仿射投影p-范数算法的研究

发布时间：2019-06-24 12:16

【摘要】：数字信号处理技术在当代技术的刺激下得到了高速发展。滤波技术作为信号处理技术中的一种被广泛应用在需要进行信号处理的系统中,该技术通过对信号进行处理滤除掉无用信息,从而得到数据信号中的有用信息。滤波器作为典型的数字信号处理系统,其中自适应滤波器就是一种时变滤波器。其中最小均方(Least Mean Square, LMS)算法以其结构简单,不需要计算相关函数,不需要求逆运算等优点得到了广泛的应用。然而当输入信号具有很强的相关性时,LMS算法滤波器就会遇到梯度噪声放大,收敛速度慢的问题。仿射投影算法(Affine Projection Algorithm, APA)可以很好的解决上述问题。AP算法通过重复利用前面的信号,当输入信号具有很强相关性情况下提高算法的收敛速度。同时最小p阶均方算法(Least Mean p-Order Algorithm, LMP)和最小混合范数算法(Least Mean Mixed Norm Algorithm, LMMN)可以在一定程度上减小算法的稳态均方误差。本文中的工作主要包含以下几个方面：1.首先需要学习了解仿射投影算法的的由来,以及AP自适应算法的收敛速度和稳态性能与不同参数之间的关系,并利用Matlab仿真对AP算法和NLMS算法之间的收敛速度进行对比分析。2.在仿射投影算法重复利用前面输入信号的基础上结合L MMN算法和LMP算法对误差信号处理的方法体处理／PMN算法和APP算法,并分别推导出APMN自适应算法和APP自适应算法的权向量更新表达式。同时分别对出APMN自适应算法和APP自适应算法的稳态误差性能进行理论分析,推导出稳态均方误差的表达式。3.最后根据它们的权向量更新表达式和稳态均方误差的表达式,利用Matlab仿真对APMN自适应算法和APP自适应算法的收敛速度以及稳态误差与不同参数之间的关系进行对比分析验证,与相关的自适应算法进行对比,并对理论分析结果进行验证。
[Abstract]:Digital signal processing technology has been developed rapidly under the stimulation of contemporary technology. As a kind of signal processing technology, filtering technology is widely used in the system that needs signal processing. This technology filters out the useless information by processing the signal, so as to obtain the useful information in the data signal. As a typical digital signal processing system, adaptive filter is a time-varying filter. Among them, the least mean square (Least Mean Square, LMS) algorithm has been widely used because of its simple structure, no need to calculate correlation functions, no need to require inverse operation and so on. However, when the input signal has a strong correlation, the LMS algorithm filter will encounter the problem of gradient noise amplification and slow convergence speed. Affine projection algorithm (Affine Projection Algorithm, APA) can solve the above problems very well. AP algorithm improves the convergence speed of the algorithm when the input signal has strong correlation by repeatedly using the previous signal. At the same time, the minimum p-order mean square algorithm (Least Mean p-Order Algorithm, LMP) and the minimum mixed norm algorithm (Least Mean Mixed Norm Algorithm, LMMN) can reduce the steady-state mean square error of the algorithm to a certain extent. The work in this paper mainly includes the following aspects: 1. First of all, we need to learn the origin of affine projection algorithm, and the relationship between convergence speed and steady-state performance of AP adaptive algorithm and different parameters, and use Matlab simulation to compare and analyze the convergence speed between AP algorithm and NLMS algorithm. 2. On the basis of reusing the previous input signal by affine projection algorithm, the volume processing / PMN algorithm and APP algorithm of L MMN algorithm and LMP algorithm for error signal processing are combined, and the weight vector update expressions of APMN adaptive algorithm and APP adaptive algorithm are derived respectively. At the same time, the steady-state error performance of APMN adaptive algorithm and APP adaptive algorithm is analyzed theoretically, and the expression of steady-state mean square error is derived. Finally, according to their weight vector update expression and steady-state mean square error expression, the convergence speed of APMN adaptive algorithm and APP adaptive algorithm and the relationship between steady-state error and different parameters are compared and verified by Matlab simulation, and compared with the related adaptive algorithm, and the theoretical analysis results are verified.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN911.7

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