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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.
Adaptive Coherent Cumulative Algorithm (ACI) is a newest improved algorithm of LMS algorithm. It has the advantages of accelerating the convergence rate of multi-layer neural network and improving the detection and tracking ability of ALE for the signal with weak input signal-to-noise ratio The joint probability density function of weight vector of ACI algorithm under Gaussian data is studied in this paper. In this paper, the conditional expectation method is used to obtain the exact expression of the joint eigenfunctions of the weight coefficient vector at n + 1, taking the weight coefficient vector at n and n-1 as the condition. Then, the conditional eigenfunctions are expanded into Taylor series and averaged with the unknown probability density function of weight coefficients, and the first-order partial differential equation satisfied by the unconditional weight coefficient eigenfunction is obtained. Under small step conditions, The results show that the vector of ACI weight coefficients obeys the joint Gaussian distribution, the first and second moment are consistent with the existing research results, and the computer simulation results confirm the correctness of the theoretical analysis.