混沌背景中的小信号检测研究
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摘要
混沌信号是由确定性系统产生的具有类随机性的信号。随着对信号检测和混沌动力学越来越深入的研究,发现在很多场合都遇到目标信号湮没在混沌背景信号中的情况。于是,如何检测混沌背景中的目标信号或提取混沌背景中目标信号的特征参数成为目前信号检测与估计领域的研究热点。
本论文利用混沌信号的几何特征,在混沌背景中信号提取与信号参数估计等方面开展了以下工作:
①研究混沌信号在重构相空间中局部切空间投影方法的特点,在数值实验的基础上研究相空间重构参数选取对局部切空间投影方法提取谐波信号的影响;
②将局部切空间投影方法应用于检测混沌背景中的瞬态信号,并通过大量的数值实验充分验证了该方法的有效性;
③根据混合信号在混沌流形局部的奇异值分解特点,提出一种混沌背景中信号提取的新方法——最小相对奇异值(MRSV)法。实例仿真表明该方法能够有效地估计出混沌背景中的AR模型的参数和正弦信号的频率。在估计AR模型参数时,较短的数据长度,本方法也能很好地估计出参数;在估计正弦信号的频率时,本方法能有效地将FFT不能分辨的强混沌背景中的正弦信号的频率估计出来。
本论文的研究工作对混沌背景中小信号检测有一定理论和应用价值。
The chaotic signal is pseudo-random and generated by a deterministic dynamical system. By more and more profound studies of signal detection and chaotic dynamics, it is found that a lot of target signals are embedded in the strong chaotic background. So some researchers that work on the signal detection and estimation field are paying attentions to detection of the target signals or extraction of the target signals’feature parameters in the chaotic background at present.
Based on the chaotic signals’geometric features, some studies on extracting the target signals and estimating the signals’parameters in the chaotic background are worked out. The main works are as followings:
①After studying the features of the local-tangent space projection method, we do many numerical experiments on the harmonic signal’s extraction from chaotic signal with the method, then analyze the experiments’results to research how the quality of the harmonic signal’s extraction depends on the phase-space reconstruction parameters.
②The local-tangent space projection method is used to detect the transient signals in the chaotic background, and many numerical experiments fully verify the validity of the method.
③A novel method, named the Minimization of Relative Singular Value(MRSV) ,to extract useful signal in chaotic background is proposed, and the method is based on the mixed-signal’s features of local singular value decomposition(SVD) on chaotic manifold. Simulations show that the method can effectively estimate the AR model’s parameters and sine wave frequencies in chaotic background. The AR model’s parameters can be estimated effectively with the short length of the data. The frequency of the sine signal not being distinguished by FFT can be estimated.
The research results of this thesis have certain theoretical and practical value in detection weak signal from chaotic background.
本论文利用混沌信号的几何特征,在混沌背景中信号提取与信号参数估计等方面开展了以下工作:
①研究混沌信号在重构相空间中局部切空间投影方法的特点,在数值实验的基础上研究相空间重构参数选取对局部切空间投影方法提取谐波信号的影响;
②将局部切空间投影方法应用于检测混沌背景中的瞬态信号,并通过大量的数值实验充分验证了该方法的有效性;
③根据混合信号在混沌流形局部的奇异值分解特点,提出一种混沌背景中信号提取的新方法——最小相对奇异值(MRSV)法。实例仿真表明该方法能够有效地估计出混沌背景中的AR模型的参数和正弦信号的频率。在估计AR模型参数时,较短的数据长度,本方法也能很好地估计出参数;在估计正弦信号的频率时,本方法能有效地将FFT不能分辨的强混沌背景中的正弦信号的频率估计出来。
本论文的研究工作对混沌背景中小信号检测有一定理论和应用价值。
The chaotic signal is pseudo-random and generated by a deterministic dynamical system. By more and more profound studies of signal detection and chaotic dynamics, it is found that a lot of target signals are embedded in the strong chaotic background. So some researchers that work on the signal detection and estimation field are paying attentions to detection of the target signals or extraction of the target signals’feature parameters in the chaotic background at present.
Based on the chaotic signals’geometric features, some studies on extracting the target signals and estimating the signals’parameters in the chaotic background are worked out. The main works are as followings:
①After studying the features of the local-tangent space projection method, we do many numerical experiments on the harmonic signal’s extraction from chaotic signal with the method, then analyze the experiments’results to research how the quality of the harmonic signal’s extraction depends on the phase-space reconstruction parameters.
②The local-tangent space projection method is used to detect the transient signals in the chaotic background, and many numerical experiments fully verify the validity of the method.
③A novel method, named the Minimization of Relative Singular Value(MRSV) ,to extract useful signal in chaotic background is proposed, and the method is based on the mixed-signal’s features of local singular value decomposition(SVD) on chaotic manifold. Simulations show that the method can effectively estimate the AR model’s parameters and sine wave frequencies in chaotic background. The AR model’s parameters can be estimated effectively with the short length of the data. The frequency of the sine signal not being distinguished by FFT can be estimated.
