Kronecker product overdetermined independent vector analysis for online blind source separation

Online blind source separation is essential for real-time speech communication and human-machine interaction. Among existing solutions, overdetermined independent vector analysis (OverIVA) has demonstrated superior separation performance by jointly exploiting source independence and the orthogonal constraint between the source and noise subspaces. However, when employed with large microphone arrays, the dimensionality of the separation filters grows rapidly, which poses significant challenges for reliable parameter estimation in online implementations. To address this limitation, this paper proposes a generalized Kronecker product decomposition for online OverIVA, in which each source extraction filter is represented as a sum of multiple Kronecker products of shorter sub-filters. The proposed formulation introduces an explicit Kronecker order that flexibly controls the model rank, enabling a smooth trade-off between representation capability and parameter efficiency. An efficient alternating optimization algorithm based on iterative projection is derived to estimate the structured extraction filters in an online manner. Simulation results demonstrate that the proposed method achieves improved separation performance and enhanced robustness.