Hyperbolic location errors due to insufficient numbers of receivers

Animal locations are sometimes estimated by measuring the difference in travel times of their sounds at pairs of receivers. Ideally, each difference specifies the animal’s location to a hyperboloid, and sufficient numbers of intersecting hyperboloids specify the location. Most bioacoustic publications state that one needs three receivers to locate animals in two spatial dimensions and four receivers in three spatial dimensions. However, the actual numbers of receivers required for locations in two and three dimensions are four and five, respectively. Significant location errors can result from using insufficient numbers of receivers. Methods are provided for determining locations of ambiguous source-location regions.

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