Performance Analysis of 3-D Direction Estimation Based on Head-Related Transfer Function

We analyze the performance of a sensor system based on the head-related transfer function (HRTF) modeling of human hearing, in finding the direction of a source in 3-D space. Thus, this system has only two sensors with a few nearby reflectors. First, we present a parametric measurement model that incorporates the diffractions associated with the head shape and the multipath reflections related to the external ear (pinna). Then, we compute the asymptotic Cramer-Rao bound on the 3-D direction estimate for a stochastic source signal of unknown parametrized spectrum. We provide a few numerical examples to illustrate our analytical results.