Contributions to the Theory of Modeling of Stochastic Processes

本研究旨在发展一种基于协方差数据的随机过程递归更新模型的理论。考虑了一般的极点-零结构的建模滤波器，同时允许滤波器的阶数随着协方差样本数量的增加而增加。滤波器的结构和待开发的识别方案依赖于某种近似分离原理，该原理适用于识别功率谱的极点和零点的任务。第二个要研究的问题是关于谱分解快速算法的发展。最近的进展有希望产生新的和快速的光谱分解算法。

This research seeks to develop a theory for recursively updated models for stochastic processes based on covariance data. A general pole-zero structure for the modeling filters is being considered while the order of the filters is permitted to increase with the number of covariance samples. The structure of the filters and the identification schemes to be developed rely on a certain approximate separation principle that applies to the tasks of identifying poles and zeros of a power spectrum. A second issue to be investigated concerns the development of fast algorithms for spectral factorization. Recent advances hold the promise of giving rise to novel and fast spectral factorization algorithms.