一种平稳子空间分析的快速不动点算法

A Fast Fixed-point Algorithm for Stationary Subspace Analysis

平稳子空间分析是新近发展的一种信号处理和数据分析技术,能够从观测到的多维非平稳信号中分离出平稳源信号。标准的平稳子空间分析算法基于Stiefel流形上的梯度下降方法。针对该算法收敛慢、耗时多的缺陷,根据关于Stiefel流形上优化问题的一阶最优性条件构造了迭代公式,提出一种新的平稳子空间分析的不动点算法。仿真实验表明,本文算法能够有效地分离出平稳源信号,分离性能优于已有的平稳子空间分析的不动点算法;与标准的基于Stiefel流形上梯度下降的算法相比,本文算法收敛更快,耗时更少。

Stationary subspace analysis is a recently developed technique for signal processing and data analysis,which is capable of separating stationary source signals from observed multidimensional nonstationary signals. The standard algorithm for stationary subspace analysis stems from the gradient descend over the Stiefel manifold,which converges slow and is time-consuming. In order to overcome those drawbacks,an iterative formula is constructed on the basis of the first-order optimality condition related to optimization problems over Stiefel manifolds,and thereby a novel fixed-point algorithm is proposed for stationary subspace analysis. Computer simulations show that the proposed algorithm is able to separate the stationary sources effectively with a better separation performance than that of the existing fixed-point algorithm,and in contrast to the standard algorithm that is based on the gradient descend over the Stiefel manifold,the proposed algorithm converges faster and is less time-consuming.