Second-Order-Statistics-Based Blind Source Separation for Non-Stationary Sources with Stationary Noise

The aim of "blind source separation" is to recover mutually independent unknown source signals from observations obtained through an unknown linear mixture system. Simultaneous diagonalization of correlation matrices (second-order statistics) of observations is one of resolutions, when the unknown source signals are non-stationary. When observation noise exists, this method needs to correct the correlation matrices based on an estimation of the variance of the noise. However, the estimation of the variance of the noise requires additional information such as redundant observations. In this paper, we propose a new method of estimating the variance of the noise without additional information by utilizing a necessary and sufficient condition that simultaneous diagonalization of the correlation matrices is always achieved. We also verify the efficacy of the proposed method by numerical examples