USING BAT AUDITORY MODELLING FOR OBJECT
DISCRIMINATION AND ECHO SEPARATION TASKS
Dragana Nikolić, Timos Papadopoulos and Robert Allen
Institute of Sound and Vibration Research, University of Southampton, University Road, Southampton, U.K.
Keywords: Bat echolocation, Acoustics modelling, Echo separation, Object discrimination.
Abstract: This paper proposes a computational echolocation model that can be used for discrimination of the specific
target object and reconstruction of the acoustic information from multiple overlapping echoes returning
back from that target. An acoustic model for estimation of the backscattering impulse responses of a rigid
disk has been developed and employed in order to simulate reflection and scattering of FM signal from the
disk surface and edges. By rotating the disk around its central axis reflected echo patterns from its edges
change allowing for small time variation between arrivals of each individual echo component. This repre-
sents the scenario of a flying insect where the distances from the bat to the insect’s head, body and wings
are slightly different with each returning a contribution to the overall echo. The echolocation signal obtained
from the rotating disk is further encoded into the spectrogram-like format characteristic for the mammalian
auditory system. The simulation results presented in this paper demonstrate that the proposed model is able
to distinguish between overlapping echoes from the spectrogram-like forms of the echolocation signals.
1 INTRODUCTION
Most bat species use echolocation to navigate in to-
tal darkness and/or to track and capture flying insect
prey by processing acoustic information based on
the reflection of sound waves from targets and inter-
cepting obstacles. These mammals can perceive the
distance to a target based on the delay between the
emitted pulse and the returning echoes with surpri-
singly fine delay acuity and are also able to deter-
mine the target position from the different arrival ti-
mes, intensity levels and spectral information of the
returning echoes. Furthermore, some species of bats,
such as the big brown bat Eptesicus fuscus, emit
frequency-modulated (FM) ultrasound of very short
duration which they use as broadband signals to
reconstruct images of the arrangement of reflecting
points and surfaces within the target. The complex
structure of the echo formed by sound scattering
from the discrete target points contains interference
peaks and notches at specific frequencies determined
by the time separation of the individual reflections.
This overall echo pattern is altered further due to the
relationship between the bat and target movements.
The phenomena that echolocating bats have
evolved, both behavioural and physiological mecha-
nisms, to resolve those difficult tasks have inspired
researchers to thoroughly study their behaviour and
understand the underlying physical principles and
signal processing techniques with the aim of develo-
ping a computational model of the echolocation pro-
cess which can be adopted in sonar system design in
the future.
The objective of this study is to develop a com-
putational echolocation model that can be used for
discrimination of the specific target object and re-
construction of the acoustic information from multi-
ple overlapping echoes returning back from that tar-
get. An acoustic model for estimation of the back-
scattering impulse responses of a rigid disk has been
developed and employed in order to simulate reflec-
tion and scattering of FM ultrasound signal from the
disk surface and edges. By rotating the disk around
its central axis reflected echo patterns from its edges
change allowing for small time variation between
arrivals of each individual echo component. This
represents the scenario of a flying insect where the
distances from the bat to the insect’s head, body and
wings are slightly different with each returning a
contribution to the overall echo. The resulting signal
containing both emission and echoes from the disk is
further encoded in the spectrogram-like format using
a set of broadband filters adapted to the properties of
the mammalian auditory system (Sailant et al, 1983).
300
Nikoli
´
c D., Papadopoulos T. and Allen R. (2010).
USING BAT AUDITORY MODELLING FOR OBJECT DISCRIMINATION AND ECHO SEPARATION TASKS.
In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 300-305
DOI: 10.5220/0002748603000305
Copyright
c
SciTePress
This paper is organised as follows: A detailed
description of the proposed model is given in section
2. Simulation results obtained at different processing
stages explained in section 2 are presented and dis-
cussed in section 3. In section 4, the obtained results
are summarised and some directions for the future
work are outlined.
2 MODEL DESCRIPTION
The proposed simulation model shown in Figure 1
consists of three processing blocks: the system mo-
del, the bioinspired cochlear block and the artificial
post-processing block. The important stages of each
block are described in the subsequent sections.
Figure 1: Simulation echolocation model used for object
discrimination and echo separation.
2.1 System Model
The system model is used to simulate echoes which
bats might receive from a specific disk-shaped
target. This is achieved by separately modelling the
emission, backscattering and reception of the ultra-
sound signal in the field. Emission is modelled using
a hyperbolic, linear period-modulated down-swept
signal in the range of frequencies from 100 kHz to
