基于Duffing混沌系统的微弱正弦信号检测方法
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摘要
在现代信息处理技术领域,微弱信号的检测是一项重要内容,同时也是工程技术中人们获取各种有用信息的一个重要手段。微弱信号检测在雷达、声纳技术、振动测量、故障诊断、通信、物理学、系统辨识等领域有着广泛的应用。随着科学技术的发展,对微弱信号进行检测的需求日益迫切。微弱信号的检测是发展高新技术、探索及发现新的自然规律的重要手段,对推动相关领域的发展具有重要意义。微弱信号幅值极小,信噪比很低,待测信号经常被噪声淹没,传统的信号检测方法很难取得令人满意的效果。而混沌理论的引入,给微弱信号检测带来了新的突破。混沌检测法利用混沌系统对初始条件的敏感依赖性来实现对微弱信号的检测,大大降低了信号检测与提取系统的输入信噪比门限,提高了微弱信号的检测精度。
本文介绍了混沌理论的特点和定义,以及混沌吸引子的有关理论。详细地讨论了Duffing振子的动力学特性,研究了混沌系统判别方法和混沌判据。在对Duffing振子系统用于微弱正弦信号检测的原理进行深入研究的基础上,提出了一种基于Duffing振子的微弱正弦信号检测方法和相关法结合起来的混合测量法,完成了对未知正弦信号幅值的测量。对Duffing振子模型进行了改进,降低了基于Duffing振子系统的微弱正弦信号检测系统的信噪比门限。提出了一种基于优化理论的未知信号频率检测方法。实验结果表明,利用本文提出的方法对强噪声背景下的微弱正弦信号进行检测和提取,效果明显优于传统的基于线性系统的检测方法,具有一定的实用价值。
Weak signal detection (WSD) is one of the important content in the area of information process, it is an important approach for human to get the useful information. Weak signal measurement has widely applied in radar, sonar technology, vibration measurement, trouble diagnosis, communication, physics, system identification and other fields. With the development of science technology, the needs of WSD becoming increasingly urgent. WSD is an important way to improve advanced technology, to explore and find natural law. It have great significance for the promotion in the relative area. The weak signal have the very small amplitude, very low signal noise ratio(SNR), the signal to be measured is often covered by noise. The traditional signal detection method can't satisfy the WSD. The chaotic theory brought the new breakthrough to WSD, the accurate of the WSD was improved.
This article introduced the characteristic and the definition of chaotic theory, and the theory about chaotic attractor. Discussed the kinetic characteristic of Duffing vibrator in detail. Studied on the chaos discrimination and the chaos criteria. With the deep research on Duffing chaotic system, we present a new method of WSD based on Duffing chaotic system and the correlation method, completed the detection of the signal amplitude. Improved the model of Duffing system, decreased the SNR threshold of Duffing criteria WSD system. Present a method to detect the frequency of the signal to be measured based on the Optimal theory. The results of the experiments showed that the method we presented in this article have much better efficiency than the traditional way, it have certain application value.
本文介绍了混沌理论的特点和定义,以及混沌吸引子的有关理论。详细地讨论了Duffing振子的动力学特性,研究了混沌系统判别方法和混沌判据。在对Duffing振子系统用于微弱正弦信号检测的原理进行深入研究的基础上,提出了一种基于Duffing振子的微弱正弦信号检测方法和相关法结合起来的混合测量法,完成了对未知正弦信号幅值的测量。对Duffing振子模型进行了改进,降低了基于Duffing振子系统的微弱正弦信号检测系统的信噪比门限。提出了一种基于优化理论的未知信号频率检测方法。实验结果表明,利用本文提出的方法对强噪声背景下的微弱正弦信号进行检测和提取,效果明显优于传统的基于线性系统的检测方法,具有一定的实用价值。
Weak signal detection (WSD) is one of the important content in the area of information process, it is an important approach for human to get the useful information. Weak signal measurement has widely applied in radar, sonar technology, vibration measurement, trouble diagnosis, communication, physics, system identification and other fields. With the development of science technology, the needs of WSD becoming increasingly urgent. WSD is an important way to improve advanced technology, to explore and find natural law. It have great significance for the promotion in the relative area. The weak signal have the very small amplitude, very low signal noise ratio(SNR), the signal to be measured is often covered by noise. The traditional signal detection method can't satisfy the WSD. The chaotic theory brought the new breakthrough to WSD, the accurate of the WSD was improved.