The research results of this thesis have certain theoretical and practical value in detection weak signal from chaotic background.
引文
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[42] Packard N H, Crutchfield J P, Farmer J D, et al. Geometry from a time series [J]. Phys. Rev. Lett., 1980, 45(9): 712-716.
[43] Broombead D S, King G P. Extracting qualitative dynamics from experimental data [J]. Physics D, 1986, 20(2/3): 217-236.
[44]王妍,徐伟,曲继圣.基于时间序列的相空间重构算法及验证(一) [J].山东大学学报(工学版), 2005, 35(4): 109-114.
[45]陈春旺.复杂经济时间序列预测和辫识方法的研究[硕士学位论文].南京:东南大学, 2001.
[46]王岩.相空间重构方法在非线性转子动力学中的应用[硕士学位论文].哈尔滨:哈尔滨工业大学, 2002.
[47]徐森林.微分拓扑[M].天津:天津教育出版社, 1997: 2-30
[48]舒斯特H G.混沌学引论[M].朱宏雄,等译.成都:四川教育出版社, 1994: 56-58
[49] Rosenstein M T, Collins J J, et al. A practical method for calculating largest lyapunov exponents from small data sets [J]. Physica D, 1993, 65(1/2): 117-134.
[50] Rosenstein M T, Collins J J, De Luca C J. Reconstruction expansion as a geometry based framework for hooding proper delay times [J]. Physica D, 1994, 73(1/2): 82-98.
[51]杨志安,王光瑞.用等间距分格子法计算互信息函数确定延迟时间[J].计算物理, 1995, 12(4): 442-448.
[52]王军,石炎福,余华瑞.相空间重构中最优滞时的确定[J].四川大学学报(工程科学版), 2001, 33(2): 47-51.
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[2] Pijn J P, Neerven J, Noest A, et al. Chaos or noise in EEG signals:dependence on state and brain site [J]. Electroencephalogr Clin Neurophysiol, 1991, 79: 371-381.
[3] Kumar A , Mullick S K. Attractor dimension, entropy and modeling of speech time series [J]. Electron. Lett., 1990, 26(21): 1790-1792.
[4]王丹丹,王怀阳,李晓燕,等.基于混沌理论的心电信号特征研究[J].微计算机信息, 2006, 22(3): 243-244.
[5] Wu Shuxian. Chua’s circuit family [J]. Proceedings of the IEEE, 1987, 75: 1022-1032.
[6] Bhattacharya J. Detection of weak chaos in infant respiration [J]. IEEE Transactions on Systems, Man and Cybernetics part-B: Cybernetics, 2001, 31: 637-642.
[7]李辉.混沌数字通信[M].北京:清华大学出社, 2006: 10-11.
[8]袁坚,肖先赐.淹没在噪声中的混沌信号最大李雅谱诺夫指数的提取[J].电子学报, 1997, 25(10): 102-106.
[9] Sauer T D, Tempkin J A, Yorke J A. Spurious Lyapunov exponents in attractor reconstruction [J]. Phys. Rev. Lett, 1998, 81(20): 4341-4344.
[10]龚云帆,徐健学.混沌信号与噪声[J].信号处理, 1997, 13(2): 112-118.
[11] Christian S, Gustavo D. Identification of deterministic chaos by an information theoretic measure of the sensitive dependence on the initial conditions [J]. Physic A, 1995, 110(3/4): 173-781.
[12] Leung H, Huang X P. Parameter estimation in chaotic noise [J]. IEEE Transactions on Signal Procedding, 1996, 44(10): 2463-2546.
[13]汪芙平,王赞基,郭静波.混沌背景下信号的盲分离[J].物理学报, 2002, 51(3): 474-481.
[14] Cuomo K M , Oppenheim A V, Strogatz S H . Synchronization of Lorenz-based chaotic circuits with applications to communications [J]. IEEE Transactions on Circuits System, 1993, 40(10): 626-633.
[15] Takens F. Detecting strange attractors in turbulence [M]. Lecture Notes in mathematics Springer, Berlin. 1981, 898: 361-381.
[16]简相超,郑君里.一种正交多项式混沌全局建模方法[J].电子学报, 2002, 30(1): 76-78.
[17]周永道,马洪,吕王勇,等.基于多元局部多项式方法的混沌时间序列预测[J].物理学报, 2007, 56(12): 6809-6814.
[18]张家树,肖先赐.用于低维混沌时间序列预测的一种非线性自适应预测滤波器[J].通信学报, 2001, 22(10): 93-98.
[19]王国光,王树勋.混沌背景下微弱谐波信号的恢复[J].吉林大学学报, 2006, 36(3): 422-428.
[20] Stark J , Arumugam B V. Extracting slowly varying signals from a chaotic background [J]. Int. J. Bifurcation and Chaos, 1992, 2(2): 413-419.
