Fundamental Researches on Statistical Systems Modeling

近年来，随着高速数字计算机的迅速发展，人们越来越关注将高阶统计量（即累积量）应用于动态或静态系统的建模问题。在这项研究中，我们考虑了一个离散时间线性系统的盲识别和盲反卷积（或盲均衡）使用的输出信号的三阶或四阶累积量被加性的白色或彩色高斯噪声污染。我们首先处理了由不可观测彩色信号驱动的多通道线性系统的识别问题。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。然后考虑了多通道线性系统的盲反卷积（或盲均衡）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。我们提出了一种新的无约束多阶段准则来解决盲解卷积问题。基于这些多阶段准则，我们开发了多通道盲反卷积的迭代算法。

Recently, with the rapid development of high-speed digital computers, there has been increasing interests in applying higher-order statistics called cumulants to several modeling problems of dynamic or static systems. In this research, we consedered blind idntification and blind deconvolution (or blind equalization) of a discrete-time linear system using the third-order or the fourth-order cumulants of the output signals contaminated by additive white or colored Gaussian noise. We first 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. Then we considered the blind deconvolution (or 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 blind equalization. We proposed a new unconstrained multistage criterion for solving the blind deconbolution problem. Based on these multistage criteria, we developed iterative algorithms for multichannel blind deconvolution.