混沌直扩信号检测与混沌同步研究
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摘要
非线性科学是研究非线性现象共性的基础学科,非线性方法能够更为合理地描述客观事实。混沌是非线性科学中的重要一员,它对现代科学技术产生了巨大的影响。混沌通信是混沌理论在工程领域最杰出的应用之一。本文开展了混沌理论及其在非合作混沌信号检测、参数估计和混沌同步中的应用研究。混沌检测是针对混沌通信信号分析建模的先决条件,它包括实现对观测时间序列混沌特性识别的混沌识别和利用混沌系统进行弱信号检测的混沌系统检测。混沌同步是实现混沌通信的有力保障,也正是单向耦合混沌同步的电路实现使得混沌通信成为可能。广义混沌同步是实现基于混沌同步的通信信号分析的主要手段之一。混沌参数调制是混沌通信的主要方式,它利用不同参数集下的混沌信号来掩盖传输信息以达到保密通信的目的,混沌参数估计是实现信息解调的必要前提。本文的主要研究成果有:
1、提出了一种有效区分混沌与噪声的方法。研究了随着嵌入维数的增长,相空间中相点间平均距离的变化趋势。根据混沌与噪声在相空间中的不同特性,从理论上推导出了区别噪声与混沌的方法。该方法可以在短数据和噪声环境中实现快速判决,不仅改善了传统方法需要人为选择多个主观参数,容易出现误判和计算量大等问题,而且在一定程度上改进了基于混沌系统特征量方法对噪声十分敏感和需要大量数据的缺点。
2、研究了基带混沌直扩信号的检测。针对混沌直扩通信中的实值扩谱方式,提出了利用伪邻近点实现信号检测的方法。实值混沌扩谱信号的检测实质上是混沌与噪声的识别问题。在分析信息码对混沌动力学影响的基础上,将基于伪邻近点构造的识别算法应用到基带实值混沌直扩信号检测,不仅克服了传统基于混沌系统特征量对噪声十分敏感和数据量大的缺点,而且能够在一定程度上实现与传统直扩方式的区别。
3、针对量化混沌直扩信号,提出了基于哈密顿量的定量Duffing振子信号检测方法。Duffing振子利用外加微扰信号使得系统动力学特性发生明显改变,而对噪声免疫来实现信号检测,极大地提高了微弱信号检测性能。本文分析了Duffing振子的动力学行为特性、时频特性、噪声免疫特性、状态跃迁阈值及微扰信号相差和频差对动力学行为的影响,分别利用相图的状态跃迁以及时序图的间歇混沌行为实现信号检测。考虑到当前基于Duffing振子微弱信号检测仍停留在定性分析和仿真分析阶段的现状,提出了利用哈密顿量构造统计量进行定量判决的方法。哈密顿量能够实时地表征系统状态的变化情况。该方法可以在低信噪比下实现微弱信号的定量判决。
4、提出了自适应实现具有未知参数和不同结构混沌系统广义混合混沌同步方案。该方案能够实现两个不同结构混沌系统的同步跟踪。考虑到系统未知参数对同步流形稳定性的影响,基于自适应原理,本文利用Lyapunov理论解析地设计了控制信号和参数更新规则。该方法能够同时实现完全同步、镜像同步和投影同步,并可推广到更一般的广义同步。该方法的研究更接近于实际的非合作信号分析环境。数值方法验证了方法的有效性。
5、提出了基于超前混沌同步的参数估计方法。考虑到混沌通信系统处在不同的地理位置,信号传输存在时延的影响,从观测数据中估计延迟耦合系统的未知参数具有重要意义。本文研究了具有时延耦合混沌系统的参数估计。基于Krasovskii-Lyapunov理论的系统稳定性分析可以导出时延独立的稳定性条件,但是时延与参数估计密切相关。本文利用数值方法研究了方案中各参数对估计方法的影响。该方案能够在时间延迟存在的情况下有效估计系统的未知参数,改进了传统基于完全同步的参数估计方法。
Nonlinear science is a basic subject which studies the common characteristics of nonlinear phenomena. Nonlinear method can describe the objective fact more reasonable. Chaos is the most important one in nonlinear science, which has generated a huge influence to modern science and technologies. Chaotic communication is one of the most excellence applications in engineering. This thesis studies the chaos theory and its application in non-cooperative chaos signal detection, chaos synchronization and parameters estimation of chaotic systems. Chaos detection is the precondition of the modeling of chaotic communication signal, which includes chaos identification and the signal detection based on chaos system. Chaos identification can identify the chaotic characters from the observed time series, and the signal detection based on chaotic system exploits a chaotic system to detect weak signal. Chaos synchronization is the powerful guarantee to implement chaotic communication. And just the achievement of the synchronization of two chaotic systems with unidirectional couple in electronic circuit, the chaotic communication becomes possible. The generalized chaos synchronization is one of the main methods to achieve the analysis of the chaotic communication signals based on chaos synchronization. Chaotic parameter modulation is the main way of chaotic communication, which uses the chaotic signal from different parameter set of the chaotic system to hide the transmit information and achieve secure communication. The parameters estimation of chaotic systems is the necessary precondition to information demodulate. The main results of this thesis are:
