q -affine Projection Algorithm and Its Steady-state Mean Square Convergence Analysis
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摘要: q梯度是基于q微分的广义梯度。为了进一步提高仿射投影算法(APA)的滤波性能,该文基于最小均方误差准则将q梯度应用于APA进而产生一种新的q-APA,在高斯噪声环境下选择合适的q值可以取得理想的滤波性能。通过理论分析,提出了保证算法收敛的充分条件,并计算出表征滤波性能的稳态额外均方误差(EMSE)。除此之外,为了进一步提高算法的滤波性能,提出一个变q的APA(V-q-APA)。在高斯噪声环境下,将q-APA和V-q-APA应用于系统辨识中。仿真结果表明:与传统的APA和变q的最小化均方(V-q-LMS)算法相比,q-APA和V-q-APA均具有更好的滤波性能。Abstract: The q-gradient is a generalized gradient based on the q-derivative concept. To improve the filtering performance of the Affine Projection Algorithm (APA), the q-gradient is applied to APA based on the minimum of the recent mean square errors, generating a novel q-Affine Projection Algorithm (q-APA). The q-APA with appropriate setting of q achieves desirable filtering performance in the presence of Gaussian noises. A sufficient condition for guaranteeing convergence of the proposed q-APA is also presented, and its steady-state Excess Mean Square Error (EMSE) of q-APA is obtained theoretically to evaluate the filtering performance. In addition, the Variable q-APA (V-q-APA) is developed to improve further the filtering performance. Simulations in the context of system identification demonstrate the superior filtering performance of the proposed algorithms compared with APA and Variable q-Least Mean Square (V-q-LMS) algorithm in the presence of Gaussian noise.
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表 1 基于100次蒙特卡罗仿真的各个算法的性能比较
算法 MSE 时间(s) APA 0.0835 10.0802 q-APA (q=10) 0.0951 10.9385 q-APA (q=0.01) 0.0819 10.9385 V-q-LMS 0.0825 15.0982 V-q-APA 0.0820 15.8802 RLS 0.0818 12.0637 -
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