On-line Convolutive Blind Source Separation of Non-Stationary Signals

A novel algorithm is proposed in this paper to solve blind source separation of post-nonlinear convolutive mixtures of non-stationary sources. Both convolutive mixing and post-nonlinear distortion are included in the proposed model. Based on the generalized Expectation-Maximization (EM) algorithm, the Maximum Likelihood (ML) approach is developed to estimate the parameters in the model. A set of polynomials is used to estimate the post-nonlinear distortion. In the E-step, the sufficient statistics associated with the source signals are estimated while in the M-step, the parameters are optimized by using these statistics. Generally, the nonlinear distortion renders the statistics intractable and difficult to be formulated in a closed form. However, the use of Extended Kalman Smoother (EKF) around a linearized point facilitates the M-step tractable and can be solved by linear equations. Keywords—Nonlinear blind source separation, convolutive mixture, non-stationary sources, Extended Kalman Smoother.