A solution to binaural direction finding described in Tamsett (Robotics 2017
, 6(1), 3) is a synthetic aperture computation (SAC) performed as the head is turned while listening to a sound. A far-range approximation in that paper is relaxed in this one and the method extended for SAC as a function of range for estimating range to an acoustic source. An instantaneous angle
(lambda) between the auditory axis and direction to an acoustic source locates the source on a small circle of colatitude (lambda circle) of a sphere symmetric about the auditory axis. As the head is turned, data over successive instantaneous lambda circles are integrated in a virtual field of audition from which the direction to an acoustic source can be inferred. Multiple sets of lambda circles generated as a function of range yield an optimal range at which the circles intersect to best focus at a point in a virtual three-dimensional field of audition, providing an estimate of range. A proof of concept is demonstrated using simulated experimental data. The method enables a binaural robot to estimate not only direction but also range to an acoustic source from sufficiently accurate measurements of arrival time/level differences at the antennae.
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