[21] Broomhead D S, Huke J P and Potts M A S. Cancelling deterministic noise by constructing nonlinear inverses to linear filters [J]. Physica D, 1996, 89(3): 439-458.
[22] Short K M. Signal extraction from chaotic communications [J]. Int. J. Bifurcation and Chaos, 1997, 7(7): 1579-1597.
[23] Leung H, Lo T. Chaotic radar signal processing over the sea [J]. IEEE Journal of Oceanic Engineering, 1993, 18(3): 287-295.
[24]何建华,杨宗凯.基于混沌和神经网络的弱信号探测[J].电子学报, 1998, 26(10): 33-37.
[25] Xiong Zhangliang, Song Yaoliang, Liu Ming, et al. Signal detection with chaotic neur-al network [J]. IEEE Neural Network & Signal Processing, 2003, 12(1): 14-17.
[26]张文爱,宁爱平.混沌背景下基于小波神经网络的弱信号检测[J].太原理工大学学报2006, 37(3): 281-294.
[27]黄显高,徐健学,何岱海,等.利用小波多尺度分解算法实现混沌系统的噪声减缩[J].物理学报, 1999, 48(10): 1810-1817.
[28] Huang Xiangao, Xu Jianxue, Huang Wei, et al. Unmasking chaotic mask by a wavelet multiscale decomposition algorithm [J]. Int. J. Bifurcation and Chaos, 2001, 11(2): 561-569.
[29]李祯燕.混沌与信号的分离方法研究[硕士学位论文].哈尔滨:哈尔滨工业大学, 2002.
[30] Hammel S M. A noise reduction method for chaotic system [J]. Phys. Lett. A. 1990, 148(8/9): 421-428.
[31] Schweizer S M, Stinick V L, Evans J L. TLS parameter estimation for filtering chaotic time series [C]. IEEE Proc. ICSSP. Atlanta GA USA: IEEE, 1996: 1609-1612.
[32] Lee C, Williams D B. Generalized iterative methods for enhancing contaminated chaotic signals [J]. IEEE Transactions on CAS-I, 1997, 44(6): 501-512.
[33] Bowen R. Morkov partitions for axion a idiom orpgisms [J]. Amer. J. Math., 1970, 92(5): 725-747.
[34]席剑辉,韩敏,孙燕楠.改进非线性局部平均算法混沌去噪研究[J].系统工程与电子技术, 2005, 27(5): 799-802
[35] Cawley R, Hsu G H. Local-geometric-projection method for noise reduction inchaotic maps and flows [J]. Phys. Rev. A, 1992, 46(6): 3057-3082.
[36] Mallat, Wenliang H. Sigularity detection and processing with wacelet [J]. IEEE Transactions on Information Theory, 1992, 82(2): 211-223.
[37] Petridis V, Kcehagias A. Modular neural networks for MAP classification of time series and partition algorithm [J]. IEEE Transactions on Neural Network, 1996, 7(1): 73-86.
[38]童勤业,严筱刚.混沌测量的一种改进方案[J].仪器仪表学报, 2000, 21(1): 22-27.
[39]童勤业,严筱刚,孔军,等.“混沌”理论在测量中的应用[J].电子科学学刊, 1999, 21(1):42-49.
[40]李月,杨宝俊.混沌振子检测引论[M].北京:电子工业出版社, 2004: 18-120
[41]李雪霞,冯久超.一种混沌信号的盲分离方法[J].物理学报, 2007, 56(2): 701-706.
[42] Packard N H, Crutchfield J P, Farmer J D, et al. Geometry from a time series [J]. Phys. Rev. Lett., 1980, 45(9): 712-716.
[43] Broombead D S, King G P. Extracting qualitative dynamics from experimental data [J]. Physics D, 1986, 20(2/3): 217-236.
[44]王妍,徐伟,曲继圣.基于时间序列的相空间重构算法及验证(一) [J].山东大学学报(工学版), 2005, 35(4): 109-114.
[45]陈春旺.复杂经济时间序列预测和辫识方法的研究[硕士学位论文].南京:东南大学, 2001.
[46]王岩.相空间重构方法在非线性转子动力学中的应用[硕士学位论文].哈尔滨:哈尔滨工业大学, 2002.
[47]徐森林.微分拓扑[M].天津:天津教育出版社, 1997: 2-30
[48]舒斯特H G.混沌学引论[M].朱宏雄,等译.成都:四川教育出版社, 1994: 56-58
[49] Rosenstein M T, Collins J J, et al. A practical method for calculating largest lyapunov exponents from small data sets [J]. Physica D, 1993, 65(1/2): 117-134.
[50] Rosenstein M T, Collins J J, De Luca C J. Reconstruction expansion as a geometry based framework for hooding proper delay times [J]. Physica D, 1994, 73(1/2): 82-98.
[51]杨志安,王光瑞.用等间距分格子法计算互信息函数确定延迟时间[J].计算物理, 1995, 12(4): 442-448.
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