A model of echolocation of multiple targets in 3D space from a single emission

Bats, using frequency-modulated echolocation sounds, can capture a moving target in real 3D space. The process by which they are able to accomplish this, however, is not completely understood. This work offers and analyzes a model for description of one mechanism that may play a role in the echolocation process of real bats. This mechanism allows for the localization of targets in 3D space from the echoes produced by a single emission. It is impossible to locate multiple targets in 3D space by using only the delay time between an emission and the resulting echoes received at two points (i.e., two ears). To locate multiple targets in 3D space requires directional information for each target. The frequency of the spectral notch, which is the frequency corresponding to the minimum of the external ear's transfer function, provides a crucial cue for directional localization. The spectrum of the echoes from nearly equidistant targets includes spectral components of both the interference between the echoes and the interference resulting from the physical process of reception at the external ear. Thus, in order to extract the spectral component associated with the external ear, this component must first be distinguished from the spectral components associated with the interference of echoes from nearly equidistant targets. In the model presented, a computation that consists of the deconvolution of the spectrum is used to extract the external-ear-dependent component in the time domain. This model describes one mechanism that can be used to locate multiple targets in 3D space.