非高斯信号的非因果非最小相位ARMA模型辨识

On Identification of Non-Minimum Phase ARMA of Non-Gaussian Process

提出了一种新的ＡＲＭＡ模型参数辨识方法，该方法以受噪声污染的系统输出信号的三阶矩和双谱作为工具，通过求解一系列线性方程组，分别估计出ＡＲＭＡ模型的ＭＡ部分和ＡＲ部分的参数。其主要特点在于应用了基本域内的所有双谱采样，从而有效的利用了信息量。计算机模拟结果表明，它具有很好的数值特性和较好的参数估计。

In our judgment, Mendel's paper in 1991 [4]remains the best theory on identification of non-minimum phase ARMA of non-Gaussian process. In this paper, we improve on Ref[4].We improve Mendel's mathematical model in the following way:Eq. (3)and Eq. (4) expressmathamatically Mendeli model. Eq. (5)and Eq. (6)are well known [2]. By substituting Eqs. (5)and (6)into Eq. (3),We obtain an improved mathematical model.We apply the improved model to studying identification of non-minimum phase ARMA process driven by an unobservable non-Gaussian i. i. d. process. We use 3-rd order cumulants andbispectrum of noise-containing output signals. The noise contained may be white Gaussinn orcolored Gaussian. By solving a set of linear equations, the parameters of MA parts and AR partsare estimated.Our method appears to be better in the fOllowing respects:(1) The structure of the proposed algorithm is flexible.(2) Noise effect can be much reduced.(3) The proposed algorithm does not need initial conditions.(4) The proposed algorithm is free of divergence problem.(5) In the case of non-causal ARMA parameters, our method can deal with all poles exceptthose lying on unit circle.