Non-stationary sources separation based on maximum likelihood criterion using source temporal-spatial model

In this paper, we propose a new non-stationary sources separation algorithm, which is referred to as autoregressive hidden Markov Gaussian process (AR-HMGP), in which the sources are non-stationary and temporally correlated. For the proposed algorithm, a generative model is employed to track the non-stationarity of the source where the temporal dependencies of sources are represented by autoregressive model (AR) and the distribution of the associated innovation process is described using non-stationary Gaussian process with hidden Markov model (HMM). We further explore the maximum likelihood (ML) method to estimate the parameters of the source model by using the expectation maximum (EM) algorithm. Our important findings reveal that (a) AR-HMGP algorithm outperforms the other three BSS algorithms for non-stationary sources separation, the instantaneous mixture system is also well corroborated with the effectiveness of our algorithm; (b) both independent and dependent non-stationary sources have been successfully separated; (c) the proposed algorithm is robust with respect to noise, while the other three algorithms are not.