Dual multivariate auto-regressive modeling in state space for temporal signal separation

Many existing independent component analysis (ICA) approaches result in deteriorated performance in temporal source separation because they have not taken into consideration of the underlying temporal structure of sources. In this paper, we model temporal sources as a general multivariate auto-regressive (AR) process whereby an underlying multivariate AR process in observation space is obtained. In this dual AR modeling, the mixing process from temporal sources to observations is the same as the mixture from the nontemporal residuals of the source AR (SAR) process to that of the observation AR (OAR) process. We can therefore avoid the source temporal effects in performing ICA by learning the demixing system on the independently distributed OAR residuals rather than the time-correlated observations. Particularly, we implement this approach by modeling each source signal as a finite mixture of generalized autoregressive conditional heteroskedastic (GARCH) process. The adaptive algorithms are proposed to extract the OAR residuals appropriately online, together with learning the demixing system via a nontemporal ICA algorithm. The experiments have shown its superior performance on temporal source separation.