A Jacobi Generalized Orthogonal Joint Diagonalization Algorithm for Joint Blind Source Separation

Abstract

Joint blind source separation (J-BSS) has emerged as a data-driven technique for multi-set data fusion applications. In this paper, we propose a Jacobi generalized orthogonal joint diagonalization (GOJD) algorithm for J-BSS of multiset signals. By the use of second-order statistics, we can obtain multiple sets of auto-covariance and cross-covariance matrices from the multi-set signals, which together admit a GOJD formulation. For computing the GOJD, we propose a computationally efficient Jacobi algorithm, which uses a sequence of Givens rotations to simultaneously diagonalize the covariance matrices. In comparison with other GOJD algorithms, the proposed algorithm is shown to have fast convergence. Moreover, as the optimal Givens rotation matrix in each update is calculated in closed-form, this algorithm is computationally very efficient. In the application aspect, we have considered the scenario where different data sets in J-BSS may have different number of sources, among which there exist both similar components that are consistently present in multiple data sets, and diverse components that are uniquely present in each data set. We have shown how J-BSS based on the proposed GOJD algorithm can effectively extract both similar and diverse source components. Simulation results are given to show the nice performance of the proposed algorithm, with regards to both speed and accuracy, in comparison with other algorithms of similar type.