2010 Asia Pacific Conference on Circuits and Systems (APCCAS 2010)
6 – 9 December 2010, Kuala Lumpur,Malaysia
Quadratic Phase Coupling Analysis for Infrasound
Vehicle Detection
Renshi Li, Vinod V. Reddy and Andy W. H. Khong
School of Electrical and Electronic Engineering
Nanyang Technological University, Singapore
Email: {rsli, e060001, andykhong}@ntu.edu.sg
Abstract—The low attenuation characteristic of infrasound
enables it to propagate long distances making it possible for the
detection of infrasound sources. In this paper, a comparison in
terms of the detection range between an acoustic microphone and
an infrasound sensor in the context of vehicle detection is made.
We propose to employ the bispectrum based quadratic phase
coupling (QPC) analysis to extract characteristic frequencies of
the vehicle signal. These frequencies can subsequently be used
to detect the presence of the vehicle in order to evaluate the
sensors’ detection range. Experimental results show that the QPC
outperforms the power spectrum estimation method for vehicle
detection. In addition, it is found that the infrasound sensor
outperforms the microphone in terms of vehicle detection range
under the same test condition.
I. I NTRODUCTION
Infrasound is defined as an acoustic phenomenon between
0.01 to 20 Hz [1]. Due to the frequency response of the human
ear, these low frequency signals cannot be detected by humans
and require microbarometers capable of low frequency data
acquisition for detection. It is also well known that natural
sources of infrasound include volcanic eruptions, earthquakes
and tsunami while man-made infrasound sources include space
shuttle launches, high-speed aircrafts and vehicles [1].
Due to the relatively low atmospheric absorption for low
frequency signals, infrasonic waves can propagate over long
distances in the atmosphere [1]. In addition, the ground serves
as a good reflecting surface that reflects most of the incoming
energy for low frequency waves [2]. Contrary to the poor
detection capability of radars for low-altitude flying aircrafts,
studies have also shown that infrasound sensors provide an
excellent sensing device since acoustic energy increases with
reducing altitude.
Since the 1970s, vehicle detection has been widely applied
and there is a great demand for applications including vehicle
detection for traffic control and management. Current highway
monitoring systems using magnetic loop detectors or high resolution video cameras have limitations in terms of scalability
and costs [3]. On the other hand, laser radar combined with
data fusion technology is often cumbersome and expensive.
As opposed to the above techniques, vehicles may be detected
from the infrasound signals they emit when their engines are
running. It is therefore conceivable that commercial vehicles
such as car, bus, and lorry can be used as infrasound sources
for data collection.
978-1-4244-7456-1/10/$26.00 ©2010 IEEE
In this work, we propose an algorithm for vehicle detection
in the infrasound frequency range. We propose to achieve this
detection by identifying characteristic frequencies (CFs) of the
vehicle. As will be shown in our experimental results, although
these CFs are slightly above that of the 20 Hz, we classify
these frequencies as infrasound. We take into account the
non-linearity between frequency components of the infrasound
signal and we propose to employ the quadratic phase coupling
(QPC) analysis for the identification of such CFs. These
identified CFs will in turn allow us to determine if a vehicle is
present in the vicinity. Utilizing this technique,we show that
the QPC analysis can better extract the CFs compared to the
well-known power spectral density (PSD) estimation method
for vehicle detection. More importantly, the proposed method
of extracting CFs from a received signal allows us to compare
the detection range between the microphone and an infrasound
sensor.
II. R EVIEW OF THE PSD
FOR
V EHICLE D ETECTION
Several approaches have been proposed for vehicle detection
over the past decade. In [3], vehicle detection is achieved
by both high and low frequencies. In addition, vision based
vehicle detection techniques such as presented in [3] have also
been proposed. These techniques extract CFs from the signal
image and require computational intensive video processing
algorithms for vehicle detection. As noted, vehicle detection
is often based on such CFs and therefore, identification of
these CFs is important for vehicle detection. By far, one of
the most commonly used technique for the identification of
CFs is through the use of PSD estimate.
The PSD maps a time-domain signal into the frequency
domain and is a common technique for analyzing a received
signal of unknown characteristics. Such frequency analysis
has been applied for speech bandwidth reduction, sonar systems localization and estimation of target location/velocity
information in radar signals. Furthermore, it has been found
that signals emitted from the vehicle are characterized by
the harmonic frequencies [4] and therefore, the PSD may be
suitable to extract these CFs.
