Successive multivariate variational mode decomposition based on instantaneous linear mixing model

In this paper, a novel Successive Multivariate Variational Mode Decomposition (SMVMD) is presented. Different from most existing multichannel signal decomposition approaches, the proposed SMVMD does not need to predefine the mode number and is able to extract the joint or common modes successively. Firstly, a general decomposition form for multichannel multicomponent signals is formulated based on the instantaneous linear mixing model, which is commonplace in the blind source separation (BSS) problem. Then, four key criteria are introduced to establish the successive variation optimization function. Finally, the alternate direction method of multipliers (ADMM) algorithm is employed to solve this optimization problem. The effectiveness and advantages of the proposed SMVMD are demonstrated by a series of numerical examples. The utility of the proposed approach is also highlighted by the analysis of real-life EEG and vibration signals.