自适应相干累积算法权系数向量的概率密度函数

On the probability Density Function of the Weight Vectors of Adaptive Coherent Integrated (ACI)Algorithm

自适应相干累积算法(ACI)是LMS算法的一种最新的改进算法,它在加速多层神经网络的收敛速度、提高ALE对弱输入信噪比条件下信号的检测和跟踪能力方面具有很好的应用前景.本文研究了高斯数据条件下ACI算法权系数向量的联合概率密度函数。文中采用求条件数学期望的方法,以n和n-1时刻的权系数向量为条件,导出了n+1时刻权系数向量的联合特征函数的精确表达式。然后将条件特征函数展开为泰勒级数,用未知的权系数概率密度函数求平均,得到了无条件的权系数特征函数所满足的一阶偏微分差分方程.在小步长条件下,求出了方程的稳态近似解.结果表明,ACI权系数向量服从联合高斯分布,其一阶和二阶矩与已有的研究结果相一致,计算机仿真结果证实了理论分析的正确性.

One of the most recent modification on LMS algorithm has been proposed for improving opera-tion. The resulting algorithm is known as Adaptive Coherent Integrated (ACI) algorithm . In this paper, thejoint probability density function of the weight vector in ACI adaptation s studied for Gaussian data models. Theexact conditional characteristic functon at any time and its approximated solution in steady-state are derived. Itis shown that the weghts are jointly Gaussian with the mean and covariance matrix given in . Some simulationresults are also given and they find good match with the theoritical results.