Multiple sources´ direction finding by using reliable component on phase difference manifold and kernel density estimator

This paper proposes a novel direction-of-arrival estimation method in a general 3-dimensional array configuration for multiple speech signals uttered simultaneously. The method is based on sparseness in the time-frequency representation of speech signal and is applicable to an underdetermined case where the sources outnumber sensors. At first, we introduce a parameterized closed surface to which we refer the phase difference manifold. This is defined in the space of phase difference vectors between sensors in order to provide the one-to-one correspondence between the induced phase difference on this sphere and a propagating direction vector of the source. Instead using the conventional pseudo-inverse mapping algorithm, the selection of phase difference vectors located or closely located on the phase difference manifold as a set of reliable observations. Finally, the author´s method utilizing kernel density algorithm is generalized for arbitrary array sensors case. The conducted experiments demonstrate that the method utilizing the reliable cell selection and the kernel density estimator with appropriate bandwidth determination performed effectively.