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基于零空间追踪的信号自适应分解及其应用
Alternative TitleAdaptive Signal Separation and its Applications based on Null Space Pursuit
衣晓蕾
Subtype工学博士
Thesis Advisor彭思龙
2015-05-29
Degree Grantor中国科学院大学
Place of Conferral中国科学院自动化研究所
Degree Discipline模式识别与智能系统
Keyword自适应分解 局部正交 模式混叠 稀疏约束 四阶龙格-库塔法 Adaptive Signal Separation Locally Orthogonal Mode Mixing Sparsity Constraint Four Order Runge-kutta Method
Abstract信号的自适应分解理论是当前数字信号处理领域中的研究热点与难点。这类分解算法通常把复杂的输入信号建模为一些基本信号之和的形式。而这些基本信号往往具有简单的或已知的性质,通过分析这些基本信号以及它们之间的相互关系来获得原始输入信号的特性。在目前的自适应信号分解算法中,我们重点关注了基于算子的自适应信号分解算法。 基于算子的信号自适应分解算法,及它的改进算法:零空间追踪算法是一类非常新颖的信号分解和分析的工具。它将信号分解建模为一个优化问题,并利用所定义的参数化算子将输入信号分解为多个子信号之和。基于算子的分解方法的优点在于我们可以根据不同的信号模型来定义不同类型的算子,并且算子的参数以及优化问题中的拉格朗日乘子等都可以自适应的估计出来。虽然这类算法具有坚实的数学基础和较强的自适应性,但仍存在一些理论和方法方面的问题亟待完善。本论文对基于算子的自适应信号分解方法和零空间追踪算法进行了重点研究,得到了一些有意义的结果。 本文的创新成果主要有以下三点: (1)放松零空间追踪算法信号模型中信号成分完全正交的条件,建立局部正交信号模型。利用Gabor变换,给出局部正交的约束,并采用反向投影策略,提出了一种新的局部零空间追踪算法,即基于算子和局部正交约束的自适应信号分解算法。我们提出的算法改善了原始零空间追踪算法中要求信号成分全局正交的条件限制,扩大了零空间追踪算法适用的信号模型的范围,并有效地解决了零空间追踪算法分解过程中产生的模式混叠问题。 (2)针对零空间追踪算法中l2范数对信号的奇异点敏感的特点,依据分段光滑信号或稀疏信号的特点,采用稀疏性约束,即将l2范数替换为l1范数,提出了基于算子和稀疏性约束的信号自适应分解算法。 该算法成功实现了将脉冲信号与局部窄带信号分离,分段光滑信号与局部窄带信号分离,推广了零空间追踪算法适用的信号模型的范围。 并且,我们通过定义一种新的微分算子,将该算法应用于两类典型的Rossler混沌系统中,成功实现了混沌信号的分离和混沌系统的参数估计。 (3)针对零空间追踪算法求解过程中需要对大矩阵进行求逆操作导致计算复杂度很高的特点,并依据算法采用微分算子的特性,将微分方程求解与零空间追踪算法整合,利用经典四阶龙格-库塔方法, 提出一种新的逐点计算的信号自适应分解方法。该算法克服了零空间追踪算法对输入信号长度要求的限制,并且去掉了龙格-库塔法在求解微分方程时对初值条件的要求。我们依据四阶龙格-库塔公式可以求解非线性微分方程的特点,可成功将零空间追踪算法推广到非线性信号模型的应用中。并且通过一些仿真信号和真实信号的分解实验,将提出的算法的实验结果与其它分解算法的实验结果进行分析、比较,对我们所提出的算法进行了性能分析和评价。实验表明,我们提出的算法具有更好的鲁棒性和准确性。
Other AbstractAdaptive signal separation is the research focus and difficulty in the current field of signal processing. Such methods are usually proposed to separate a complex signal into a mixture of several additive coherent subcomponents, and These subcomponents tend to have simple or known properties. We obtain properties of the original input signal by analyzing these subcomponents and their relationship. Among the adaptive approaches, we focus on an operator-based approach to adaptive signal separation. The operator-based signal separation approach and null space pursuit algorithm are very innovative tools for signal decomposition and analysis. They can be formulated as an optimization problem, and use an adaptive operator to separate a signal into additive subcomponents. The charming features of using the approach to solve the signal separation problem are that the design of the operator can be customized to the target signal and the parameters can be adaptively estimated. Although this kind of algorithms has a solid mathematical foundation and strong adaptability, there are still some problems to be improved in theory and method. In this thesis, we focus on the operator-based signal separation approach and null space pursuit algorithm, and obtain some meaningful results. There are three main innovations of this paper: We build the locally orthogonal signal model by relaxing the completely orthogonal assumption in the null space pursuit algorithm. We propose an approach to adaptive signal separation based on operator and locally orthogonal constraint by using the Gabor transform and a back projection strategy. The proposed algorithm can expand the range of the signal model and effectively resolve the mode mixing problem. Since l2-norm is very sensitive to singular points of a piecewise smooth signal, we adopt l1-norm constraint instead of l2-norm constraint in null space pursuit algorithm, and propose an operator-based and sparsity-based approach to adaptive signal separation. The proposed algorithm can successfully separate a sparse signal and local narrow band signals, or a piecewise smooth signal and local narrow band signals. Moreover, we define a new differential operator and apply the proposed algorithm to two typical Rossler chaotic systems. We have achieved the separation of chaotic signals and parameters estimation of the chaotic system. Because large matrix inverse operation leads to high computational complexity in the null space pursuit alg...
Other Identifier200918014628064
Language中文
Document Type学位论文
Identifierhttp://ir.ia.ac.cn/handle/173211/6729
Collection毕业生_博士学位论文
Recommended Citation
GB/T 7714
衣晓蕾. 基于零空间追踪的信号自适应分解及其应用[D]. 中国科学院自动化研究所. 中国科学院大学,2015.
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