仿射投影类自适应滤波算法的改进算法研究

发布时间：2018-05-05 08:02

本文选题：自适应滤波算法 + 仿射投影算法　；参考：《重庆邮电大学》2015年硕士论文

【摘要】：自适应滤波器在工程实践中应用广泛，如系统辨识、信道均衡、干扰消除、线性与非线性预测等。常见的自适应滤波算法有最小均方算法(Least Mean Square,LMS)与最小二乘算法(Recursive Least Square, RLS)。LMS算法计算复杂度低，但收敛速度缓慢。RLS与其相反，即收敛速度快，但计算复杂度高。为提高LMS的收敛速度，常用仿射投影算法(Affine Projection Algorithm, APA)替代LMS以提高算法收敛速度。但标准APA算法有两个主要缺点：1.大步长或小正则因子APA算法收敛速度快，但稳态误差高；小步长或大正则因子APA算法稳态误差低，但收敛速度慢。因此，标准APA算法不能满足工程实践对自适应算法应具有高收敛速度与低稳态误差性能的需求。2.当系统遭受冲激噪声干扰时，标准APA算法的跟踪性能衰减严重，即鲁棒性能差。本文从提高APA类型算法的跟踪性能与鲁棒性能两个方面进行研究，具有重要的理论与实践意义。首先，本文简要阐述标准仿射投影算法及其典型的改进算法。其次，针对APA算法跟踪性能差的问题，，本文提出一种变正则因子仿射投影算法(Variable Regularization APA, VR-APA)。区别于传统文献中以尽可能使后验错误为零作为标准来推导变正则因子表达式的方法，本文提出通过最小化无噪后验错误矢量信号能量来推导自适应变正则因子表达式的方法。在实践逼近中，该方法利用测量噪声的统计方差特性，并提出一种更加光滑且更加容易控制的指数缩放因子评估方法。除此之外，文中还讨论了该算法的稳定性能。系统辨识的仿真结果表明新算法比现有方法收敛速度更快且稳态误差更低。最后，针对APA算法在冲激噪声干扰下鲁棒性能差的问题，本文提出通过凸组合技术来提高算法跟踪性能与鲁棒性能的方法。仿真实验结果表明提出算法不仅收敛速度快，稳态误差低，而且在冲激噪声干扰下鲁棒性能好。
[Abstract]:Adaptive filters are widely used in engineering practice, such as system identification, channel equalization, interference cancellation, linear and nonlinear prediction and so on. The common adaptive filtering algorithms are least Mean squared (LMS) and least square algorithm (RLS).LMS), which have low computational complexity, but slow convergence rate. RLS is the opposite, that is, the convergence speed is fast, but the computational complexity is high. In order to improve the convergence rate of LMS, affine Projection algorithm (LMS) is commonly used instead of LMS to improve the convergence speed of the algorithm. But the standard APA algorithm has two main drawbacks: 1. The large step size or small regular factor APA algorithm converges fast, but the steady-state error is high, while the small step size or large regular factor APA algorithm has a low steady state error but a slow convergence rate. Therefore, the standard APA algorithm can not meet the need of engineering practice that adaptive algorithm should have high convergence rate and low steady-state error performance. When the system is disturbed by impulse noise, the tracking performance of the standard APA algorithm attenuates seriously, that is, the robust performance is poor. This paper focuses on improving the tracking performance and robust performance of APA type algorithms, which has important theoretical and practical significance. First, this paper briefly describes the standard affine projection algorithm and its typical improved algorithm. Secondly, aiming at the poor tracking performance of APA algorithm, a variable variable Regularization APA (VR-APA) algorithm is proposed in this paper. Different from the traditional method of deducing variable canonical factor expressions by minimizing the energy of noise free posteriori error vector signals, this paper presents a method to derive adaptive variable regular factor expressions by minimizing the energy of noise free posteriori error vector signals. In practical approximation, this method utilizes the statistical variance characteristics of measurement noise, and proposes a more smooth and easily controlled exponential scaling factor evaluation method. In addition, the stability of the algorithm is discussed. The simulation results of system identification show that the new algorithm converges faster and the steady-state error is lower than the existing methods. Finally, aiming at the problem of poor robustness of APA algorithm under impulse noise interference, this paper proposes a method to improve the tracking performance and robust performance of the algorithm by convex combination technique. The simulation results show that the proposed algorithm not only has the advantages of fast convergence, low steady-state error, but also good robustness under impulse noise interference.
【学位授予单位】：重庆邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713

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