混沌信号的非线性自适应预测技术及其应用研究
摘要
本文主要围绕混沌信号的实时或准实时预测技术及其在混沌控制与同步、捷变频雷
达频率预测中的应用问题展开研究，主要研究内容包括：（1）、混沌信号的神经网络建模
预测及其应用研究；（2）、提出混沌信号的非线性自适应预测新方法，研究了混沌信号的
非线性自适应预测性能；（3）、提出了多种非线性自适应滤波（预测）器及其非线性NLMS
自适应算法；（4）、提出并研究了混沌系统的非线性自适应预测控制与同步新方法；（5）、
捷变频雷达频率序列预测的新方法研究。
本文的主要创新之处包括：
1、混沌信号的神经网络建模预测及其应用研究
（1）针对BP算法训练的神经网络预测器对（含噪）混沌信号建模预测存在的一致性
较差的问题，利用一种快速进化算法训练前馈神经网络预测器，从而实现了含噪混沌信
号和混沌吸引子的一致预测。而一步预测性能良好的BP网络预测器所重构的吸引子不
具有一致性正好说明：混沌时间序列预测模型的动力学不一定非要具备与原动力系统相
同的吸引子结构，即不必去追求模型的等价性。这一结果为我们构造其它预测模型提供
了依据。
（2）针对混沌序列多步预测的难题，用RLS算法和一种简化的RNN研究了混沌信
号的多步预测问题，研究结果证实了这种简化的RNN比前馈神经网络具有更好的多步预
测性能。
（3）针对单一混沌映射或系统产生混沌信号的局限性，利用神经网络权值更新的灵
活性，提出了混沌信号源的神经网络设计预测同步方法，能在统一的系统结构下产生多
种混沌信号。
（4）针对单一混沌映射或系统设计的混沌保密通信容易被预测破译的问题，提出了
一种基于混沌映射切换的参数调制保密通信方案，并用神经网络设计的混沌信号源和构
造的一种广义混沌映射进行了研究，在信噪比（SNR）＞10dB时，能较好地恢复信号。若辅
以非均匀跳时切换策略，保密性能更好。
2、针对混沌相空间预测技术难以满足工程应用的问题，提出了混沌信号的非线性
自适应预测这一新技术和新方法
（1）混沌信号的非线性自适应预测技术是根据当前预测误差，采用自适应技术在线
实时调整预测滤波器的参数来跟踪混沌运动的当前轨迹，能够满足实时或准实时预测应
用的要求。与全局建模预测相比，要求的训练样本少、训练时间短，且具有更好的预测
性能和易于工程实现等优点。
（2）采用非线性自适应预测技术预测混沌信号时，非线性自适应预测滤波器的输入
维数（相当于线性滤波器的阶数）不受Takens嵌入定理的约束，能在欠嵌入条件下实现有
效预测。
（3）首次研究了超混沌、时空混沌信号的非线性自适应预测问题，它们的非线性自
适应预测性能主要取决于预测器的非线性表达能力和自适应算法的选择，与其它因素无
关；
3、针对Volterra滤波器实现的复杂性，提出并研究了多种非线性自适应滤波器及其
非线性自适应算法，并用它们研究了混饨信号的非线性自适应预测性能，主要创新成果
包括
（l）首先用二阶VOiterY’a滤波器（SOVF）研究了混油信号非线性自适应预测性能，在
此基础上，提出并研究了SOW的四种线性FIR ＃波器乘积耦合型近似实现结构，通过
仿真研究找到了它们稳定收敛的非线性NLMS算法中辅助收敛参数之间的选择关系。
（二）提出并研究了一大类基于非线性有界函数约束变换的新型线性PIR ＃波器乘积
耦合非线性自适应（预测）滤波器，给出了非线性有界变换函数应满足的条件，较为系统地
研究其中三类非线性变换器构造成的这种非线性预测器、两种非线性自适应算法对混饨
信号的非线性自适应预测性能。
（3）基于混饨信号高阶累积量分析结果，提出了一种高阶非线性自适应预测滤波
器，较为系统地研究了这种预测滤波器的不同实现结构和算法对含噪混饨信号、超馄饨
信号和时空混饨信号的非线性自适应预测性能。
4、针对现有馄饨控制与同步方法要求精确己知系统的数学模型，而很多工程混饨难
以建立精确的系统模型和比较容易获得系统状态的观察序列特点，提出了混饨系统的非
线性自适应预测控制与同步新概念和新方法，并用本文提出的两种非线性自适应预测滤
波器进行了研究，主耍成果包括：
＊）只用被控系统状态的观察时间序列，通过在线实时非线性预测技术能够将确定
性混饨系统、不确定性混饨系统、耦合超混饨系统控制到任意外加目标上；
（2）只用被控系统状态的观察时间序列，通过在线实时非线性预测技术能够将存在
模型失配（包括模型完全不同）的混饨系统进行同步。
5、目前，捷变频雷达的频率序列尚无有效的预测方法。根据捷变频码构造的确定性
和非线性机制，分别研究了具有混饨特征和非混饨的捷变频雷达频率序列的预测技术。
主要研究成果为：
＊）具有混饨特征的捷变频雷达频率序列，采用非线性自适应预测技术比采用建模
预测技术进行预测更有效；
（）优化估计非混炖的乘同余模型参数为预测乘同余捷变频频率序列提供了某种
可能性。
The real time or quasi-real time predictions of chaotic signals, nonlinear adaptive filtering
technologies and their applications are studied in this paper. Main contents studied include: (1)
Study on neural networks modeling of (noisy) chaotic time series and their applications; (2)
Nonlinear adaptive predictions of chaotic signals, and the nonlinear adaptive prediction
performance of chaotic signals; (3) Some new nonlinear adaptive (predictive) filters and
nonlinear NLMS algorithms; (4) Nonlinear adaptive predicting control and synchronization
