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.
REFERENCES
1.
J. L.
Spiesberger
and K. M.
Fristrup
, “Passive localization of calling animals and sensing of their acoustic environment using acoustic tomography
,” Am. Nat.
135
, 107
–153
(1990
).2.
M. D.
Collins
and W. A.
Kuperman
, “Focalization: Environmental focusing and source localization
,” J. Acoust. Soc. Am.
90
, 1410
–1422
(1991
).3.
J. P.
Van Etten
, “Loran C system and product development
,” Electrical Commun.
45
, 100
–115
(1970
).4.
R. O.
Schmidt
, “A new approach to geometry of range difference location
,” IEEE Trans. Aerosp. Electron. Syst.
AES-8
, 821
–835
(1972
).5.
W. A. Tyrrell, “Design of acoustic systems,” in Marine Bioacoustics, edited by W. N. Tavolga (Pergamon, Oxford, U.K., 1964), pp. 65–86.
6.
H. C.
Schau
and A. Z.
Robinson
, “Passive source localization employing intersecting spherical surfaces from time-of-arrival differences
,” IEEE Trans. Acoust., Speech, Signal Process.
ASSP-35
, 1223
–1225
(1987
).7.
N.
Marchand
, “Error distributions of best estimate of position from multiple time difference hyperbolic networks
,” Aerosp. Navigational Electron.
11
, 96
–100
(1964
).8.
H. B.
Lee
, “A novel procedure for assessing the accuracy of hyperbolic multilateration systems
,” IEEE Trans. Aerosp. Electron. Syst.
AES-11
, 2
–15
(1975
).9.
W. H.
Foy
, “Position-location solutions by Taylor-series estimation
,” IEEE Trans. Aerosp. Electron. Syst.
AES-12
, 187
–194
(1976
).10.
J. M.
Delosme
, M.
Morf
, and B.
Friedlander
, “Source location from time differences of arrival: Identifiability and estimation
,” IEEE Int. Conf. Acoust., Speech, Signal Process.
, 818
–824
(1980
).11.
W. A. Watkins and W. E. Schevill, “Four hydrophone arrays for acoustic three-dimensional location,” Woods Hole Oceanographic Technical Report No. 71–60 (1971).
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