Abstract Bats perceive the three-dimensional (3D) environment by emitting ultrasound pulses from their nose or mouth and receiving echoes through both ears. To detect the position of a target object, it is necessary to know the distance and direction of the target. Certain bat species synchronize the movement of their pinnae with pulse emission, and it is this behavior that enables 3D direction detection. 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 3D direction detection. The theory suggests that only certain ear motions, namely three-axis rotation, accomplish accurate and robust 3D direction detection. Our theoretical analysis also strongly supports the behavior whereby bats move their pinnae in the antiphase mode. In addition, we provide the conditions for ear motions to ensure accurate and robust direction detection, suggesting that simple shaped hearing directionality and well-selected uncomplicated ear motions are sufficient to achieve precise and robust 3D direction detection. Our findings and mathematical approach have the potential to be used in the design of active sensing systems in various engineering fields. Author Summary Many mammals use visual sensing for primary perception of their surroundings, whereas bats accomplish spatial perception by active acoustic sensing. In particular, by emitting ultrasound pulses and listening to the echoes, bats localize reflective objects, a process known as echolocation. Certain bat species move both of their ears while receiving the echoes, but the essential theory behind this ear movement remains unclear. This paper describes a simple mathematical model for investigating the active listening strategy employed by bats. The theory suggests that the ear motions employed by bats enables highly accurate direction detection that is robust to observation errors. In addition, we determine what kind of ear motions are optimal for 3D direction detection. This study not only reveals the significance of pinnae motions in bats, but also opens up the possibility of engineering applications for active listening systems.

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