methods of chaotic systems; (5) Study on new prediction methods for frequency series
prediction of frequency agile radar.
Several valuable and important results which bring forth new ideas are achieved and listed
as following:
1. Neural networks modeling and prediction of (noisy) chaotic time series:
(1) To account for performing inconsistently for reconstructing strange attractor by
MLP BP-trained, a fast evolutionary programming (FEP) is proposed to train MLP for noisy
chaotic time series modeling and predictions. Simulation results show that the FEP can help
MLP better capture dynamics from noisy chaotic time series than the BP algorithm and
produce more consistently modeling and attractor predictions.
(2) RLS algorithm and the simplified RNN are proposed to make the multi-step
prediction for chaotic signals based on few data, numerical results show that the proposed R.NN
is a very powerful tool for making multi-step prediction for chaotic signals.
(3) A neural network based method is proposed to design chaotic signal generator that
can be synchronized by the nonlinear feedback methods. This chaos generator can produce
many kinds of chaotic signals by means of switching different synapse weights of neural
networks.
(4) A new chaotic secure communication scheme is proposed based on parameter
modulation and chaotic-map-switching, the neural network chaos generators and an extended
chaotic map 醝e used to implement this secure scheme. Simulation results show that this secure
communication scheme can better recover information signals while SNR> 10 dB, and has
better security than that based on single chaotic map or system.
2. Nonlinear adaptive prediction of chaotic signals, which is a new concept that is clearly
different from the chaotic prediction theory based on phase space, is proposed.
(1) Nonlinear adaptive prediction scheme can make real-time or quasi-real-time
prediction of chaotic time series and meet the engineering demands with adaptively updating
nonlinear predictor抯 coefficients. The adaptive algorithms enable the predictor to track current
chaotic trajectory by using current predictive error for adjusting filter parameters rather than
approximating global or local map of chaotic series. Nonlinear adaptive prediction technologies
demand less datum and shorter time to train predictors than global prediction methods, and are
of better prediction performance.
(2) The input dimension of nonlinear adaptive predictor is not limited by die Takens?
embedding dimension. The proposed nonlinear adaptive prediction methods can effectively
predict chaotic signals under ill-embedding condition.