We review the estimation of the PSD by first defining
x(n) as the received signal of a sensor with auto-correlation
sequence
891
rxx (m) = E x(n + m)x(n) ,
(1)
2010 Asia Pacific Conference on Circuits and Systems (APCCAS 2010)
6 – 9 December 2010, Kuala Lumpur,Malaysia
4
where n and m are time indices while E[·] is the expectation
operator. Defining f as the normalized frequency and assuming that the auto-correlation sequence of the signal has been
estimated for lags −L ≤ n ≤ L, the PSD Pxx (f ) can be
estimated using the Wiener-Khinchine theorem from which
L
Pxx (f ) =
−j2πnf
rxx (n)e
,
6
(2)
III. V EHICLE D ETECTION VIA QPC A NALYSIS
In PSD estimation, only linear mechanisms governing the
process are analyzed since phase relations between spectral
components are suppressed [5]. The information contained in
the power spectrum would suffice for the complete statistical
description of a Gaussian process with known mean. However,
practical scenarios exist where one needs to look beyond the
power spectrum to obtain information pertaining to any deviations from Gaussianity and the presence of nonlinearities [6].
To address the shortcomings of second-order statistics, higher
order statistics have been proposed.
The third order moments of a received signal x(n) is given
by [6]
(3)
C3x (k, l) = E x(n)x(n + k)x(n + l) ,
where k and l are integers. Furthermore, the third-order
polyspectrum (bispectrum) is defined as the Fourier transform
of the corresponding cumulant sequence given by [6]
S3x (f1 , f2 ) =
∞
∞
C3x (k, l)e−j2πf1 k e−j2πf2 l .
(4)
k=−∞ l=−∞
In contrast to the power spectrum being real and nonnegative,
the bispectrum is complex and is a function of two frequencies.
It is important to note that the nonlinear interaction between
harmonic components often results in phase coupling. As an
illustrative example, three harmonics with frequencies fk and
phases φk , k = 1, 2, 3, are said to be quadratically phase
coupled if f3 = f1 + f2 and φ3 = φ1 + φ2 . The process
of generating these multiple phase relations is known as the
QPC. Unlike QPC, the PSD peaks at frequencies irrespective
of the phases of signal waveforms and hence, the information
pertaining to phase relations is lost.
In practice, if a parametric model such as pth-order autoregressive (AR) model is used, the bispectrum of x(n) can be
obtained by [7]
x(n) +
p
ai x(n − i) = w(n),
i=1
where w(n) is another non-Gaussian process with
E[w(n)] = 0,
E[w(n)w(n + k)] = αδ(k),
E[w(n)w(n + k)w(n + l)] = βδ(k, l),
(5)
5
Bispectrum Peak
60
4
2
f (Hz)
80
n=−L
√
where j = −1, L ≈ N/10 and N is the total number of
samples within a windowed sequence of x(n) while rxx (n) is
the estimate of rxx (n) defined in (1).
x 10
100
40
3
20
2
0
1
0
20
40
60
f1 (Hz)
80
100
Fig. 1. QPC analysis of stationary lorry test at 10 m away recorded by
infrasound sensor.
such that δ is an impulse function, ai is the AR model
parameter and α, β are constants. The bispecrum can then
be obtained by [8]
S3x (f1 , f2 ) = βH(f1 )H(f2 )H ∗ (f1 + f2 ),
(6)
where H(f ) is the transfer function of the process such that
H(f ) =
1+
1
.
−j2πf i
i=1 ai e
p
(7)
The third order moment is obtained by applying (3) to (5)
C3x (−k, −l) +
p
ai C3x (i − k, i − l) = βδ(k, l).
(8)
i=1
Equation (8) is denoted as the third-order recursion which can
be solved using the Levinson’s algorithm [7].
Figure 1 shows an example QPC analysis of infrasound data
for a stationary lorry positioned at 10 m from the sensors. The
recorded data is sampled at 44.1 kHz and filtered with a lowpass filter (with a cut-off frequency of 100 Hz) before being
downsampled to 1 kHz. This plot is generated using (4) where
the color indicates the amplitudes of the bispectrum for the
signal. The x- and y-axis are two frequencies corresponding to
f1 and f2 in (4). It can be seen from Fig. 1 that the maximum
energies of the bispectrum for infrasound data are centered
at approximately (25 Hz, 25 Hz) while no significant peaks
are detected for the high frequencies. This illustrative example
also indicates that the 25 Hz frequency is phase coupled with
itself.
