng)計信號處理的研究和應(yīng)用有所裨益。
- 信號處理 /
- 相關(guān)熵 /
- 循環(huán)相關(guān)熵 /
- 非高斯 /
- 非平穩(wěn)
Abstract:
In radio monitoring and target location applications, the received signals are often affected by complex electromagnetic environment, such as impulsive noise and cochannel interference. Traditional signal processing methods based on second-order statistics often fail to work properly. The signal processing methods based on fractional lower order statistics also encounter difficulties due to their dependence on prior knowledge of signals and noises. In recent years, the theory and method of correntropy and cyclic correntropy signal processing, which are widely concerned in the field of signal processing, are put forward. They are effective technical means to solve the problems of signal analysis and processing, parameter estimation, target location and other applications to complex electromagnetic environment. They promote greatly the development of the theory and application of non-Gaussian and non-stationary signal processing. This paper reviews systematically the basic theory and methods of correntropy and cyclic correntropy signal processing, including the background, definition, properties and characteristics of correntropy and cyclic correntropy, as well as their mathematical and physical meanings. This paper introduces also the applications of correntropy and cyclic correntropy signal processing to many fields, hoping to benefit the research and application of non-Gaussian and non-stationary statistical signal processing.
- Signal processing /
- Correntropy /
- Cyclic correntropy /
- Non-Gaussian /
- Non-stationary

HTML全文

圖 1 2D空間CIM等高線圖^[5]

下載: 全尺寸圖片幻燈片

圖 2 循環(huán)相關(guān)熵譜與常規(guī)的循環(huán)相關(guān)譜及分數(shù)低階循環(huán)相關(guān)譜的對比^[6]

下載: 全尺寸圖片幻燈片

參考文獻(79)

SHAO M and NIKIAS C L. Signal processing with fractional lower order moments: Stable processes and their applications[J]. Proceedings of the IEEE, 1993, 81(7): 986–1010. doi: 10.1109/5.231338

NIKIAS C L and SHAO M. Signal Processing with Alpha-Stable Distributions and Applications[M]. New York: Wiley, 1995: 1–3.

LIU Weifeng, POKHAREL P P, and PRINCIPE J C. Correntropy: A localized similarity measure[C]. 2006 IEEE International Joint Conference on Neural Network Proceedings, Vancouver, Canada, 2006: 4919–4924.

GUNDUZ A and PRINCIPE J C. Correntropy as a novel measure for nonlinearity tests[J]. Signal Processing, 2009, 89(1): 14–23. doi: 10.1016/j.sigpro.2008.07.005

LIU Weifeng, POKHAREL P P, and PRINCIPE J C. Correntropy: Properties and applications in non-Gaussian signal processing[J]. IEEE Transactions on Signal Processing, 2007, 55(11): 5286–5298. doi: 10.1109/TSP.2007.896065

LUAN Shengyang, QIU Tianshuang, ZHU Yongjie, et al. Cyclic correntropy and its spectrum in frequency estimation in the presence of impulsive noise[J]. Signal Processing, 2016, 1204: 503–508.

FONTES A I R, REGO J B A, DE M MARTINS A, et al. Cyclostationary correntropy: Definition and applications[J]. Expert Systems with Applications, 2017, 69: 110–117. doi: 10.1016/j.eswa.2016.10.029

MILLER G. Properties of certain symmetric stable distributions[J]. Journal of Multivariate Analysis, 1978, 8(3): 346–360. doi: 10.1016/0047-259X(78)90058-1

CAMBANIS S and MILLER G. Linear problems in p-th order and stable processes[J]. SIAM Journal on Applied Mathematics, 1981, 41(1): 43–69. doi: 10.1137/0141005

郭瑩, 邱天爽. 基于分數(shù)低階統(tǒng)計量的盲多用戶檢測算法[J]. 電子學報, 2007, 35(9): 1670–1674. doi: 10.3321/j.issn:0372-2112.2007.09.011

GUO Ying and QIU Tianshuang. Blind multiuser detector based on FLOS in impulse noise environment[J]. Acta Electronica Sinica, 2007, 35(9): 1670–1674. doi: 10.3321/j.issn:0372-2112.2007.09.011

MA Xinyu and NIKIAS C L. Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics[J]. IEEE Transactions on Signal Processing, 1996, 44(11): 2669–2687. doi: 10.1109/78.542175

