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As is well known, people has been suffering noise interference for a long time, and more and more researches show that a lot of weak signals such as pulse signal are embedded in the strong chaotic noise. The purpose of weak signal detection and recovery is to retrieve useful signal from strong noise. It is very difficult to detect and estimate the weak pulse signal which is mixed in the chaotic background interference. Therefore, the detection and recovery of weak signal are significant and have application value in signal processing area, especially for the weak pulse signal detection and recovery. By studying various methods of detecting and estimating the weak pulse signal in strong chaotic background noise, in this paper, we propose an efficient hybrid processing technique. First, based on the short-term predictability and sensitivity to the tiny disturbance, a new method is proposed, which can be used for detecting and estimating the weak pulse signals in chaotic background that the nonlinear mapping is unknown. We reconstruct a phase space according to Takens delay embedding theorem; then we establish the local linear autoregressive model to predict the short-term chaotic signal and obtain the fitting error, and judge whether there are weak pulse signals. Second, we establish a single-jump model for pulse signals, and combine the local linear autoregressive model with it to build a double local linear (DLL) model for estimating the weak pulse signal. DLL model contains two parameters, and the two parameters affect each other. We use the back-fitting algorithm to estimate model parameters and ultimately recover the weak pulse signals. Detecting and estimating the pulse signals in chaotic background turns into estimating the parameters of DLL model. The minimum fitting error criterion is used as the objective function to estimate the parameters of the DLL model. To make the estimation more exact, we can use the formula of mean square error. The new algorithm presented here in this paper does not need to know the prior knowledge of the chaotic background nor weak pulse signal, and this algorithm is also simple and effective. Finally, the simulation results show that the method is effective for detecting and estimating the weak pulse signals based on the chaotic background noise. Specifically, the weak pulse signal can be extracted well with low SNR and the minimum mean square error or the minimum normalized mean squared error is very low.
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Keywords:
- chaotic noise /
- weak pulse signal detection /
- local linear autoregressive model /
- double local linear model
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[2] Zhang K L, Zhu H M 2009 Avionics Technol. 40 30 (in Chinese) [章克来, 朱海明 2009 航空电子技术 40 30]
[3] Xia J Z, Liu Y H, Leng Y G, Ge J T 2011 Noise Vib. Control. 31 156 (in Chinese) [夏均忠, 刘远宏, 冷永刚, 葛纪桃 2011 噪声与振动控制 31 156]
[4] L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Application (Wuhan: Wuhan University Press) p8 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第8页]
[5] Su L Y, Li C L 2015 Discrete Dyn. Nat. Soc. 2015 329487
[6] Wang D S, Chen L, Shi Y D 2010 J. Dyn. Control 8 48 (in Chinese) [王德石, 谌龙, 史跃东 2010动力学与控制学报 8 48]
