Theoretical investigation of active listening behavior based on the echolocation of CF-FM bats

Bats perceive the three-dimensional environment by emitting ultrasound pulses from their nose or mouth and receiving echoes through both ears. To determine the position of a target object, it is necessary to know the distance and direction of the target. Certain bat species that use a combined signal of long constant frequency and short frequency modulated ultrasounds synchronize their pinnae movement with pulse emission, and this behavior has been regarded as helpful for localizing the elevation angle of a reflective sound source. However, the significance of bats' ear motions remains unclear. In this study, we construct a model of an active listening system including the motion of the ears, and conduct mathematical investigations to clarify the importance of ear motion in direction detection of the reflective sound source. In the simulations, direction detection under rigid ear movements with interaural level differences was mathematically investigated by assuming that bats accomplish direction detection using the amplitude modulation in the echoes caused by ear movements. In particular, the ear motion conditions required for direction detection are theoretically investigated through exhaustive simulations of the pseudo-motion of the ears, rather than simulations of the actual ear motions of bats. The theory suggests that only certain ear motions, namely three-axis rotation, allow for accurate and robust direction detection. Our theoretical analysis also strongly supports the behavior whereby bats move their pinnae in the antiphase mode. In addition, we suggest that simple shaped hearing directionality and well-selected uncomplicated ear motions are sufficient to achieve precise and robust direction detection. Our findings and mathematical approach have the potential to be used in the design of active sensing systems in various engineering fields.