邱天爽, 王宏禹, 孫永梅. 一種基于分數(shù)低階協(xié)方差的自適應(yīng)EP潛伏期變化檢測方法[J]. 電子學報, 2004, 32(1): 91–95. doi: 10.3321/j.issn:0372-2112.2004.01.022

QIU Tianshuang, WANG Hongyu, and SUN Yongmei. A fractional lower-order covariance based adaptive latency change detection for evoked potentials[J]. Acta Electronica Sinica, 2004, 32(1): 91–95. doi: 10.3321/j.issn:0372-2112.2004.01.022

KONG Xuan and QIU Tianshuang. Adaptive estimation of latency change in evoked potentials by direct least mean p-norm time-delay estimation[J]. IEEE Transactions on Biomedical Engineering, 1999, 46(8): 994–1003. doi: 10.1109/10.775410

LIU T H and MENDEL J M. A subspace-based direction finding algorithm using fractional lower order statistics[J]. IEEE Transactions on Signal Processing, 2001, 49(8): 1605–1613. doi: 10.1109/78.934131

GEORGIOU P G, TSAKALIDES P, and KYRIAKAKIS C. Alpha-stable modeling of noise and robust time-delay estimation in the presence of impulsive noise[J]. IEEE Transactions on Multimedia, 1999, 1(3): 291–301. doi: 10.1109/6046.784467

SANTAMARIA I, POKHAREL P P, and PRINCIPE J C. Generalized correlation function: Definition, properties, and application to blind equalization[J]. IEEE Transactions on Signal Processing, 2006, 54(6): 2187–2197. doi: 10.1109/TSP.2006.872524

VAPNIK V N. The Nature of Statistical Learning Theory[M]. New York: Springer Verlag, 1995: 2-4.

BACH F R and JORDAN M I. Kernel independent component analysis[J]. Journal of Machine Learning Research, 2002, 3: 1–48.

PRINCIPE J C. Information Theoretic Learning: Renyi’s Entropy and Kernel Perspectives[M]. New York: Wiley, 1988: 1.

POKHAREL P P, LIU Weifeng, and PRINCIPE J C. A low complexity robust detector in impulsive noise[J]. Signal Processing, 2009, 89(10): 1902–1909. doi: 10.1016/j.sigpro.2009.03.027

PARZEN E. On estimation of a probability density function and mode[J]. The Annals of Mathematical Statistics, 1962, 33(3): 1065–1076. doi: 10.1214/aoms/1177704472

HUBER P J. Robust Statistics[M]. New York: Wiley, 1981: 1–2.

GARDE A, S?RNMO L, JANé R, et al. Correntropy-based spectral characterization of respiratory patterns in patients with chronic heart failure[J]. IEEE Transactions on Biomedical Engineering, 2010, 57(8): 1964–1972. doi: 10.1109/TBME.2010.2044176

SINGH A and PRINCIPE J C. Using correntropy as a cost function in linear adaptive filters[C]. 2009 International Joint Conference on Neural Networks, Atlanta, USA, 2009: 2950–2955.

宋愛民, 邱天爽, 佟祉諫. 對稱穩(wěn)定分布的相關(guān)熵及其在時間延遲估計上的應(yīng)用[J]. 電子與信息學報, 2011, 33(2): 494–498.

SONG Aimin, QIU Tianshuang, and TONG Zhijian. Correntropy of the symmetric stable distribution and its application to the time delay estimation[J]. Journal of Electronics &Information Technology, 2011, 33(2): 494–498.

WANG Lingfeng and PAN Chunhong. Robust level set image segmentation via a local correntropy-based K-means clustering[J]. Pattern Recognition, 2014, 47(5): 1917–1925. doi: 10.1016/j.patcog.2013.11.014

JIN Fangxiao and QIU Tianshuang. Adaptive time delay estimation based on the maximum correntropy criterion[J]. Digital Signal Processing, 2019, 88: 23–32. doi: 10.1016/j.dsp.2019.01.014

PENG Siyuan, CHEN Badong, SUN Lei, et al. Constrained maximum correntropy adaptive filtering[J]. Signal Processing, 2017, 140: 116–126. doi: 10.1016/j.sigpro.2017.05.009

LI Yingsong, JIANG Zhengxiong, SHI Wanlu, et al. Blocked maximum correntropy criterion algorithm for cluster-sparse system identifications[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2019, 66(11): 1915–1919. doi: 10.1109/TCSII.2019.2891654

GUIMAR?ES J P F, FONTES A I R, REGO J B A, et al. Complex correntropy: Probabilistic interpretation and application to complex-valued data[J]. IEEE Signal Processing Letters, 2017, 24(1): 42–45. doi: 10.1109/LSP.2016.2634534

朝樂蒙, 邱天爽, 李景春, 等. 廣義復相關(guān)熵與相干分布式非圓信號DOA估計[J]. 信號處理, 2019, 35(5): 795–801.

