基于不完整自然梯度的盲分离算法研究

发布时间：2018-08-18 11:50

【摘要】：盲源分离(BSS)是在混合矩阵未知的情况下,从一系列的混合信号中分离和还原不可观测的原信号的过程。BSS是信号处理与通信领域中的基本问题,特别是在语音识别、生物医信号处理、远程传感、雷达与通信系统、地震勘探等方面均具有突出的作用。首先,本文介绍了盲源分离的技术背景和国内外的研究现状,概括了有关盲源分离的基本理论,包括概率论、矩阵、信息论的相关内容以及盲源分离的数学模型等,阐述了盲源分离的一般求解过程；简单介绍了盲源分离算法中的自然梯度算法与不完整的自然梯度算法,分析了算法的不足之处。然后,针对自然梯度算法与不完整自然梯度算法的不足之处,提出了基于符号算子的变步长不完整自然梯度算法,将不完整自然梯度算法与从一般的动态分离模型中推导出的符号算子相结合,并且加入了基于代价函数梯度的变步长。符号算子的引入加快了算法的收敛速度,基于代价函数梯度的变步长平衡了收敛速度与稳态误差之间的矛盾。同时,针对非平稳环境问题,本文提出了一种新的基于不完整自然梯度的约束算法,利用系统上的扰动对代价函数进行约束,为了加快收敛速度,对算法的约束因子采用自适应形式,根据分离情况对约束因子进行自适应调整,很好地解决了收敛速度与稳态误差之间的矛盾。计算机仿真结果证明,相比于传统算法,新算法都可以达到更理想的分离效果。最后,对本文的工作进行了总结,并指出盲源分离仍有一些问题有待进一步研究和解决,包括含噪问题、欠定问题等,理论与应用仍有很大的发展空间。
[Abstract]:Blind source separation (BSS) is a process of separating and restoring unobservable original signals from a series of mixed signals under the condition of unknown mixing matrix. BSS is a basic problem in signal processing and communication, especially in speech recognition. Biomedical signal processing, remote sensing, radar and communication systems, seismic exploration and other aspects have a prominent role. First of all, this paper introduces the technical background of blind source separation and the research status at home and abroad, summarizes the basic theory of blind source separation, including probability theory, matrix, information theory and mathematical model of blind source separation. In this paper, the general solution process of blind source separation is introduced, the natural gradient algorithm and incomplete natural gradient algorithm are introduced, and the shortcomings of the algorithm are analyzed. Then, aiming at the shortcomings of natural gradient algorithm and incomplete natural gradient algorithm, a variable step size incomplete natural gradient algorithm based on symbol operator is proposed. The incomplete natural gradient algorithm is combined with the symbol operator derived from the general dynamic separation model and the variable step size based on the gradient of the cost function is added. The introduction of symbol operator accelerates the convergence speed of the algorithm. The variable step size based on the gradient of cost function balances the contradiction between convergence speed and steady state error. At the same time, a new constraint algorithm based on incomplete natural gradient is proposed to solve the non-stationary environment problem. The cost function is constrained by the disturbance of the system. In order to speed up the convergence rate, this paper proposes a new constraint algorithm based on incomplete natural gradient. The constraint factor of the algorithm is adaptively adjusted according to the separation condition, which solves the contradiction between the convergence speed and the steady-state error. The computer simulation results show that compared with the traditional algorithm, the new algorithm can achieve a better separation effect. Finally, the work of this paper is summarized, and it is pointed out that there are still some problems to be further studied and solved in blind source separation, including noise-containing problems, underdetermined problems, and so on. There is still a lot of room for development in theory and application.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7

【相似文献】