Sequential blind extraction of instantaneously mixed sources

This paper presents a general approach to sequential blind extraction of instantaneously mixed sources for several major ill-conditioned cases as well as the regular case of full column rank mixing matrices. Four ill-conditioned cases are considered: The mixing matrix is square but singular; the number of sensors is less than that of sources; the number of sensors is larger than that of sources, but the column rank of the mixing matrix is deficient; and the number of sources is unknown and the column rank of the mixing matrix is deficient. First, a solvability analysis is presented for a general case. A necessary and sufficient condition for extractability is derived. A sequential blind extraction approach is then proposed to extract all theoretically separable sources. Next, a principle and a cost function based on fourth-order cumulants are presented for blind source extraction. By minimizing the cost function under a nonsingularity constraint of the extraction matrix, all theoretically separable sources can be extracted sequentially. Finally, simulation results are presented to demonstrate the validity and performance of the blind source extraction approach.