Self-clustering non-Euclidean kernels for improving the estimation of multidimensional TDOA of multiple sources

This paper addresses the problem of estimating multidimensional propagation time-delay parameters for multiple competitive sources. Complex-valued mixing parameters, measuring the high-order coherence of the acoustic waves recorded at microphone pairs, are estimated applying the Independent Component Analysis (ICA). A statistical framework is used to model the pdf of the whole underlying time-delay distribution and an approximated Gaussian kernel density estimator is derived. Especially for frequencies affected by high spatial aliasing (which occurs when using a large microphone spacing) an overestimation of the kernel bandwidth may reduce the quality of the estimated density or generate high likelihood regions in false locations. To reduce the interference problem among different sources and propagation dimensions we propose an enhancement of the original kernel through a twofold extension: 1) the introduction of non-Euclidean metrics in the multidimensional space 2) the adoption of self-clustering techniques to tackle the permutation problem from a data association point of view. The improved kernel explicitly models in one shot the high-order structure of the entire parameters estimated by ICA and offers a considerably better rejection of the interference across sources as well as across propagation dimensions. Extensive numerical simulations are reported to support the theoretical analysis.