20 kHz. Time duration of this signal used for all
simulation sets was 1 ms with 300 μs rise-fall time
and unity signal amplitude. The sampling frequency
was set to 100 MHz. This signal is a close replica of
the FM signal commonly used by some bat species
(FM signal emitted by the big brown bat Eptesicus
fuscus is within the same frequency range).
The input signal is further filtered through the
synthetically-generated backscattering impulse res-
ponse of the rotating disk, to obtain reflection com-
ponents associated to a relative position of the disk
to the source and the receiver. The output of the sys-
tem model block consists of the emission and echoes
produced by the disk positioned at a certain angle re-
lative to the axis perpendicular to the source-receiver
axis. The effects involved in the reception of the sig-
nal such as those from the bat’s head and ears are
being considered in a parallel study.
2.1.1 Analytical Modelling of the Disk
Backscattering Impulse Response
The physical setup considered here is that of an ideal
point monopole source, an acoustically rigid disk-
shaped target of finite depth D between its two cir-
cular surfaces of radius r and a receiver positioned
along the line joining the source and the center of
mass of the disk (Figure 2). The disk is positioned
such that the axis parallel to its circular surfaces and
passing through its center of mass is perpendicular
to the source-receiver axis. Cases are considered
where the disk target is rotated around the axis that
is parallel to its circular surfaces.
Figure 2: System model geometry used for estimation of
the backscattering impulse responses of the disk target.
The emission-backscattering-reception process is
modelled as the output of a linear time-invariant sys-
tem. The input to this system is the source strength
q(t), taken here to be equal to the chosen FM signal.
The system’s output, i.e. the acoustic pressure p(t)
created at a single point of the generated sound field,
is modelled by the convolution integral:
() ( )( )
() () () ( )
0
0
=−
⎡⎤
=++
⎣⎦
dir ref diff
pt h qt d
hhhqtd
τττ
τ
ττττ
(1)
where h
dir
and h
ref
describe the direct propagation
from the source to the sampling point and the specu-
lar reflection from the planar disk surface. They
amount to delayed and attenuated Dirac delta pulses
h
i
= δ(τd
i
/c)/d
i
with d
i
denoting the corresponding
path length distances and c the speed of sound. The
performance of bioinspired time-frequency auditory
models using such geometrical-acoustics-derived in-
put signals has been examined in numerous studies
in the past (see (Neretti et al, 2003), and (Saillant et
al, 1993) and references therein). A novel approach
in this study is the inclusion of the third term h
diff
which models the contribution of diffraction from
USING BAT AUDITORY MODELLING FOR OBJECT DISCRIMINATION AND ECHO SEPARATION TASKS
301
the circular edges of the target. It should be clear
that as the disk is rotated from the source-receiver
axisymmetric position, the point on its circular face
that contributes to specular reflection progressively
moves towards the circumference and eventually
meets it at certain angle of rotation. For larger rotati-
on angles, the time-concentrated part of impulse res-
ponse due to h
ref
vanishes, leaving only time-extend-
ed contribution of h
diff
in the generated echo. The be-
haviour of the proposed model for such time-smear-
ed echoes is one of the objectives of the present
study.
For the computation of the diffraction part of the
impulse responses the time-domain solution present-
ed in (Svensson et al, 1999, 2006) was used. This is
based on the use of directional secondary sources
positioned along a finite-length edge, with strength,
timing and directivity adjusted to conform to pre-
vious solutions of the infinite-length edge diffraction
problem. The diffraction impulse response h
diff
is
thus derived as a line-integral over the length of the
edge of the contribution of those secondary sources.
A set of Matlab scripts for the determination of the
edge parts that contribute to the overall diffraction
impulse response, the derivation of the related
directivity functions and timings and the discretisa-
tion of the line integral computation provided in
http://www.iet.ntnu.no/~svensson/downloads/ was
used for the computation of the impulse responses in
this study. The circular faces of the target were
approximated with a 256-sides polygons and the
sampling rate was set to 10 MHz. Only first-order
diffraction was included in these results. A sampling
rate of 100 times the highest frequency of interest
(100 kHz) was chosen in order to minimise the
effect of the discretisation of the line integral com-
putation (Svensson et al, 1999).
2.2 Bio-inspired Cochlear Block
The auditory processing of the echo signal reaching
the bat’s ear after returning from the target object is
performed by the cochlear block, named after the
main auditory part of the inner ear known as the
cochlea. A major function of the cochlear block is to
model the sound signal that arrives at the outer ear
canal into the spectral format that is characteristic
for the mammalian auditory system. The frequency
selectivity and tonotopic organisation of the basilar
membrane has been modelled by the gammatone
filterbank (Patterson et al, 1992). The shape of the
auditory filters is characterised in terms of the equi-
valent rectangular bandwidth (ERB) scale (Glasberg
and Moore, 1990). This has been widely used appro-
