Convergence Analysis of Gevers-Wouters Algorithm for Scalar Spectral Factorization
Zili Deng · Science Technology and Engineer · 2005
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.