Fundamental Research on Statistical Modeling of Dynamic or Static Systems

近年来，随着高速数字计算机的迅速发展，人们对将高阶统计量（称为累积量）应用于动态或静态系统的建模问题越来越感兴趣。在本研究中，我们首先提出了一种基于累积量的离散线性系统识别方法，该方法利用输入和输出信号的四阶累积量，这两个信号都被加性彩色高斯噪声污染。然后，在假设输入信号为白色的情况下，我们提出了一种仅利用输出信号的三阶或四阶累积量估计ARMA模型参数的方法。研究了由不可观测彩色信号驱动的多通道线性系统的辨识问题。证明了未知系统的传递函数矩阵可以通过广义置换矩阵的后乘来辨识。同时考虑了多通道线性系统的盲均衡问题，提出了求解该问题的多阶段最大化准则和单阶段最大化准则。给出了多通道盲均衡的一个充分必要条件。

Recently, with the rapid development of high-speed digital computers, there has been an increasing interest in applying higher-order statistics called cumulants to several modeling problems of dynamic or static systems. In this research, we first proposed a cumulant-based identification method for a discrete-time linear system using the fourth-order cumulants of the imput and output signals, both of which are contaminated by additive colored Gaussian noise. Then, under the assumpytion that the input signal is white, we proposed an estiomation method of parameters of an ARMA model using the third-order or the fourth-order cumulants only of the output signal. We dealt with the problem of identification of multichannel linear systems driven by unobservable colored signals. It was shown that the transfer function matrix of an unknown system is identified up to post-multiplication of a generalized permutation matrix. We also considered the blind equalization problem of multichannel linear systems, and propose a multistage maximization criterion and a single-stage maximization criterion for solving this problem. We derived a necessary and sufficient condition for multichannel blid equalization.