类仿射投影算法的改进研究
发布时间：2019-02-20 21:46
【摘要】：自适应滤波算法在实际应用中越来越普遍。经典的自适应滤波算法,如最小均方(Least Mean Square,LMS)算法和仿射投影算法(Affine Projection Algorithm,APA)虽然在多种自适应过程中都有优秀的表现。但是,当信道为稀疏信道时,这两种自适应算法的收敛速度将会严重下降。成比例类的自适应算法利用了回声路径脉冲响应稀疏的结构特性,广泛应用于回声消除领域。本论文以类仿射投影(AffineProjection Like,APL)算法为核心,针对稀疏系统(声学回声信道系统和网络回声信道系统),通过成比例思想、M估计思想和凸组合思想进行了详细的分析和研究工作。首先,为了解决APL算法针对稀疏系统时收敛速度缓慢的问题,本论文将成比例的思想引入到了 APL算法。根据不同的成比例控制因子计算准则,提出了三种成比例APL算法(标准PAPL算法、IPAPL算法、MPAPL算法)。通过实验仿真验证了这三种算法相对于APL算法在应对稀疏系统时在收敛速度上的优越性。其次,为了使算法具备抗冲激能力,本论文将M估计的思想引入成比例APL算法,提出了基于M估计的成比例类仿射投影算法(标准PAPLM算法、IPAPLM算法、MPAPLM算法)。通过实验仿真验证了提出的算法在冲激噪声环境下依然能够保持良好的性能。最后,为了解决固定步长算法无法兼顾收敛速度和稳态误差的问题,本论文将凸组合的思想引入M估计的成比例类仿射投影算法,通过权值转移策略对凸组合思想进行改良,以IPAPLM算法为例,提出了权向量转移策略的凸组合M估计成比例类仿射投影(CIPAPLMWT)算法。通过实验仿真验证了提出的算法既能具备较快的收敛速度,又能得到较低的稳态误差。
[Abstract]:Adaptive filtering algorithm is becoming more and more popular in practical applications. Classical adaptive filtering algorithms, such as the least mean square (Least Mean Square,LMS) algorithm and the affine projection algorithm (Affine Projection Algorithm,APA), have excellent performance in many adaptive processes. However, when the channel is sparse, the convergence speed of the two adaptive algorithms will decrease seriously. The proportional adaptive algorithm takes advantage of the sparse structure of echo path impulse response and is widely used in the field of echo cancellation. In this paper, the affine projection (AffineProjection Like,APL) algorithm is taken as the core. For sparse systems (acoustic echo channel system and network echo channel system), the proportional thought is adopted. M estimation and convex combination are analyzed and studied in detail. Firstly, in order to solve the problem of slow convergence rate of APL algorithm for sparse systems, this paper introduces the idea of proportionality to APL algorithm. Three proportional APL algorithms (standard PAPL algorithm, IPAPL algorithm, MPAPL algorithm) are proposed according to different criteria for calculating proportional control factors. The superiority of the three algorithms in the convergence speed of the sparse system is verified by the simulation results compared with the APL algorithm. Secondly, in order to make the algorithm have the ability of shock resistance, this paper introduces the idea of M estimation into proportional APL algorithm, and proposes a proportional class affine projection algorithm based on M estimation (standard PAPLM algorithm, IPAPLM algorithm, MPAPLM algorithm). The experimental results show that the proposed algorithm can maintain good performance in impulse noise environment. Finally, in order to solve the problem that the fixed step size algorithm can not take into account the convergence rate and steady state error, this paper introduces the idea of convex combination into the proportional affine projection algorithm of M estimation, and improves the convex combination idea by weight transfer strategy. Taking the IPAPLM algorithm as an example, a weighted vector transfer strategy based on convex combination M estimator is proposed, which is proportional class affine projection (CIPAPLMWT) algorithm. The experimental results show that the proposed algorithm not only has a fast convergence rate, but also can get a lower steady state error.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7
本文编号：2427316
[Abstract]:Adaptive filtering algorithm is becoming more and more popular in practical applications. Classical adaptive filtering algorithms, such as the least mean square (Least Mean Square,LMS) algorithm and the affine projection algorithm (Affine Projection Algorithm,APA), have excellent performance in many adaptive processes. However, when the channel is sparse, the convergence speed of the two adaptive algorithms will decrease seriously. The proportional adaptive algorithm takes advantage of the sparse structure of echo path impulse response and is widely used in the field of echo cancellation. In this paper, the affine projection (AffineProjection Like,APL) algorithm is taken as the core. For sparse systems (acoustic echo channel system and network echo channel system), the proportional thought is adopted. M estimation and convex combination are analyzed and studied in detail. Firstly, in order to solve the problem of slow convergence rate of APL algorithm for sparse systems, this paper introduces the idea of proportionality to APL algorithm. Three proportional APL algorithms (standard PAPL algorithm, IPAPL algorithm, MPAPL algorithm) are proposed according to different criteria for calculating proportional control factors. The superiority of the three algorithms in the convergence speed of the sparse system is verified by the simulation results compared with the APL algorithm. Secondly, in order to make the algorithm have the ability of shock resistance, this paper introduces the idea of M estimation into proportional APL algorithm, and proposes a proportional class affine projection algorithm based on M estimation (standard PAPLM algorithm, IPAPLM algorithm, MPAPLM algorithm). The experimental results show that the proposed algorithm can maintain good performance in impulse noise environment. Finally, in order to solve the problem that the fixed step size algorithm can not take into account the convergence rate and steady state error, this paper introduces the idea of convex combination into the proportional affine projection algorithm of M estimation, and improves the convex combination idea by weight transfer strategy. Taking the IPAPLM algorithm as an example, a weighted vector transfer strategy based on convex combination M estimator is proposed, which is proportional class affine projection (CIPAPLMWT) algorithm. The experimental results show that the proposed algorithm not only has a fast convergence rate, but also can get a lower steady state error.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7
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