零极值目标函数系统辨识算法

A System Identification Algorithm by Minimizing the Zero-Minimum Target Function

该文提出一种零极值目标函数最小化系统辨识算法。目标函数为系统均方误差与系统噪声方差之差的平方,其极小值为零。在系统辨识过程中采用滑动平均法在线估计系统均方误差、输入自相关矩阵以及输入与期望响应的互相关向量。推导出自适应滤波器权值向量的更新表达式。算法的步长能够根据统计量自适应地调整,使得在得到较小稳态误差的同时提高算法收敛速度。分析了算法的稳定性,得到了算法收敛的条件。对比实验结果表明,该算法具有更快的收敛速度,更小的稳态误差以及更好的稳定性。

A system identification algorithm which is based on minimizing the zero-minimum target function is proposed. The target function presented in this paper is the square of the difference between the mean square error and the variance of the noise. And the minimum of the target function is zero. During the system identification process, the system mean square error, the correlation matrix of the tap inputs and the cross-correlation vector between the tap inputs of the adaptive filter and the desired response are estimated online by employing moving average method. Then, a recursive relation for updating the tap-weight vector is derived. The step size of the algorithm presented here could be adjusted adaptively according to the value of the statistics obtained online, which makes the algorithm be capable of accelerating the speed of convergence without sacrificing the steady state error. Further, the analysis of stability of the algorithm is provided, and then the convergent condition is obtained. The experimental results of the system identification setting demonstrate that the algorithm proposed here has faster convergence and smaller steady state error comparing with the algorithms mentioned in other literatures. It＇s also shown that the algorithm has better stability.