[7] Su L Y 2010 Comput. Math. Appl. 59 737
[8] Wang X L, Wang W B 2015 Chin. Phys. B 24 080203
[9] Lu P, Li Y 2005 Acta Electron. Sin. 33 527 (in Chinese) [路鹏, 李月 2005 电子学报 33 527]
[10] Su L Y, Ma Y J, Li J J 2012 Chin. Phys. B 21 020508
[11] Li M P, Xu X M, Yang B C, Ding J F 2015 Chin. Phys. B 24 060504
[12] He G T, Luo M K 2012 Chin. Phys. Lett. 29 060204
[13] Liu L S, Zhang L 2009 Electron. Test 8 19 (in Chinese) [刘连生, 张磊 2009 电子测试 8 19]
[14] Li Y, Yang B J, Du L Z, Yuan Y 2003 J. Electron. Infor. Technol. 25 195 (in Chinese) [李月, 杨宝俊, 杜立志, 袁野 2003 电子与信息学报 25 195]
[15] Dai Y S 1994 Weak Signal Detection Method and Instrument (Beijing: National Defend Industry Press) pp268-275 (in Chinese) [戴逸松 1994 微弱信号检测方法及仪器 (北京: 国防工业出版社) 第268275页]
[16] Li Y, Lu P, Yang B J 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李月, 路鹏, 杨宝俊 2006 55 1672]
[17] Swami A, Mendel J M 1988 Cumulant-based Approach to the Harmonic Retrieval Problem New York, USA, April 11-14, 1988 pp2264-2267
[18] Chang N N, Lu C H, Liu C 2006 J. Electron. Meas. Instrum. 20 86 (in Chinese) [苌凝凝, 鲁昌华, 刘春 2006 电子测量与仪器学报 20 86]
[19] Li J Y 2010 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China) (in Chinese) [李继永 2010 硕士学位论文 (成都: 电子科技大学)]
[20] Ma Y, Shi Y W, Kang X T 2002 Acta Electron. Sin. 30 14 (in Chinese) [马彦, 石要武, 康小涛 2002 电子学报 30 14]
[21] Xing H Y, Zhang Q, Xu W 2015 Acta Phys. Sin. 64 040506 (in Chinese) [行鸿彦, 张强, 徐伟 2015 64 040506]
[22] Xing H Y, Zhu Q Q, Xu W 2014 Acta Phys. Sin. 63 100505 (in Chinese) [行鸿彦, 朱清清, 徐伟 2014 63 100505]
[23] Zhu Z W, Leung H 2002 IEEE Trans. Circ. Sys. I 49 170
[24] Ma J W, Qing C Y 2013 Sig. Process. 29 1609 (in Chinese) [马尽文, 青慈阳 2013 信号处理 29 1609]
[25] Zhang Q, Xing H Y 2015 Acta Electron. Sin. 43 901 (in Chinese) [张强, 行鸿彦 2015 电子学报 43 901]
[26] Liu H, Liu D, Li Q 2005 J. Sys. Sci. Infor. 25 94 (in Chinese) [刘涵, 刘丁, 李琦 2005 系统工程理论与实践 25 94]
[27] Zheng H L, Xing H Y, Xu W 2015 Sig. Process. 31 336 (in Chinese) [郑红利, 行鸿彦, 徐伟 2015 信号处理 31 336]
[28] Leung H 2014 Chaotic Signal Processing (Beijing: Higher Education Press) pp110-113
[29] Li Y, Yang B J, Deng X Y, Lin H B 2005 J. Electro. Infor. Technol. 27 731 (in Chinese) [李月, 杨宝俊, 邓小英, 林红波 2005 电子与信息学报 27 731]
[30] Takens F 1981 Lecture Notes Math. 898 366
[31] Lin J Y, Wang Y K, Huang Z P 1999 Sig. Process. 15 220 (in Chinese) [林嘉宇, 王跃科, 黄芝平 1999 信号处理 15 220]
[32] Cao L Y 1997 Physica D 110 43
[33] Peng X W, Su L Y, Li C L, Yin Y, Sun H H 2015 Stat. Appl. 4 56 (in Chinese) [彭相武, 苏理云, 李晨龙, 殷勇, 孙唤唤 2015 统计学与应用 4 56]
[34] Su L Y, Li C L 2015 Math. Problems Eng. 2015 901807
[35] Li C L 2015 M. S. Thesis (Chongqing: Chongqing University of Technology) (in Chinese) [李晨龙 2015 硕士学位论文 (重庆: 重庆理工大学)]
[36] Li C, Su L 2017 Mech. Syst. Sig. Proc. 84 499
[37] She D, Yang X 2010 Math. Problems Eng. 2010 205438
[38] Fan J, Yao Q, Cai Z 2003 J. Royal Stat. Soc. 65 57
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[1] Cai Z Q 2014 M. S. Thesis (Baotou: Inner Mongolia University of Science Technology) (in Chinese) [蔡志全 2014 硕士学位论文 (包头: 内蒙古科技大学)]
[2] Zhang K L, Zhu H M 2009 Avionics Technol. 40 30 (in Chinese) [章克来, 朱海明 2009 航空电子技术 40 30]
[3] Xia J Z, Liu Y H, Leng Y G, Ge J T 2011 Noise Vib. Control. 31 156 (in Chinese) [夏均忠, 刘远宏, 冷永刚, 葛纪桃 2011 噪声与振动控制 31 156]
