Synthetic Aperture Computation as the Head is Turned in Binaural Direction Finding

Binaural systems measure instantaneous time/level differences between acoustic signals received at the ears to determine angles λ between the auditory axis and directions to acoustic sources. An angle λ locates a source on a small circle of colatitude (a lamda circle) on a sphere symmetric about the auditory axis. As the head is turned while listening to a sound, acoustic energy over successive instantaneous lamda circles is integrated in a virtual/subconscious field of audition. The directions in azimuth and elevation to maxima in integrated acoustic energy, or to points of intersection of lamda circles, are the directions to acoustic sources. This process in a robotic system, or in nature in a neural implementation equivalent to it, delivers its solutions to the aurally informed worldview. The process is analogous to migration applied to seismic profiler data, and to that in synthetic aperture radar/sonar systems. A slanting auditory axis, e.g., possessed by species of owl, leads to the auditory axis sweeping the surface of a cone as the head is turned about a single axis. Thus, the plane in which the auditory axis turns continuously changes, enabling robustly unambiguous directions to acoustic sources to be determined.