(3) Nonlinear adaptive predictions of hyper-chaotic and spatio-temporal time series
are studied first time. The nonlinear adaptive prediction performance of hyper-chaotic and
spatio-temporal time series is only determined by the nonlinear approximation of predictors
and its adaptive algorithm. Due to diversity of chaotic c
达频率预测中的应用问题展开研究，主要研究内容包括：（1）、混沌信号的神经网络建模
预测及其应用研究；（2）、提出混沌信号的非线性自适应预测新方法，研究了混沌信号的
非线性自适应预测性能；（3）、提出了多种非线性自适应滤波（预测）器及其非线性NLMS
自适应算法；（4）、提出并研究了混沌系统的非线性自适应预测控制与同步新方法；（5）、
捷变频雷达频率序列预测的新方法研究。
本文的主要创新之处包括：
1、混沌信号的神经网络建模预测及其应用研究
（1）针对BP算法训练的神经网络预测器对（含噪）混沌信号建模预测存在的一致性
较差的问题，利用一种快速进化算法训练前馈神经网络预测器，从而实现了含噪混沌信
号和混沌吸引子的一致预测。而一步预测性能良好的BP网络预测器所重构的吸引子不
具有一致性正好说明：混沌时间序列预测模型的动力学不一定非要具备与原动力系统相
同的吸引子结构，即不必去追求模型的等价性。这一结果为我们构造其它预测模型提供
了依据。
（2）针对混沌序列多步预测的难题，用RLS算法和一种简化的RNN研究了混沌信
号的多步预测问题，研究结果证实了这种简化的RNN比前馈神经网络具有更好的多步预
测性能。
（3）针对单一混沌映射或系统产生混沌信号的局限性，利用神经网络权值更新的灵
活性，提出了混沌信号源的神经网络设计预测同步方法，能在统一的系统结构下产生多
种混沌信号。
（4）针对单一混沌映射或系统设计的混沌保密通信容易被预测破译的问题，提出了
一种基于混沌映射切换的参数调制保密通信方案，并用神经网络设计的混沌信号源和构
造的一种广义混沌映射进行了研究，在信噪比（SNR）＞10dB时，能较好地恢复信号。若辅
以非均匀跳时切换策略，保密性能更好。
2、针对混沌相空间预测技术难以满足工程应用的问题，提出了混沌信号的非线性
自适应预测这一新技术和新方法
（1）混沌信号的非线性自适应预测技术是根据当前预测误差，采用自适应技术在线
实时调整预测滤波器的参数来跟踪混沌运动的当前轨迹，能够满足实时或准实时预测应
用的要求。与全局建模预测相比，要求的训练样本少、训练时间短，且具有更好的预测
性能和易于工程实现等优点。
（2）采用非线性自适应预测技术预测混沌信号时，非线性自适应预测滤波器的输入
维数（相当于线性滤波器的阶数）不受Takens嵌入定理的约束，能在欠嵌入条件下实现有
效预测。
（3）首次研究了超混沌、时空混沌信号的非线性自适应预测问题，它们的非线性自
适应预测性能主要取决于预测器的非线性表达能力和自适应算法的选择，与其它因素无
关；
3、针对Volterra滤波器实现的复杂性，提出并研究了多种非线性自适应滤波器及其
非线性自适应算法，并用它们研究了混饨信号的非线性自适应预测性能，主要创新成果
包括
（l）首先用二阶VOiterY’a滤波器（SOVF）研究了混油信号非线性自适应预测性能，在
此基础上，提出并研究了SOW的四种线性FIR ＃波器乘积耦合型近似实现结构，通过
仿真研究找到了它们稳定收敛的非线性NLMS算法中辅助收敛参数之间的选择关系。
（二）提出并研究了一大类基于非线性有界函数约束变换的新型线性PIR ＃波器乘积
耦合非线性自适应（预测）滤波器，给出了非线性有界变换函数应满足的条件，较为系统地
研究其中三类非线性变换器构造成的这种非线性预测器、两种非线性自适应算法对混饨
信号的非线性自适应预测性能。
（3）基于混饨信号高阶累积量分析结果，提出了一种高阶非线性自适应预测滤波
器，较为系统地研究了这种预测滤波器的不同实现结构和算法对含噪混饨信号、超馄饨
信号和时空混饨信号的非线性自适应预测性能。
4、针对现有馄饨控制与同步方法要求精确己知系统的数学模型，而很多工程混饨难
以建立精确的系统模型和比较容易获得系统状态的观察序列特点，提出了混饨系统的非
线性自适应预测控制与同步新概念和新方法，并用本文提出的两种非线性自适应预测滤
波器进行了研究，主耍成果包括：
＊）只用被控系统状态的观察时间序列，通过在线实时非线性预测技术能够将确定
性混饨系统、不确定性混饨系统、耦合超混饨系统控制到任意外加目标上；
（2）只用被控系统状态的观察时间序列，通过在线实时非线性预测技术能够将存在
模型失配（包括模型完全不同）的混饨系统进行同步。
5、目前，捷变频雷达的频率序列尚无有效的预测方法。根据捷变频码构造的确定性
和非线性机制，分别研究了具有混饨特征和非混饨的捷变频雷达频率序列的预测技术。
主要研究成果为：
＊）具有混饨特征的捷变频雷达频率序列，采用非线性自适应预测技术比采用建模
预测技术进行预测更有效；
（）优化估计非混炖的乘同余模型参数为预测乘同余捷变频频率序列提供了某种
可能性。
The real time or quasi-real time predictions of chaotic signals, nonlinear adaptive filtering
technologies and their applications are studied in this paper. Main contents studied include: (1)
Study on neural networks modeling of (noisy) chaotic time series and their applications; (2)
Nonlinear adaptive predictions of chaotic signals, and the nonlinear adaptive prediction
performance of chaotic signals; (3) Some new nonlinear adaptive (predictive) filters and
nonlinear NLMS algorithms; (4) Nonlinear adaptive predicting control and synchronization
methods of chaotic systems; (5) Study on new prediction methods for frequency series
