Blind Source Separation of Instantaneous Mixture of Delayed Sources Using High‐Order Taylor Approximation

This paper deals with the problem of blind source separation (BSS), where observed signals are a mixture of delayed sources. In reference to a previous work, when the delay time is small such that the first‐order Taylor approximation holds, delayed observations are transformed into an instantaneous mixture of original sources and their derivatives, for which an extended second‐order blind identification (SOBI) approach is used to recover sources. Inspired by the results of this previous work, we propose to generalize its first‐order Taylor approximation to suit higher‐order approximations in the case of a large delay time based on a similar version of its extended SOBI. Compared to SOBI and its extended version for a first‐order Taylor approximation, our method is more efficient in terms of separation quality when the delay time is large. Simulation results verify the performance of our approach under different time delays and signal‐to‐noise ratio conditions, respectively.