[4] L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Application (Wuhan: Wuhan University Press) p8 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第8页]
[5] Su L Y, Li C L 2015 Discrete Dyn. Nat. Soc. 2015 329487
[6] Wang D S, Chen L, Shi Y D 2010 J. Dyn. Control 8 48 (in Chinese) [王德石, 谌龙, 史跃东 2010动力学与控制学报 8 48]
[7] Su L Y 2010 Comput. Math. Appl. 59 737
[8] Wang X L, Wang W B 2015 Chin. Phys. B 24 080203
[9] Lu P, Li Y 2005 Acta Electron. Sin. 33 527 (in Chinese) [路鹏, 李月 2005 电子学报 33 527]
[10] Su L Y, Ma Y J, Li J J 2012 Chin. Phys. B 21 020508
[11] Li M P, Xu X M, Yang B C, Ding J F 2015 Chin. Phys. B 24 060504
[12] He G T, Luo M K 2012 Chin. Phys. Lett. 29 060204
[13] Liu L S, Zhang L 2009 Electron. Test 8 19 (in Chinese) [刘连生, 张磊 2009 电子测试 8 19]
[14] Li Y, Yang B J, Du L Z, Yuan Y 2003 J. Electron. Infor. Technol. 25 195 (in Chinese) [李月, 杨宝俊, 杜立志, 袁野 2003 电子与信息学报 25 195]
[15] Dai Y S 1994 Weak Signal Detection Method and Instrument (Beijing: National Defend Industry Press) pp268-275 (in Chinese) [戴逸松 1994 微弱信号检测方法及仪器 (北京: 国防工业出版社) 第268275页]
[16] Li Y, Lu P, Yang B J 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李月, 路鹏, 杨宝俊 2006 55 1672]
[17] Swami A, Mendel J M 1988 Cumulant-based Approach to the Harmonic Retrieval Problem New York, USA, April 11-14, 1988 pp2264-2267
[18] Chang N N, Lu C H, Liu C 2006 J. Electron. Meas. Instrum. 20 86 (in Chinese) [苌凝凝, 鲁昌华, 刘春 2006 电子测量与仪器学报 20 86]
[19] Li J Y 2010 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China) (in Chinese) [李继永 2010 硕士学位论文 (成都: 电子科技大学)]
[20] Ma Y, Shi Y W, Kang X T 2002 Acta Electron. Sin. 30 14 (in Chinese) [马彦, 石要武, 康小涛 2002 电子学报 30 14]
[21] Xing H Y, Zhang Q, Xu W 2015 Acta Phys. Sin. 64 040506 (in Chinese) [行鸿彦, 张强, 徐伟 2015 64 040506]
[22] Xing H Y, Zhu Q Q, Xu W 2014 Acta Phys. Sin. 63 100505 (in Chinese) [行鸿彦, 朱清清, 徐伟 2014 63 100505]
[23] Zhu Z W, Leung H 2002 IEEE Trans. Circ. Sys. I 49 170
[24] Ma J W, Qing C Y 2013 Sig. Process. 29 1609 (in Chinese) [马尽文, 青慈阳 2013 信号处理 29 1609]
[25] Zhang Q, Xing H Y 2015 Acta Electron. Sin. 43 901 (in Chinese) [张强, 行鸿彦 2015 电子学报 43 901]
[26] Liu H, Liu D, Li Q 2005 J. Sys. Sci. Infor. 25 94 (in Chinese) [刘涵, 刘丁, 李琦 2005 系统工程理论与实践 25 94]
[27] Zheng H L, Xing H Y, Xu W 2015 Sig. Process. 31 336 (in Chinese) [郑红利, 行鸿彦, 徐伟 2015 信号处理 31 336]
[28] Leung H 2014 Chaotic Signal Processing (Beijing: Higher Education Press) pp110-113
[29] Li Y, Yang B J, Deng X Y, Lin H B 2005 J. Electro. Infor. Technol. 27 731 (in Chinese) [李月, 杨宝俊, 邓小英, 林红波 2005 电子与信息学报 27 731]
[30] Takens F 1981 Lecture Notes Math. 898 366
[31] Lin J Y, Wang Y K, Huang Z P 1999 Sig. Process. 15 220 (in Chinese) [林嘉宇, 王跃科, 黄芝平 1999 信号处理 15 220]
[32] Cao L Y 1997 Physica D 110 43
[33] Peng X W, Su L Y, Li C L, Yin Y, Sun H H 2015 Stat. Appl. 4 56 (in Chinese) [彭相武, 苏理云, 李晨龙, 殷勇, 孙唤唤 2015 统计学与应用 4 56]
[34] Su L Y, Li C L 2015 Math. Problems Eng. 2015 901807
[35] Li C L 2015 M. S. Thesis (Chongqing: Chongqing University of Technology) (in Chinese) [李晨龙 2015 硕士学位论文 (重庆: 重庆理工大学)]
[36] Li C, Su L 2017 Mech. Syst. Sig. Proc. 84 499
[37] She D, Yang X 2010 Math. Problems Eng. 2010 205438
[38] Fan J, Yao Q, Cai Z 2003 J. Royal Stat. Soc. 65 57
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