Source separation: A TITO system identification approach

The blind source separation problem is studied in this paper using a system identiication approach. Two unmeasurable source signals are mixed by means of a channel system resulting in two measurable output signals. The measurable signals can be used in a TITO (Two Inputs Two Outputs) system identiication approach in order to extract the sources. The system to be identiied can be described by two parts, namely a model of the source generating lters and a model of the mixing channels. Both the source generating lters and the mixing channels are modeled as ARMA-lters. It is shown that the system, under various weak conditions, is identiiable using second order statistics only. These conditions are presented along with identiiability results. Furthermore, with some minor additional restrictions, the sources can be recovered. One method to perform this system identiication is by using the Prediction Error Method (PEM). PEM is a general method which is statistically eecient under the Gaussian hypothesis. To be able to perform the separation in an on-line manner, a recursive version of PEM is used. Simulation results using this approach are presented, both with computer generated and real world signals.