The physical principles and signal processing techniques underlying bat echolocation are investigated. It is shown, by calculation and simulation, how the measured echolocation performance of bats can be achieved.
REFERENCES
1.
This term was coined by Donald R. Griffin, an early researcher in the field of bat sonar. Echolocation refers to the ability of bats to orient themselves by using the echoes of sounds they produce.
2.
M. Brock
Fenton
, “Eavesdropping on the echolocation and social calls of bats
,” Mammal Review
33
, 193
–204
(2003
).3.
N.
Neretti
, M. I.
Sanderson
, J. A.
Simmons
, and N. J.
Intrator
, “Time-frequency computational model for echo-delay resolution in sonar images of the big brown bat, Eptesicus fuscus
,” J. Acoust. Soc. Am.
113
, 2137
–2145
(2003
).4.
P. A.
Saillant
, J. A.
Simmons
, S.
Dear
, and T. A.
McMullen
, “A computational model of echo processing and acoustic imaging in frequency-modulated echolocating bats: The spectrogram correlation and transformation receiver
,” J. Acoust. Soc. Am.
94
, 2691
–2712
(1993
).5.
R. A.
Altes
, “Radar/sonar acceleration estimation within linear-period modulated waveforms
,” IEEE Trans. Aerosp. Electron. Syst.
26
, 914
–924
(1990
).6.
B.
Verboom
, A. M.
Boonman
, and H. J.
Limpens
, “Acoustic perception of landscape elements by the pond bat Myotis dasycneme
,” J. Zool.
248
, 59
–66
(1999
).7.
J.
Habersetzer
, “Adaptive echolocation sounds in the bat
,” J. Comp. Physiol. [A]
144
, 559
–566
(1981
).8.
M. I.
Sanderson
and J. A.
Simmons
, “Neural responses to overlapping FM sounds in the inferior colliculus of echolocating bats
,” J. Neurophysiol.
83
, 1840
–1855
(2000
).9.
T.
Nagel
, “What is it like to be a bat?
” Phil. Rev.
83
, 435
–450
(1974
).10.
J. A.
Simmons
, D. J.
Howell
, and N.
Suga
, “Information content of bat sonar echoes
,” Am. Sci.
63
, 204
–215
(1975
).11.
J. R.
Speakman
, “The evolution of flight and echolocation in bats: Another leap in the dark
,” Mammal Review
31
, 111
–130
(2001
).12.
M. J.
Novacek
, “Evidence for echolocation in the oldest known bats
,” Nature (London)
315
, 140
–141
(1985
);M. J.
Novacek
, “Aspects of the morphology of the cochlea in microchiropteran bats: an investigation of character transformation
,” Bull. Am. Museum Natural History
206
, 84
–100
(1991
).13.
H. U.
Schnitzler
and E. K.
Kalko
, “Echolocation by insect-eating bats
,” BioScience
51
, 558
–569
(2001
).14.
C. F.
Moss
and A. J.
Surlykke
, “Auditory scene analysis by echolocation in bats
,” J. Acoust. Soc. Am.
110
, 2207
–2226
(2001
).15.
Some bats transmit a fundamental frequency plus at least one harmonic. Thus, the frequency-dependence of atmospheric attenuation may permit a crude range estimate from the received harmonic power ratio. We do not know if any bat species makes use of this technique.
16.
B. D.
Lawrence
and J. A.
Simmons
, “Measurements of atmospheric attenuation at ultrasonic frequencies and the significance for echolocation by bats
,” J. Acoust. Soc. Am.
71
, 585
–590
(1982
).17.
M. B.
Fenton
, D.
Audet
, M. K.
Obrist
, and J.
Rydell
, “Signal strength, timing and self-deafening: the evolution of echolocation in bats
,” Paleobiology
21
, 229
–242
(1995
).18.
In the radar field, the electromagnetic equivalent of reverberation is called clutter.
19.
20.
S. A.
Kick
, “Target detection by the echolocating bat, Eptesicus fuscus
,” J. Comp. Physiol. [A]
145
, 431
–435
(1982
).21.
M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1980), Chap. 10.
22.
D. Waters and H. Abulula, “The virtual bat: Echolocation in virtual reality,” Proc. International Conf. on Auditory Display, Espoo: Finland, 2001, pp. 191–196.
23.
C. F. Moss, Echolocation in Encyclopedia of the Cognitive Sciences, edited by R. Wilson and F. Keil (MIT Press, Cambridge, MA, 1999), pp. 253–255.
