  Non-orthogonal joint diagonalization (NJD) free of prewhitening has been
widely studied in the context of blind source separation (BSS) and array signal
processing, etc. However, NJD is used to retrieve the jointly diagonalizable
structure for a single set of target matrices which are mostly formulized with
a single dataset, and thus is insufficient to handle multiple datasets with
inter-set dependences, a scenario often encountered in joint BSS (J-BSS)
applications. As such, we present a generalized NJD (GNJD) algorithm to
simultaneously perform asymmetric NJD upon multiple sets of target matrices
with mutually linked loading matrices, by using LU decomposition and successive
rotations, to enable J-BSS over multiple datasets with indication/exploitation
of their mutual dependences. Experiments with synthetic and real-world datasets
are provided to illustrate the performance of the proposed algorithm.