CHAO Lemeng, QIU Tianshuang, LI Jingchun, et al. Generalized complex correntropy and DOA estimation for coherently distributed noncircular sources[J]. Journal of Signal Processing, 2019, 35(5): 795–801.

CHEN Badong, XING Lei, ZHAO Haiquan, et al. Generalized correntropy for robust adaptive filtering[J]. IEEE Transactions on Signal Processing, 2016, 64(13): 3376–3387. doi: 10.1109/TSP.2016.2539127

LUO Xiong, SUN Jiankun, WANG Long, et al. Short-term wind speed forecasting via stacked extreme learning machine with generalized correntropy[J]. IEEE Transactions on Industrial Informatics, 2018, 14(11): 4963–4971. doi: 10.1109/TII.2018.2854549

ZHAO Ji and ZHANG Hongbin. Kernel recursive generalized maximum correntropy[J]. IEEE Signal Processing Letters, 2017, 24(12): 1832–1836. doi: 10.1109/LSP.2017.2761886

CHEN Liangjun, QU Hua, and ZHAO Jihong. Generalized correntropy based deep learning in presence of non-Gaussian noises[J]. Neurocomputing, 2018, 278: 41–50. doi: 10.1016/j.neucom.2017.06.080

GIANNAKIS G B and ZHOU GUOTONG. Harmonics in multiplicative and additive noise: Parameter estimation using cyclic statistics[J]. IEEE Transactions on Signal Processing, 1995, 43(9): 2217–2221. doi: 10.1109/78.414790

GHOGHO M, SWAMI A, and GAREL B. Performance analysis of cyclic statistics for the estimation of harmonics in multiplicative and additive noise[J]. IEEE Transactions on Signal Processing, 1999, 47(12): 3235–3249. doi: 10.1109/78.806069

NAPOLITANO A. Cyclostationarity: New trends and applications[J]. Signal Processing, 2016, 120: 385–408. doi: 10.1016/j.sigpro.2015.09.011

LIU Tao, QIU Tianshuang, and LUAN Shengyang. Cyclic Correntropy: Foundations and theories[J]. IEEE Access, 2018, 6: 34659–34669. doi: 10.1109/ACCESS.2018.2847346

MA Jitong and QIU Tianshuang. Automatic modulation classification using cyclic correntropy spectrum in impulsive noise[J]. IEEE Wireless Communications Letters, 2019, 8(2): 440–443. doi: 10.1109/LWC.2018.2875001

LIU Tao, QIU Tianshuang, and LUAN Shengyang. Cyclic frequency estimation by compressed cyclic correntropy spectrum in impulsive noise[J]. IEEE Signal Processing Letters, 2019, 26(6): 888–892. doi: 10.1109/LSP.2019.2910928

JIN Fangxiao, QIU Tianshuang, and LIU Tao. Robust cyclic beamforming against cycle frequency error in Gaussian and impulsive noise environments[J]. AEU-International Journal of Electronics and Communications, 2019, 99: 153–160. doi: 10.1016/j.aeue.2018.11.035

GARDNER W A. The spectral correlation theory of cyclostationary time-series[J]. Signal Processing, 1986, 11(1): 13–36. doi: 10.1016/0165-1684(86)90092-7

GARDNER W A, NAPOLITANO A, and PAURA L. Cyclostationarity: Half a century of research[J]. Signal Processing, 2006, 86(4): 639–697. doi: 10.1016/j.sigpro.2005.06.016

郭瑩, 邱天爽, 張艷麗, 等. 脈沖噪聲環(huán)境下基于分數(shù)低階循環(huán)相關(guān)的自適應(yīng)時延估計方法[J]. 通信學報, 2007, 28(3): 8–14. doi: 10.3321/j.issn:1000-436X.2007.03.002

GUO Ying, QIU Tianshuang, ZHANG Yanli, et al. Novel adaptive time delay estimation method based on the fractional lower order cyclic correlation in impulsive noise environment[J]. Journal on Communications, 2007, 28(3): 8–14. doi: 10.3321/j.issn:1000-436X.2007.03.002

LIU Yang, QIU Tianshuang, and SHENG Hu. Time-difference-of-arrival estimation algorithms for cyclostationary signals in impulsive noise[J]. Signal Processing, 2012, 92(9): 2238–2247. doi: 10.1016/j.sigpro.2012.02.016

KWON H and NASRABADI N M. Hyperspectral target detection using kernel matched subspace detector[C]. 2004 International Conference on Image Processing (ICIP), Singapore, 2004: 3327–3330.

