{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:11:36Z","timestamp":1760242296157,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,4,19]],"date-time":"2017-04-19T00:00:00Z","timestamp":1492560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>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    \u03bb    (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.<\/jats:p>","DOI":"10.3390\/robotics6020010","type":"journal-article","created":{"date-parts":[[2017,4,19]],"date-time":"2017-04-19T10:22:01Z","timestamp":1492597321000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Binaural Range Finding from Synthetic Aperture Computation as the Head is Turned"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1791-5472","authenticated-orcid":false,"given":"Duncan","family":"Tamsett","sequence":"first","affiliation":[{"name":"Environmental Research Institute, North Highland College, University of the Highlands and Islands, Thurso, Caithness KW14 7EE, UK"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,19]]},"reference":[{"key":"ref_1","unstructured":"Lollmann, H.W., Barfus, H., Deleforge, A., Meier, S., and Kellermann, W. 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