1、An efficient method of distinguishing chaos from noise is proposed. The changing trend of the average distance between phase points in phase space is studied with the increase of the embedding dimension. According to the different characteristics between chaos and noise in phase space, this thesis deduces a method which can distinguish chaos from noise. This method can do decision quickly even when the data are short and contaminated. This method not only overcomes the shortage of the subjectivity of parametric choice and time consuming of traditional method, but also improves the shortcoming of both the requirement for a large number of data and the noise sensitivity of the invariant of chaotic system to some extent.
2、The detection of baseband chaotic direct sequence spread spectrum signal(CDSSS) is studied. In allusion to the real number chaotic spread spectrum mode in CDSSS communication, this thesis proposes to do detection by false neighbor method. Essentially, the detection of the real number CDSSS signal is the problem of distinguishing chaos from noise. Based on the analysis of the influence of information code to chaotic dynamics, this paper uses the identification algorithm which based on false neighbor to detect the baseband real number CDSSS signal. This method not only overcomes the shortage of both the requirement for a large number of data and the noise sensitivity of the invariant of chaos system, but also can distinguish traditional DSSS signal to some extent.
3、For quantization CDSSS signal, this thesis proposes a quantitative signal detection method by using Duffing oscillator based on Hamiltonian. Duffing oscillator exploits the characteristics that additional perturbation signals make the dynamics of the system change obviously and immune to noise to detect weak signal. This improves the performance of the weak signal detection greatly. According to the analysis of the dynamics characteristic, the time-frequency characteristic, the immune to noise characteristic, the state transition characteristic and the influence of the frequency and phase difference with the perturbation signal of Duffing oscillator, this paper proposes to use state transition of the phase portrait and intermittent chaos of the time series diagram to detect signal respectively. Considering most of the existing weak signal detection methods based on Duffing oscillator are stay on qualitative and simulative analysis also, this paper proposes to use Hamiltonian to construct statistic to do quantitative decision. Hamiltonian can depict the dynamics real time. This scheme can detect weak signal quantitatively in lower signal-noise-ratio. 4、An adaptive hybrid generalized synchronization of two different chaotic system with unknown parameters is proposed. This scheme can achieve synchronization and track of two different chaotic systems. Considering the influence of unknown parameters to the stability of the synchronization manifold, based on adaptive theory, this paper exploits the Lyapunov stability theory to design the control signals and parameters update laws analytically. This scheme can achieve complete synchronization, anti-synchronization, projective synchronization, simultaneously, and it can be extended to more general generalized chaos synchronization. The modeling circumstance is closer to the actual non-cooperative signal analysis. Numerical simulations verify the effectiveness of the proposed scheme.
