非最小相位系统的辩识

IDENTIFICATION OF NON-MINIMUM PHASE SYSTEM

1.引言 在时间序列分析中,多数文献讨论的是线性高斯模型,在高斯假设下,最小二乘估计就是最大似然估计;最小二乘估计只利用了时间序列的自相关信息,所形成的方程是一组线性方程即Wiener-Hopf方程。因此,最小二乘估计被广泛地应用于时间序列的建模。但是,自相关序列是“相盲”的,相关建模方法不能准确地表征非最小相位的参数信号;在自相关(功率谱)域中,所能做到的只是重建功率谱意义下等效的最小相位信号。

Causal AR models can only provide minimum-phase information accurately whereas anti-causal AR models provide maximum-phase information . The parameters of causal and anti-causal AR models are estimated by using third-order cumulant sequences on the same data and properly utilized to obtain non-minimum phase function of signals. The estimated non-minimum phase function can be used as reference-phase function to resolve the true location of signal zeros by minimum square error criterion. The results of computer simulations are included to illustrate the conclusions in the paper.