This article introduced the characteristic and the definition of chaotic theory, and the theory about chaotic attractor. Discussed the kinetic characteristic of Duffing vibrator in detail. Studied on the chaos discrimination and the chaos criteria. With the deep research on Duffing chaotic system, we present a new method of WSD based on Duffing chaotic system and the correlation method, completed the detection of the signal amplitude. Improved the model of Duffing system, decreased the SNR threshold of Duffing criteria WSD system. Present a method to detect the frequency of the signal to be measured based on the Optimal theory. The results of the experiments showed that the method we presented in this article have much better efficiency than the traditional way, it have certain application value.
引文
[1].康海雷,基于DUFFING振子的微弱信号检测方法与实现,2009,西安科技大学.
[2].陈争,混沌背景中的小信号检测研究,2008,湘潭大学.
[3].Zhang, W. and B. Xiang, A Duffing oscillator algorithm to detect the weak chromatographic signal. Analytica Chimica Acta,2007.585(1):p.55-59.
[4].胡艳华,负信噪比直接序列扩频信号的检测及参数估计研究,2008,汕头大学.
[5].韩振榕,基于Duffing振子的微弱信号检测研究,2006,苏州大学.
[6].路鹏,基于Duffing振子的微弱信号检测,2005,吉林大学.
[7].MorrisW,美.,微分方程、动力系统与混沌导论.2008,北京：人民邮电出版社.336.
[8].乐波,基于混沌振子与小波的低信噪比信号检测研究与应用,2009,电子科技大学.
[9].彭建华,刘秉正,非线性动力学.2005：高等教育出版社.
[10].曹磊,王东升,混沌、分形及其应用.1995：中国科学技术大学出版社.
[11].任艳春,混沌理论在雷达通信中的应用研究,2007,哈尔滨工程大学.
[12].J. Thompson, H.B.S., Nonlinear dynamics and chaos.2002.
[13].梁堃,基于混沌理论的微弱信号测量系统研究,2007,哈尔滨理工大学.
[14].赵建勋,赵树杰,信号检测与估计理论.2005：清华大学出版社.
[15].黄润生,混沌及其应用.2000：武汉大学出版社.
[16].刘曾荣,混沌研究中的解析方法.2002：上海大学出版社.
[17].李目,混沌时间序列预测及其微弱目标信号检测方法研究,2007,湖南大学.
[18].何建华,杨宗凯与王殊,基于混沌和神经网络的弱信号探测.电子学报,1998(10)：第33-37页.
[19].王福友等,基于时空混沌的海杂波背景下小目标检测.仪器仪表学报,2009(06)：第1180-1185页.
[20].毕红博,基于混沌振子FSK微弱信号检测方法的研究,2008,华北电力大学(河北)
[21].李方方,微弱信号检测与采集技术的研究,2006,哈尔滨工业大学.
[22].徐凯,基于混沌系统几何特征量的微弱信号检测,2008,吉林大学.
[23].邓嘉,基于混沌理论的非线性信号预测及检测,2006,电子科技大学.
[24].孙海欣,混沌噪声背景下周期信号的频率估计的方法研究,2008,吉林大学.
[25].李虎明,小信号混沌检测研究,2005,西安理工大学.
[26].王兴元,复杂非线性系统中的混沌.2003.电子工业出版社.
[27]. Li Iy, Y.J., Period three implies chaos,Amer math,monthly.1975.
[28].吉启超,混沌噪声背景下谐波参数估计方法研究,2009,吉林大学.
[29].李清都,杨晓松,混沌系统与混沌电路.2007：科学出版社.
[30].宁爱平,混沌背景下弱信号检测方法的研究,2006,太原理工大学.
[31].陈颖,湮没在混沌背景下的微弱信号检测,2006,苏州大学.