5、The anticipating chaotic synchronization based parameter estimation of chaotic system is proposed. Considering the communication systems are at difference places, the signal transmit has time delay to each other, the estimation of the unknown parameters of the delay coupled chaotic system from the observed time series is significant. This paper investigates the parameter estimation of time delay coupled chaotic systems. Although the Krasovskii-Lyapunov functional method often results in delay-independent stability condition, time delay closely relates to the parameter estimation. The numerical method is used to study the influence of the parameters of the proposed scheme to unknown parameter estimation scheme. This scheme can estimate the unknown parameter correctly even when the time delay exists, and improve the parameter estimation based on complete synchronization.
1、提出了一种有效区分混沌与噪声的方法。研究了随着嵌入维数的增长,相空间中相点间平均距离的变化趋势。根据混沌与噪声在相空间中的不同特性,从理论上推导出了区别噪声与混沌的方法。该方法可以在短数据和噪声环境中实现快速判决,不仅改善了传统方法需要人为选择多个主观参数,容易出现误判和计算量大等问题,而且在一定程度上改进了基于混沌系统特征量方法对噪声十分敏感和需要大量数据的缺点。
2、研究了基带混沌直扩信号的检测。针对混沌直扩通信中的实值扩谱方式,提出了利用伪邻近点实现信号检测的方法。实值混沌扩谱信号的检测实质上是混沌与噪声的识别问题。在分析信息码对混沌动力学影响的基础上,将基于伪邻近点构造的识别算法应用到基带实值混沌直扩信号检测,不仅克服了传统基于混沌系统特征量对噪声十分敏感和数据量大的缺点,而且能够在一定程度上实现与传统直扩方式的区别。
3、针对量化混沌直扩信号,提出了基于哈密顿量的定量Duffing振子信号检测方法。Duffing振子利用外加微扰信号使得系统动力学特性发生明显改变,而对噪声免疫来实现信号检测,极大地提高了微弱信号检测性能。本文分析了Duffing振子的动力学行为特性、时频特性、噪声免疫特性、状态跃迁阈值及微扰信号相差和频差对动力学行为的影响,分别利用相图的状态跃迁以及时序图的间歇混沌行为实现信号检测。考虑到当前基于Duffing振子微弱信号检测仍停留在定性分析和仿真分析阶段的现状,提出了利用哈密顿量构造统计量进行定量判决的方法。哈密顿量能够实时地表征系统状态的变化情况。该方法可以在低信噪比下实现微弱信号的定量判决。
4、提出了自适应实现具有未知参数和不同结构混沌系统广义混合混沌同步方案。该方案能够实现两个不同结构混沌系统的同步跟踪。考虑到系统未知参数对同步流形稳定性的影响,基于自适应原理,本文利用Lyapunov理论解析地设计了控制信号和参数更新规则。该方法能够同时实现完全同步、镜像同步和投影同步,并可推广到更一般的广义同步。该方法的研究更接近于实际的非合作信号分析环境。数值方法验证了方法的有效性。
5、提出了基于超前混沌同步的参数估计方法。考虑到混沌通信系统处在不同的地理位置,信号传输存在时延的影响,从观测数据中估计延迟耦合系统的未知参数具有重要意义。本文研究了具有时延耦合混沌系统的参数估计。基于Krasovskii-Lyapunov理论的系统稳定性分析可以导出时延独立的稳定性条件,但是时延与参数估计密切相关。本文利用数值方法研究了方案中各参数对估计方法的影响。该方案能够在时间延迟存在的情况下有效估计系统的未知参数,改进了传统基于完全同步的参数估计方法。
Nonlinear science is a basic subject which studies the common characteristics of nonlinear phenomena. Nonlinear method can describe the objective fact more reasonable. Chaos is the most important one in nonlinear science, which has generated a huge influence to modern science and technologies. Chaotic communication is one of the most excellence applications in engineering. This thesis studies the chaos theory and its application in non-cooperative chaos signal detection, chaos synchronization and parameters estimation of chaotic systems. Chaos detection is the precondition of the modeling of chaotic communication signal, which includes chaos identification and the signal detection based on chaos system. Chaos identification can identify the chaotic characters from the observed time series, and the signal detection based on chaotic system exploits a chaotic system to detect weak signal. Chaos synchronization is the powerful guarantee to implement chaotic communication. And just the achievement of the synchronization of two chaotic systems with unidirectional couple in electronic circuit, the chaotic communication becomes possible. The generalized chaos synchronization is one of the main methods to achieve the analysis of the chaotic communication signals based on chaos synchronization. Chaotic parameter modulation is the main way of chaotic communication, which uses the chaotic signal from different parameter set of the chaotic system to hide the transmit information and achieve secure communication. The parameters estimation of chaotic systems is the necessary precondition to information demodulate. The main results of this thesis are:
1、An efficient method of distinguishing chaos from noise is proposed. The changing trend of the average distance between phase points in phase space is studied with the increase of the embedding dimension. According to the different characteristics between chaos and noise in phase space, this thesis deduces a method which can distinguish chaos from noise. This method can do decision quickly even when the data are short and contaminated. This method not only overcomes the shortage of the subjectivity of parametric choice and time consuming of traditional method, but also improves the shortcoming of both the requirement for a large number of data and the noise sensitivity of the invariant of chaotic system to some extent.
