Blind Source Separation Using Temporal Correlation, Non-Gaussianity and Conditional Heteroscedasticity

Abstract

Independent component analysis separates latent sources from a linear mixture by assuming sources are statistically independent. In real world applications, hidden sources are usually non-Gaussian and have dependence among samples. In such case, both attributes should be considered jointly to obtain a successful separation. To capture sample dependence, a latent source is sometimes modeled by autoregressive or moving average models with an independent and identically distributed error or residual. However, these models are limited by assuming only linear dependence among a source's samples. This paper proposes a new blind source separation algorithm based on an autoregressive-autoregressive conditional heteroscedasticity (AR-ARCH) model, which captures linear correlations, non-Gaussianity, and squared residuals' dependence. The AR part of the AR-ARCH model captures the correlation among samples. The ARCH part of the model captures the non-Gaussianity and nonlinear dependence among samples. The ARCH model also assumes the time-varying conditional variances for sources. We derive the Cramér Rao lower bound (CRLB) for the mixing matrix based on the AR-ARCH model. We perform simulations on both synthetic and real data. The results show that the proposed method outperforms the baseline algorithms especially for a small number of samples and approaches the CRLB.