纯量谱分解的Gevers-Wouters算法收敛性分析

滑动平均(MA)模型参数估计问题等价于一个谱分解问题,用Kalman滤波方法基于MA模型到状态空间模型的变换,证明了纯量可逆的MA模型参数估计的Gevers-Wouters算法的一致性和指数收敛性,且证明了收敛速度由MA多项式的零点决定。当MA多项式的零点不接近单位圆周时,Gevers-Wouters算法可高精度快速给出MA参数估值,是一种快速、简单、有效的谱分解算法,为状态估计、信号处理、时间序列分析、系统辨识提供了一种重要的工具。

Convergence Analysis of Gevers-Wouters Algorithm for Scalar Spectral Factorization

The parameter estimation problem to the moving average (MA) model is equivalent to a spectral factorization problem, which is a very difficult nonlinear estimation one. By the Kalman filtering, based on the transformation of the moving average (MA) model into the state space model, the consistence and exponential convergence of the Gevers-Wouters algorithm for scalar invertible MA model parameter estimation, is proved, and it is proved that the convergence rate is determined by the zeros of the MA polynomial. When the zoro points of stable MA polynomial are not approximate to the unit circle, the Gevers-Wouters algorithm can quickly give the MA paremeter estimates with the higher accuracy, and becomes a fast, simple and efficient spectral factorization algorithm. It provides an important tool for state estimation, signal processing, time series analysis system identification.