ERDOGMUS D, AGRAWAL R, and PRINCIPE J C. A mutual information extension to the matched filter[J]. Signal Processing, 2005, 85(5): 927–935. doi: 10.1016/j.sigpro.2004.11.018

JEONG K H, LIU Weifeng, HAN S, et al. The correntropy MACE filter[J]. Pattern Recognition, 2009, 42(5): 871–885. doi: 10.1016/j.patcog.2008.09.023

ZHAO Songlin, CHEN Badong, and PRíNCIPE J C. Kernel adaptive filtering with maximum correntropy criterion[C]. 2011 International Joint Conference on Neural Networks, San Jose, USA, 2011: 2012–2017.

CHEN Badong and PRINCIPE J C. Maximum correntropy estimation is a smoothed MAP estimation[J]. IEEE Signal Processing Letters, 2012, 19(8): 491–494. doi: 10.1109/LSP.2012.2204435

CHEN Badong, XING Lei, LIANG Junli, et al. Steady-state mean-square error analysis for adaptive filtering under the maximum correntropy criterion[J]. IEEE Signal Processing Letters, 2014, 21(7): 880–884. doi: 10.1109/LSP.2014.2319308

WU Zongze, SHI Jiahao, ZHANG Xie, et al. Kernel recursive maximum correntropy[J]. Signal Processing, 2015, 117: 11–16. doi: 10.1016/j.sigpro.2015.04.024

CHEN Badong, LIU Xi, ZHAO Haiquan, et al. Maximum correntropy Kalman filter[J]. Automatica, 2017, 76: 70–77. doi: 10.1016/j.automatica.2016.10.004

LIU Xi, CHEN Badong, ZHAO Haiquan, et al. Maximum correntropy Kalman filter with state constraints[J]. IEEE Access, 2017, 5: 25846–25853. doi: 10.1109/ACCESS.2017.2769965

LIU Xi, CHEN Badong, XU Bin, et al. Maximum correntropy unscented filter[J]. International Journal of Systems Science, 2017, 48(8): 1607–1615. doi: 10.1080/00207721.2016.1277407

LIU Xi, QU Hua, ZHAO Jihong, et al. Maximum correntropy unscented Kalman filter for spacecraft relative state estimation[J]. Sensors, 2016, 16(9): 1530. doi: 10.3390/s16091530

KRIM H and VIBERG M. Two decades of array signal processing research: The parametric approach[J]. IEEE Signal Processing Magazine, 1996, 13(4): 67–94. doi: 10.1109/79.526899

YOU Guohong, QIU Tianshuang, and YANG Jiao. A novel DOA estimation algorithm of cyclostationary signal based on UCA in impulsive noise[J]. AEU-International Journal of Electronics and Communications, 2013, 67(6): 491–499. doi: 10.1016/j.aeue.2012.11.006

ZHANG Jingfeng, QIU Tianshuang, SONG Aimin, et al. A novel correntropy based DOA estimation algorithm in impulsive noise environments[J]. Signal Processing, 2014, 104: 346–357. doi: 10.1016/j.sigpro.2014.04.033

王鵬, 邱天爽, 任福全, 等. 對稱穩(wěn)定分布噪聲下基于廣義相關(guān)熵的DOA估計新方法[J]. 電子與信息學報, 2016, 38(8): 2007–2013.

WANG Peng, QIU Tianshuang, REN Fuquan, et al. A novel generalized correntropy based method for direction of arrival estimation in symmetric alpha stable noise environments[J]. Journal of Electronics &Information Technology, 2016, 38(8): 2007–2013.