prediction of frequency agile radar.
Several valuable and important results which bring forth new ideas are achieved and listed
as following:
1. Neural networks modeling and prediction of (noisy) chaotic time series:
(1) To account for performing inconsistently for reconstructing strange attractor by
MLP BP-trained, a fast evolutionary programming (FEP) is proposed to train MLP for noisy
chaotic time series modeling and predictions. Simulation results show that the FEP can help
MLP better capture dynamics from noisy chaotic time series than the BP algorithm and
produce more consistently modeling and attractor predictions.
(2) RLS algorithm and the simplified RNN are proposed to make the multi-step
prediction for chaotic signals based on few data, numerical results show that the proposed R.NN
is a very powerful tool for making multi-step prediction for chaotic signals.
(3) A neural network based method is proposed to design chaotic signal generator that
can be synchronized by the nonlinear feedback methods. This chaos generator can produce
many kinds of chaotic signals by means of switching different synapse weights of neural
networks.
(4) A new chaotic secure communication scheme is proposed based on parameter
modulation and chaotic-map-switching, the neural network chaos generators and an extended
chaotic map 醝e used to implement this secure scheme. Simulation results show that this secure
communication scheme can better recover information signals while SNR> 10 dB, and has
better security than that based on single chaotic map or system.
2. Nonlinear adaptive prediction of chaotic signals, which is a new concept that is clearly
different from the chaotic prediction theory based on phase space, is proposed.
(1) Nonlinear adaptive prediction scheme can make real-time or quasi-real-time
prediction of chaotic time series and meet the engineering demands with adaptively updating
nonlinear predictor抯 coefficients. The adaptive algorithms enable the predictor to track current
chaotic trajectory by using current predictive error for adjusting filter parameters rather than
approximating global or local map of chaotic series. Nonlinear adaptive prediction technologies
demand less datum and shorter time to train predictors than global prediction methods, and are
of better prediction performance.
(2) The input dimension of nonlinear adaptive predictor is not limited by die Takens?
embedding dimension. The proposed nonlinear adaptive prediction methods can effectively
predict chaotic signals under ill-embedding condition.
(3) Nonlinear adaptive predictions of hyper-chaotic and spatio-temporal time series
are studied first time. The nonlinear adaptive prediction performance of hyper-chaotic and
spatio-temporal time series is only determined by the nonlinear approximation of predictors
and its adaptive algorithm. Due to diversity of chaotic c
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