Blind source separation without optimization criteria?

Blind source separation aims to extract a set of independent signals from a set of observed linear mixtures. After whitening the sensor output, the separation is achieved by estimating an orthogonal transformation, which in the real-mixture two-source two-sensor case is entirely characterized by a single rotation angle. This contribution studies an estimator of such an angle. Even though it is derived from geometric notions based on the scatter-plots of the signals involved, it is found, empirically, to exhibit a performance clearly up to the mark of other methods based on optimality criteria and, theoretically, to improve and generalize one of such procedures. The simplicity of the suggested estimator results in a straightforward adaptive version, which converges regardless of the source distribution, for quite mild conditions, and whose asymptotic analysis is easy to carry out. The applicability of the estimator in a full separation system is also illustrated