ach in similar modelling work to represent auditory
filters in the peripheral auditory system of the mam-
mals and humans.
The gammatone filterbank has been designed as
a series of 81 eight-order IIR gammatone bandpass
filters with center frequencies spaced from 20 kHz
to 100 kHz. The implementation of this filterbank is
based on (Slaney, 1993) and modified to accommo-
date the frequency range of interest for this study.
Although there is no agreement regarding the den-
sity of frequency channels in the auditory filter and a
varying number of filters is employed in different
frequency ranges, the number of filters that has been
chosen in this study appears to be reasonable compa-
red to similar models (Sailant et al, 1983).
The mechanical motion in the basilar membrane
that resolves the frequency is further converted into
neural activity by the inner hair cells. This stage is
modelled by half-wave rectification followed by the
1st-order low-pass filtering with the cut-off frequen-
cy of 3 kHz applied in order to remove unwanted
frequency components generated by half-wave rec-
tification.
2.3 Artificial Post-processing Block
The concept of the bioinspired cochlear block results
in the multichannel output signal that represents the
auditory spectrogram-like image of the FM transmi-
ssion and echoes. It is known that the bat has ability
to transform such perceived acoustic image from the
spectral domain into spatial image that explicitly re-
veals the placements of echoes along the range axis
showing the small differences in the distance to dif-
ferent parts of the target (Saillant et al, 1993). Since
echo delays are related to distances to different parts
of the target object, by acquiring these delays infor-
mation related to the object range, size and shape is
also obtained.
In order to extract information about delay of dif-
ferent components of complex FM echoes from an
auditory image derived from the cochlear block in
the present study, it is necessary to additionally pro-
cess the output of the cochlear block. Thus, the pur-
pose of the further processing in the artificial block
is to obtain an image constructed from the delays of
different components of complex echoes.
3 RESULTS AND DISCUSSION
The backscattering impulse responses of the four
circular disks with the radiuses set to 30, 50 and
150 mm and thicknesses of 1, 15, 30 and 50 mm
BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing
302
were calculated based on acoustic modelling descri-
bed in section 2.1.1, and used for further simulation
purposes. The relative distances between the source,
receiver and the disk center of mass, are kept
constant through all simulations. The main geo-
metrical parameters used for simulations are listed in
Table 1.
Table 1: The parameter sets used in simulations.
Set no. r [mm] D [mm] d
SR
[cm] d
R
D
[cm]
1 30 1 10 150
2 50 15 10 150
3 150 30 10 150
4 150 50 10 150
For each given set of parameters, the disk place-
ment relative to the source-receiver axis is changed
by rotating the disk around its lateral axis which
results in different impulse response. The rotation
angle α is varied from 0 to 90° with 1 degree step.
The value of α=0° corresponds to the position where
the circular surfaces of the disk are perpendicular to
the source-receiver axis (marked as shaded region in
Figure 2) and α=90° corresponds to the position
where the circular surfaces are parallel with the
source-receiver axis.
In Figure 3, the estimated backscattering impulse
responses are plotted for the parameters nominated
as set 3 in Table 1 but stacked with a vertical offset
of 6x10
-5
and zoomed-in in the time interval of the
backscattering part. These responses are low-pass
filtered through a first-order Butterworth filter with
the cut-off frequency set to 200 kHz. This figure
shows the evolution of the h
ref
and h
diff
parts of
Eq. (1) as the disk rotation angle increases. As
mentioned above, the component of the impulse res-
ponse h
ref
becomes negligible and diminishes as α
increases leaving only the contribution of h
diff
in the
reflected part of the impulse response. For α=0°
(top-most response in Figure 3), the impulse respon-
se comprises a positive delta pulse due to the spe-
cular reflection from the circular face of the disk
followed by a negative delta pulse due to the
contribution of the edge diffraction from the circular
edge of the disk. In the α=0° axisymmetric geome-
try, this edge diffraction contribution is time-aligned
and hence appears concentrated in a single pulse. As
soon as the disk is rotated from the axisymmetric
degree, this time-alignment of the diffraction con-
tribution is disrupted, and the negative pulse
progressively splits into two parts, their distance
being determined by the path length difference bet-
ween the source to the leading or trailing edge-point
of the disk and back to the receiver. Furthermore, the
specular reflection pulse moves forward in time and
becomes attenuated as the reflection point on the
circular face of the disk moves outwards from the
center. For a rotation angle of α=6°, the specular
reflection part h
ref
vanishes leaving only the diffra-
ction part h
diff
in the plotted impulse responses. This
part evolves in three parts with increasing angles of
rotation. The onset of these three parts correspond to
the geometric paths from the source to the front
leading (FL) edge, back leading (BL) edge and front
trailing (FT) edge of the disk (Figure 2).
  



