论文标题
高斯信号非平稳源分离的大样本特性
Large-Sample Properties of Non-Stationary Source Separation for Gaussian Signals
论文作者
论文摘要
非平稳来源分离是具有许多不同方法的盲源分离的一个完善的分支。但是，对于这些方法都没有大样本结果可用。为了弥合这一差距，我们开发了NSS-JD的大样本理论，NSS-JD是一种基于块的协方差矩阵的联合对角线化的流行方法。我们在独立的高斯非平稳源信号的瞬时线性混合模型以及一组非常通用的假设下工作：除了有界条件之外，我们做出的唯一假设是，源表现出有限的依赖性，并且它们的方差函数差异很大，足以不可分割地分离。在以前的条件下显示，Unmixing估计器的一致性及其在标准平方根速率下以标准平方根速率以限制高斯分布的一致性。模拟实验用于验证理论结果并研究块长度对分离的影响。
Non-stationary source separation is a well-established branch of blind source separation with many different methods. However, for none of these methods large-sample results are available. To bridge this gap, we develop large-sample theory for NSS-JD, a popular method of non-stationary source separation based on the joint diagonalization of block-wise covariance matrices. We work under an instantaneous linear mixing model for independent Gaussian non-stationary source signals together with a very general set of assumptions: besides boundedness conditions, the only assumptions we make are that the sources exhibit finite dependency and that their variance functions differ sufficiently to be asymptotically separable. The consistency of the unmixing estimator and its convergence to a limiting Gaussian distribution at the standard square root rate are shown to hold under the previous conditions. Simulation experiments are used to verify the theoretical results and to study the impact of block length on the separation.
