基于非负性约束的自适应算法研究

发布时间：2018-03-01 05:18

本文关键词： 自适应非负性约束系统识别最小四次均方性能分析　出处：《苏州大学》2015年硕士论文　论文类型：学位论文

【摘要】：自适应滤波技术在回声消除、信道均衡、系统辨识、信号增强、自适应波束形成、噪声消除以及主动噪声控等领域具有广泛的应用。在一些应用中,由于受到系统内在的物理特性的限制,在进行系统辨识时,需要对待估计的未知系统系数的最优值添加非负性约束条件。非负性约束条件下的最优化问题在理论和工程实践中经常涉及,是目前的研究热点之一,例如非负最小二乘、非负矩阵分解等理论及其在天体物理图像去模糊、计量化学光谱发散反卷积、高光谱图像分析等问题中的应用。传统的最小二乘法需要进行批处理,因此不适合用来在线处理非负性约束条件下的系统辨识问题。为了解决非负约束下的系统识别问题,Chen等人基于定点迭代策略和随机梯度法,提出了非负最小均方算法(NNLMS),并分析了该算法的权值和二阶矩性能。由于非负最小均方算法是迭代进行系统辨识的,因而该算法适用于实时系统识别问题。尽管NNLMS算法实现简单且其计算复杂度较低,但当系统干扰不是高斯白噪声时,如余弦噪声、均与分布噪声以及二值分布噪声,其收敛速度较慢。本文首先以估计误差四次方的期望值作为代价函数,然后基于定点迭代策略推导出了非负最小四阶矩算法。实验结果表明,当系统干扰是大功率的余弦噪声、均匀分布噪声或二值分布噪声时,它比非负最小均方算法具有更优的性能。其次本文还分析了该自适应算法的权值性能以及均方误差性能。最后,本文还提出了一种非负最小对数绝对误差(NNLLAD)算法。实验结果表明,在系统输出端叠加干扰是脉冲噪声时,该算法比已有的符号非负最小均方算法具有更优的性能。
[Abstract]:Adaptive filtering is widely used in the fields of echo cancellation, channel equalization, system identification, signal enhancement, adaptive beamforming, noise cancellation and active noise control. Because of the limitation of the inherent physical characteristics of the system, in the identification of the system, The problem of optimization under nonnegative constraints is often involved in theory and engineering practice, and it is one of the research hotspots at present, such as non-negative least squares. The theory of nonnegative matrix factorization and its application in astrophysical image deblurring, stoichiometric spectrum divergence deconvolution, hyperspectral image analysis, etc. In order to solve the problem of system identification under non-negative constraints, Chen et al based on fixed point iterative strategy and stochastic gradient method. A non-negative least mean square algorithm (NNLMS) is proposed, and its weight and second-order moment performance are analyzed. Since the non-negative least mean square algorithm is iterated to identify the system, Although the NNLMS algorithm is simple to implement and its computational complexity is low, when the system interference is not Gao Si white noise, such as cosine noise, both distributed noise and binary distributed noise. The convergence rate is slow. First, the expected value of the fourth power of the estimation error is taken as the cost function, then the non-negative minimum fourth order moment algorithm is derived based on the fixed-point iterative strategy. The experimental results show that the system interference is a high-power cosine noise. In the case of uniformly distributed noise or binary distributed noise, it has better performance than the non-negative least mean square algorithm. Secondly, the weight performance and mean square error performance of the adaptive algorithm are analyzed. In this paper, a non-negative minimum logarithmic absolute error (NNLLAD) algorithm is also proposed. The experimental results show that the proposed algorithm has better performance than the existing signed nonnegative least mean square algorithm when the superimposed interference at the output end of the system is impulsive noise.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713

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