 

 










D
Figure 3: The backscattering impulse responses calculated
for the parameters designated as set 3 in Table 1.
The objective of the results and analysis present-
ed in the following part of the paper is to identify
these features in the spectrogram-type output of the
cochlear block output. The generated down-swept
FM signal is filtered through the backscattering
impulse response estimated for the particular disk
geometry. The impulse response of the direct
transmission path between the source and receiver
(delta pulse) is normalised to unity while the back-
scattering part of the impulse response is normalised
to 0.25. This is done with intention to enhance the
relatively small contribution of the backscattered
part to the overall impulse response and does not
have a negative affect on the results since the main
goal is to distinguish between the reflected echoes
based on their arrival times. Moreover, this approach
imitates what bats do by contracting the middle ear
muscle to attenuate the sensitivity of the ear and
decrease the intensity of the emitted pulses to the
certain level to protect the hearing system from
overstimulation (Kick and Simmons, 1984). The
resulting echolocation signal encompassing both
emission and the complex echo signal is further pro-
cessed through the gammatone filterbank and de-
composed into 81 filter channels. Each gammatone
USING BAT AUDITORY MODELLING FOR OBJECT DISCRIMINATION AND ECHO SEPARATION TASKS
303
filter is followed by half-wave rectifier and first-
order low-pass filter with cut-off frequency of 3 kHz
producing smoothed envelopes across all channels.
In order to classify the echo components present
in the spectrogram, the output of the cochlear block
is dechirped and the integration over all frequency
channels aligned in time is performed. This proce-
dure describes the function of the artificial block.
The local maxima in the overall smoothed envelope
correspond to main echo components present in the
backscattering part of the echolocation signal
(Figure 4).












 
    

 
 
Figure 4: The received echo signal (top), the dechirped
output of the cochlear block (middle) and the output of the
artificial post-processing block (bottom) obtained for the
parameters designated as set 3 in Table 1 and the rotation
angle α=30°.
The overall signal envelopes calculated for each
simulation set and the angle of rotation are plotted in
Figure 5. Two echo components from the leading
and trailing disk edges are evident in all simulation
sets for rotation angles larger than 10 degrees. The
distance between these two echoes corresponds to
the disk radius. For the disk of 50 mm radius and
15 mm thickness (set 2), the main echo component
formed by the leading disk edge splits into two sub-
components as a result of diffractions from the front
and back face edges (Figure 5a). This effect can not
been seen for the disk of only 1 mm thickness (set 1)
since the time delay between those two echo compo-
nents is less than 5 μs for all rotation angles (Figure
5b). However, for the sets 3 and 4 (Figure 5c-d),
where two disks of larger size are used, the separa-
tion effect between echo components formed by the
front and back leading edges is more significant.
Finally, time delays between the separated
echoes obtained using the model proposed in this
paper are compared with the real geometry of the
disks used in this simulation. The results of this
assessment are presented in Figure 6. Here, the time
differences between the front leading and front
trailing edges (FT-FL) and the front leading and
back leading edges (FL-BL) are calculated from the
disk geometry for each angle of rotation and compa-
red with the time delays of the main echo compo-
nents, denoted as Δt
R
and Δt
D
, derived from the
model outputs plotted in Figure 5. For this illustra-
tion, peripheral points on the front and back disk
circumferences which are farest from the axis of
rotation are chosen to represent each of these edges.
Therefore, the time differences between them are
calculated based on the path length distances from
the source to the each of these points and back to the
receiver. The rotation angle for which the back lead-
ing edge of the disk become visible is denoted as α
C
.
The main echo components are defined as local ma-
xima in the overall signal envelope. A close match-
ing between the results obtained by using the audi-
tory images with the ones defined by real geometry
of the disk is evident for all 4 simulation sets. These
demonstrate that the auditory images directly repro-
duce the geometrical parameters of the disks since
the time delays Δt
R
and Δt
D
are linked to the disk
radius and thickness.
4 CONCLUSIONS
The bat-inspired echolocation model developed in
this study and presented in this paper demonstrates
ability to separate multiple overlapping echoes that
are present in the echolocation signals formed by the
rotating disk-shaped target object. A close matching
between the results obtained by using this simulation
model with the ones defined by real geometry of the
disk proves that the proposed model has ability to
distinguish between overlapping echo components
from the disk edges and, therefore, to discriminate
between different disk-shape targets.
Further study has been carried out to enhance
the performance of the proposed echolocating model
by employing more advanced signal processing
techniques in the analysis of the spectrogram-like
auditory images. It would be also of interest to test
this model using experimentally measured back-
scattering impulse responses of different targets at
different orientations.
BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing
304
(a) Set 1 (b) Set 2
(c) Set 3 (d) Set 4
Figure 5: Auditory images of the echolocation signals
formed by the rotating disks defined in Table 1.
       