24.
J. M.
Wooton
, R. L.
Jension
, and D. J.
Hartley
, “The combination of echolocation emission and ear reception enhances directional spectral cues of the big brown bat, Eptesicus fuscus
,” J. Acoust. Soc. Am.
101
, 1723
–1733
(1997
).25.
We outline the steps in this calculation as follows. The bat estimates η from the power received in left and right ears: The echo power for constant SNR is proportional to receiver gain: assuming Here S is the target power received at range R, and N is the noise power. From this the error in estimating η, due to noise contaminating the signal, is determined. We substitute Δη into the right side of Eq. (7) and find Δθ as a function of θ. For realistic parameter values Δθ is insensitive to θ, as observed in Fig. 3. For a target of constant cross section, it is more realistic to hold the noise power constant than to say SNR is fixed, in which case In this case the SNR is a maximum at θ=0, and decreases as θ increases. So from Fig. 4 we see that Δθ increases with θ.
26.
M. B.
Fenton
and G. P.
Bell
, “Recognition of species of insectivorous bats by their echolocation calls
,” J. Mammal.
62
, 233
–243
(1981
).27.
D. K. Barton, Radar Systems Analysis (Artech House, Dedham, MA, 1976), Chap. 3.
28.
J. A.
Simmons
and L.
Chen
, “The acoustic basis for target discrimination by FM echolocating bats
,” J. Acoust. Soc. Am.
86
, 1333
–1350
(1989
).29.
D. R.
Griffin
, J. H.
Friend
, and F. A.
Webster
, “Target discrimination by the echolocation of bats
,” J. Exp. Zool.
158
, 155
–168
(1965
).30.
W. E.
O’Neill
and N.
Suga
, “Encoding of target range and its representation in the auditory cortex of the mustached bat
,” J. Neurosci.
2
, 17
–31
(1982
).31.
This is in theory the best resolution that can be attained for a signal of bandwidth B. In practice many FM bat species get very close to this resolution.
32.
B.
Boashash
, “Estimating and interpreting the instantaneous frequency of a signal—Part 1: Fundamentals
,” Proc. IEEE
80
, 520
–538
(1992
).33.
34.
R. M.
Barclay
, “Interindividual use of echolocation calls: Eavesdropping by bats
,” Behav. Ecol. Sociobiol.
10
, 271
–275
(1982
);M. L.
Leonard
and M. B.
Fenton
, “Echolocation calls of Euderma maculatum (Chiroptera: Vespertilionidae): Use in orientation and communication
,” J. Mammal.
65
, 122
–126
(1984
).35.
J. A.
Simmons
, M. J.
Ferragamo
, and C. F.
Moss
, “Echo-delay resolution in sonar images of the big brown bat, Eptesicus fuscus
,” Neurobiology
95
, 12647
–12652
(1998
);J.
Habersetzer
and B.
Vogler
, “Discrimination of surface-structured targets by the echolocating bat Myotis-myotis during flight
,” J. Comp. Physiol.
152
, 275
–282
(1983
);S.
Schmidt
, “Evidence for a spectral basis of texture perception in bat sonar
,” Nature (London)
331
, 617
–619
(1988
).36.
Thus, for the terminal phase resolutions of Sec. VII we find that, if the bat images what it sees in front of it to a range of 1 m, then it must process 350 000 resolution cells 200 times per second.
37.
B.
Boashash
, “Estimating and interpreting the instantaneous frequency of a signal—Part 2: Algorithms and applications
,” Proc. IEEE
80
, 540
–568
(1992
);B. Boashash, in Advances in Spectrum Estimation and Array Processing, edited by S. Haykin (Prentice Hall, Englewood Cliffs, NJ, 1991), Vol. 1, pp. 418–517;
L. Cohen, in Time-Frequency Signal Analysis, edited by B. Boashash (Wiley, NY, 1992), pp. 3–42.
38.
T.
Collins
and P.
Atkins
, “Non-linear frequency modulation chirps for active sonar
,” IEE Proc. F, Radar Signal Process.
146
, 312
–316
(1999
);T.
Collins
and P.
Atkins
, “Doppler-sensitive active sonar pulse designs for reverberation processing
,” IEE Proc. F, Radar Signal Process.
145
, 347
–353
(1998
);T.
Collins
and P.
Atkins
, “Doppler processing using comb spectrum transmission pulses
,” Proc. Inst. Acoustics
20
, 41
–48
(1998
).
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