基于共轭梯度搜索的广义特征对追踪算法

Generalized eigen-pairs tracking based on conjugate gradient method

研究广义特征对追踪算法,通过探索基于共轭梯度搜索的标准特征向量追踪算法,将其引入到广义特征对的提取.所提算法具有自适应步长机制,使不同特征搜索方向上的广义瑞利熵达到最优,并适用于提取平稳矩阵束和非平稳矩阵束的广义特征对.数值仿真中将所提算法与多个自适应广义特征向量提取算法进行了比较,实验结果验证了所提算法的有效性.

Generalized eigenvalue decomposition plays a vital role in statistical signal processing.Generalized decomposition aims to enhance the signal by seeking the directions that capture most of signal component but are orthogonal to the spaces constituting the noise component.Each generalized eigenvalue represents the optimal signal-to-noise ratio that can be obtained by projecting an observation into the corresponding eigen-direction.This paper proposes a generalized eigen-pairs tracking method based on conjugate gradient searching.The proposed method is variable step-size that seeks the generalized eigenvector in a sense that generalized Rayleigh quotient is optimal in the corresponding searching direction.It is suitable for extracting generalized eigenvectors from stationary and non-stationary matrix pencil.We compare the proposed method with multiple adaptive generalized extraction algorithms.The effectiveness of the proposed method is validated via numerical simulations.