D
  P
D
 


'
'
       






D
  P
D
 


'
'
(a) Set 1 (b) Set 2
        









D
  P
D
 


'
'
(c) Set 3 (d) Set 4
Figure 6: Time differences between the front leading and
front trailing edges (FT-FL) and the front leading and back
leading edges (FL-BL) of the disk and the time delays (Δt
R
and Δt
D
) derived from the auditory images shown in
Figure 5.
ACKNOWLEDGEMENTS
The authors are very grateful to RCUK for support
through the BIAS Basic Technology Programme.
We gratefully acknowledge the use of the EDTB
code made publicly available by Prof. U.P. Svensson
of the Norwegian University of Science and Techno-
logy. The authors would also like to thank R. Collier
for proofreading of this paper and useful comments.
REFERENCES
Glasberg, B. R., and Moore, B. C. J., 1990. Derivation of
auditory filter shapes from notched noise data. Hear-
ing Research, 47(1-2), pp. 103–138.
Kick, S. A. and Simmons, J. A., 1984. Automatic gain
control in the bat’s sonar receiver and the neuroethol-
ogy of echolocation. J. Neurosci. 4, pp. 2725-2737.
Neretti, N., Sanderson, M. I., Intrator, N., and Simmons,
J.A., 2003. Time-frequency model for echo-delay
resolution in wideband biosonar. Journal of Acoustic
Society of America, 113(4), pp. 2137-2145.
Papadopoulos, T. and Allen, R., 2007. Experimental
method for the acoustical modelling of the echoloca-
tion process in bats. Proceedings of the Institute of
Acoustics, 29(3)
Patterson, R. D., Robinson, K., Holdsworth, J., Mckeown,
D., Zhang, C., and Allerhand, M. H., 1992. Complex
sounds and auditory images, Auditory Physiology and
Perception, (Eds.) Cazals, Y., Demany, L., Horner. K.,
Pergamon, Oxford.
Saillant, P. A., Simmons, J. A., and Dear, S. P., 1993. A
Computational Model of Echo Processing and Acous-
tic Imaging in Frequency-Modulated Echolocating
Bats – the Spectrogram Correlation and Transforma-
tion Receiver. Journal of Acoustic Society of America,
94(5), pp. 2691-2712.
Simmons, J. A., Saillant, P.A., Wotton, J.M., Haresign, T.,
Ferragamo, M.J., Moss, C.F., 1995. Composition of
biosonar images for target recognition by echolocating
bats. Neural Networks, 8(7-8), pp. 1239-1261.
Slaney, M., 1993. An Efficient Implementation of the
Patterson-Holdsworth Auditory Filter Bank, Apple
Computer Technical Report 35, Perception Group-
Advanced Technology Group (1993).
Svensson, U.P., Fred, R.I., and Vanderkooy, J., 1999. An
analytic secondary source model of edge diffraction
impulse responses. Journal of Acoustic Society of
America, 106(5), pp. 2331-2344.
Svensson, U.P. and Calamia, P.T., 2006. Edge-diffraction
impulse responses near specular-zone and shadow-
zone boundaries. Acta Acustica United with Acustica,
92(4), pp. 501-512.
USING BAT AUDITORY MODELLING FOR OBJECT DISCRIMINATION AND ECHO SEPARATION TASKS
305