[32].韩振榕,基于混沌振子的微弱信号测频研究.苏州大学学报(工科版),2009(06)：第55-57页.
[33]. N, L.E., The Essence of chaos.1993:USA:university of Washington press.
[34].乔宏志,基于DUFFING振子微弱信号检测方法及DSP实现,2006,华北电力大学(河北)
[35].王树禾,微分方程模型与混沌.1999.中国科学技术大学出版社.
[36].刘洋,混沌背景中信号提取的相空间投影法,2009,吉林大学.
[2].陈争,混沌背景中的小信号检测研究,2008,湘潭大学.
[3].Zhang, W. and B. Xiang, A Duffing oscillator algorithm to detect the weak chromatographic signal. Analytica Chimica Acta,2007.585(1):p.55-59.
[4].胡艳华,负信噪比直接序列扩频信号的检测及参数估计研究,2008,汕头大学.
[5].韩振榕,基于Duffing振子的微弱信号检测研究,2006,苏州大学.
[6].路鹏,基于Duffing振子的微弱信号检测,2005,吉林大学.
[7].MorrisW,美.,微分方程、动力系统与混沌导论.2008,北京：人民邮电出版社.336.
[8].乐波,基于混沌振子与小波的低信噪比信号检测研究与应用,2009,电子科技大学.
[9].彭建华,刘秉正,非线性动力学.2005：高等教育出版社.
[10].曹磊,王东升,混沌、分形及其应用.1995：中国科学技术大学出版社.
[11].任艳春,混沌理论在雷达通信中的应用研究,2007,哈尔滨工程大学.
[12].J. Thompson, H.B.S., Nonlinear dynamics and chaos.2002.
[13].梁堃,基于混沌理论的微弱信号测量系统研究,2007,哈尔滨理工大学.
[14].赵建勋,赵树杰,信号检测与估计理论.2005：清华大学出版社.
[15].黄润生,混沌及其应用.2000：武汉大学出版社.
[16].刘曾荣,混沌研究中的解析方法.2002：上海大学出版社.
[17].李目,混沌时间序列预测及其微弱目标信号检测方法研究,2007,湖南大学.
[18].何建华,杨宗凯与王殊,基于混沌和神经网络的弱信号探测.电子学报,1998(10)：第33-37页.
[19].王福友等,基于时空混沌的海杂波背景下小目标检测.仪器仪表学报,2009(06)：第1180-1185页.
[20].毕红博,基于混沌振子FSK微弱信号检测方法的研究,2008,华北电力大学(河北)
[21].李方方,微弱信号检测与采集技术的研究,2006,哈尔滨工业大学.
[22].徐凯,基于混沌系统几何特征量的微弱信号检测,2008,吉林大学.
[23].邓嘉,基于混沌理论的非线性信号预测及检测,2006,电子科技大学.
[24].孙海欣,混沌噪声背景下周期信号的频率估计的方法研究,2008,吉林大学.
[25].李虎明,小信号混沌检测研究,2005,西安理工大学.
[26].王兴元,复杂非线性系统中的混沌.2003.电子工业出版社.
[27]. Li Iy, Y.J., Period three implies chaos,Amer math,monthly.1975.
[28].吉启超,混沌噪声背景下谐波参数估计方法研究,2009,吉林大学.
[29].李清都,杨晓松,混沌系统与混沌电路.2007：科学出版社.
[30].宁爱平,混沌背景下弱信号检测方法的研究,2006,太原理工大学.
[31].陈颖,湮没在混沌背景下的微弱信号检测,2006,苏州大学.
[32].韩振榕,基于混沌振子的微弱信号测频研究.苏州大学学报(工科版),2009(06)：第55-57页.
[33]. N, L.E., The Essence of chaos.1993:USA:university of Washington press.
[34].乔宏志,基于DUFFING振子微弱信号检测方法及DSP实现,2006,华北电力大学(河北)
[35].王树禾,微分方程模型与混沌.1999.中国科学技术大学出版社.
[36].刘洋,混沌背景中信号提取的相空间投影法,2009,吉林大学.
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