  The steered response power phase transform (SRP-PHAT) is a beamformer method
very attractive in acoustic localization applications due to its robustness in
reverberant environments. This paper presents a spatial grid design procedure,
called the geometrically sampled grid (GSG), which aims at computing the
spatial grid by taking into account the discrete sampling of time difference of
arrival (TDOA) functions and the desired spatial resolution. A new SRP-PHAT
localization algorithm based on the GSG method is also introduced. The proposed
method exploits the intersections of the discrete hyperboloids representing the
TDOA information domain of the sensor array, and projects the whole TDOA
information on the space search grid. The GSG method thus allows to design the
sampled spatial grid which represents the best search grid for a given sensor
array, it allows to perform a sensitivity analysis of the array and to
characterize its spatial localization accuracy, and it may assist the system
designer in the reconfiguration of the array. Experimental results using both
simulated data and real recordings show that the localization accuracy is
substantially improved both for high and for low spatial resolution, and that
it is closely related to the proposed power response sensitivity measure.