2、The detection of baseband chaotic direct sequence spread spectrum signal(CDSSS) is studied. In allusion to the real number chaotic spread spectrum mode in CDSSS communication, this thesis proposes to do detection by false neighbor method. Essentially, the detection of the real number CDSSS signal is the problem of distinguishing chaos from noise. Based on the analysis of the influence of information code to chaotic dynamics, this paper uses the identification algorithm which based on false neighbor to detect the baseband real number CDSSS signal. This method not only overcomes the shortage of both the requirement for a large number of data and the noise sensitivity of the invariant of chaos system, but also can distinguish traditional DSSS signal to some extent.
3、For quantization CDSSS signal, this thesis proposes a quantitative signal detection method by using Duffing oscillator based on Hamiltonian. Duffing oscillator exploits the characteristics that additional perturbation signals make the dynamics of the system change obviously and immune to noise to detect weak signal. This improves the performance of the weak signal detection greatly. According to the analysis of the dynamics characteristic, the time-frequency characteristic, the immune to noise characteristic, the state transition characteristic and the influence of the frequency and phase difference with the perturbation signal of Duffing oscillator, this paper proposes to use state transition of the phase portrait and intermittent chaos of the time series diagram to detect signal respectively. Considering most of the existing weak signal detection methods based on Duffing oscillator are stay on qualitative and simulative analysis also, this paper proposes to use Hamiltonian to construct statistic to do quantitative decision. Hamiltonian can depict the dynamics real time. This scheme can detect weak signal quantitatively in lower signal-noise-ratio. 4、An adaptive hybrid generalized synchronization of two different chaotic system with unknown parameters is proposed. This scheme can achieve synchronization and track of two different chaotic systems. Considering the influence of unknown parameters to the stability of the synchronization manifold, based on adaptive theory, this paper exploits the Lyapunov stability theory to design the control signals and parameters update laws analytically. This scheme can achieve complete synchronization, anti-synchronization, projective synchronization, simultaneously, and it can be extended to more general generalized chaos synchronization. The modeling circumstance is closer to the actual non-cooperative signal analysis. Numerical simulations verify the effectiveness of the proposed scheme.
5、The anticipating chaotic synchronization based parameter estimation of chaotic system is proposed. Considering the communication systems are at difference places, the signal transmit has time delay to each other, the estimation of the unknown parameters of the delay coupled chaotic system from the observed time series is significant. This paper investigates the parameter estimation of time delay coupled chaotic systems. Although the Krasovskii-Lyapunov functional method often results in delay-independent stability condition, time delay closely relates to the parameter estimation. The numerical method is used to study the influence of the parameters of the proposed scheme to unknown parameter estimation scheme. This scheme can estimate the unknown parameter correctly even when the time delay exists, and improve the parameter estimation based on complete synchronization.
引文
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