WANG Peng, QIU Tianshuang, REN Fuquan, et al. A robust DOA estimator based on the correntropy in alpha-stable noise environments[J]. Digital Signal Processing, 2017, 60: 242–251. doi: 10.1016/j.dsp.2016.10.002

王鵬, 邱天爽, 金芳曉, 等. 脈沖噪聲下基于稀疏表示的韌性DOA估計方法[J]. 電子學報, 2018, 46(7): 1537–1544. doi: 10.3969/j.issn.0372-2112.2018.07.001

WANG Peng, QIU Tianhsuang, JIN Fangxiao, et al. A robust DOA estimation method based on sparse representation for impulsive noise environments[J]. Acta Electronica Sinica, 2018, 46(7): 1537–1544. doi: 10.3969/j.issn.0372-2112.2018.07.001

KNAPP C and CARTER G C. The generalized correlation method for estimation of time delay[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1976, 24(4): 320–327. doi: 10.1109/TASSP.1976.1162830

CARTER G C. Time delay estimation for passive sonar signal processing[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1981, 29(3): 463–470. doi: 10.1109/TASSP.1981.1163560

WANG Gang and HO K C. Convex relaxation methods for unified near-field and far-field TDOA-based localization[J]. IEEE Transactions on Wireless Communications, 2019, 18(4): 2346–2360. doi: 10.1109/TWC.2019.2903037

YU Ling, QIU Tianshuang, and LUAN Shengyang. Fractional time delay estimation algorithm based on the maximum correntropy criterion and the Lagrange FDF[J]. Signal Processing, 2015, 111: 222–229. doi: 10.1016/j.sigpro.2014.12.018

LUO Yuanzhe, SUN Guolu, ZHANG Xiaotong, et al. Adaptive time-delay estimation based on normalized maximum correntropy criterion for near-field electromagnetic ranging[J]. Computers & Electrical Engineering, 2018, 67: 404–414.

CHEN Xing, QIU Tianshuang, LIU Cheng, et al. TDOA estimation algorithm based on generalized cyclic correntropy in impulsive noise and cochannel interference[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2018, 101-A(10): 1625–1630.

LI Sen, LIN Bin, DING Yabo, et al. Signal-selective time difference of arrival estimation based on generalized cyclic correntropy in impulsive noise environments[C]. The 13th International Conference on Wireless Algorithms, Systems, and Applications, Tianjin, China, 2018: 274–283.

HE Ran, ZHENG Weishi, and HU Baogang. Maximum correntropy criterion for robust face recognition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33(8): 1561–1576. doi: 10.1109/TPAMI.2010.220

ZHOU Sanping, WANG Jinjun, ZHANG Mengmeng, et al. Correntropy-based level set method for medical image segmentation and bias correction[J]. Neurocomputing, 2017, 234: 216–229. doi: 10.1016/j.neucom.2017.01.013

PENG Jiangtao and DU Qian. Robust joint sparse representation based on maximum correntropy criterion for hyperspectral image classification[J]. IEEE Transactions on Geoscience and Remote Sensing, 2017, 55(12): 7152–7164. doi: 10.1109/TGRS.2017.2743110

HASSAN M, TERRIEN J, MARQUE C, et al. Comparison between approximate entropy, correntropy and time reversibility: Application to uterine electromyogram signals[J]. Medical Engineering & Physics, 2011, 33(8): 980–986.

BARQUERO-PéREZ O, S?RNMO L, GOYA-ESTEBAN R, et al. Fundamental frequency estimation in atrial fibrillation signals using correntropy and Fourier organization analysis[C]. The 3rd International Workshop on Cognitive Information Processing (CIP), Baiona, Spain, 2012: 1–6.

NAPOLITANO A. Cyclostationarity: Limits and generalizations[J]. Signal Processing, 2016, 120: 323–347. doi: 10.1016/j.sigpro.2015.09.013

ZHAO Xuejun, QIN Yong, HE Changbo, et al. Rolling element bearing fault diagnosis under impulsive noise environment based on cyclic correntropy spectrum[J]. Entropy, 2019, 21(1): 50. doi: 10.3390/e21010050

HUIJSE P, ESTEVEZ P A, ZEGERS P, et al. Period estimation in astronomical time series using slotted correntropy[J]. IEEE Signal Processing Letters, 2011, 18(6): 371–374. doi: 10.1109/LSP.2011.2141987

DUAN Jiandong, QIU Xinyu, MA Wentao, et al. Electricity consumption forecasting scheme via improved LSSVM with maximum correntropy criterion[J]. Entropy, 2018, 20(2): 112. doi: 10.3390/e20020112

相關(guān)文章

施引文獻

資源附件(0)

訪問統(tǒng)計