IV. E XPERIMENTAL R ESULTS
We now investigate and compare the detection range between the infrasound sensor and a microphone for a vehicle.
We also compare the detection performance between the PSD
and QPC. The focus here is to apply such techniques for the
identification of CFs which in turn allows one to estimate the
detection range of the sensors. The target vehicle is positioned
at various distances from the closest point of approach (CPA)
to determine the detection range of the sensors.
The infrasound data acquisition system consists of a
PreSonus A/D converter, two portable 12 V batteries, a laptop,
and an infrasound sensor. In addition, a microphone supplied
892
2010 Asia Pacific Conference on Circuits and Systems (APCCAS 2010)
6 – 9 December 2010, Kuala Lumpur,Malaysia
B. Vehicle Detection Using PSD
We investigate how the PSD varies with distance for the
CF identified in Section IV-A. As described, the CF of our
vehicle is located at low frequency range. Therefore, both
the infrasound data and microphone data are filtered with a
low-pass filter with a cut-off frequency at 500 Hz. Data is
then processed using the correlation based PSD estimate using
L=10000.
Figure 3 (a) and (b) show how the magnitude of 25 Hz
varies with distance for data collected by the microphone and
the infrasound sensor, respectively. The average background
PSDs across frequencies and three independent recordings
have also been included for these sensors as a reference.
As can be seen, the PSD of the identified CF reduces with
increasing distance for both sensors. More importantly, we
10
Magnituede (dB)
Magnituede (dB)
0
-10
-20
-30
-40
0
-10
-20
-30
-40
0
10
20
30
Frequency (Hz)
0
40
10
(a)
40
5
Magnituede (dB)
Magnituede (dB)
20
30
Frequency (Hz)
(b)
0
A. Identification of CFs
-10
-20
-30
0
-5
-10
-15
-20
-40
0
10
20
30
Frequency (Hz)
10
40
(c)
20
30
Frequency (Hz)
40
(d)
Fig. 2. The PSD estimation of 10 m test recorded by (a) microphone and
(b) infrasound senors and background test recorded by (c) microphone and
(d) infrasound sensor.
20
20
(a)
(b)
15
Magnitude in dB
15 Microphone PSD
Magnitude in dB
Identification of the feature frequencies of the vehicle is
important since detection range can only be determined after
these frequencies have been identified. Therefore, the PSDs of
background and vehicle signals are first compared to determine
these CFs.
Figures 2 (a) and (b) show, for the microphone and infrasound sensor respectively, the PSD of the stationary vehicle
positioned at 10 m away from the CPA. The recorded data
from these sensors were first downsampled to 1 kHz after
which the PSD was computed using a window size of 256
with an overlapping factor of 50%. Figures 2 (c) and (d) show
PSD of the background recording for the microphone and
infrasound sensor, respectively. Comparing Figs. 2 (a) with (c)
for the microphone and Figs. 2 (b) and (d) for the infrasound
sensor, it is found that the energy of 25 Hz is significantly
higher when a vehicle is 10 m away compared to that of the
background recording.
In addition to the above, additional experiments indicated
that 50, 75 and 100 Hz also have significant energies. It is
useful to note that these frequencies are the harmonics of
25 Hz which in turn verifies that 25 Hz is a CF of the vehicle.
We note that although 25 Hz is identified as the CF, this CF can
vary within ±2 Hz due to variation of the engine revolution
and environmental interference.
20
10
by Panasonic (WM-61A) is employed as a reference for the
comparison of the detection range. The infrasound sensor is
supplied by Chaparral Physics (Model 25) and has a frequency
response ranging from 0.14 to 200 Hz. The infrasound data
is collected in the northern part of Singapore, where there is
thick vegetation.
The sensors were positioned on an elevated grass patch
beside the CPA which is approximately 10 m away from the
control station. Each data collection lasts approximately 30 s
and data is collected at a sampling rate of 44.1 kHz. This long
duration is due to the low frequency signals involved. Most
of the infrasound data were recorded at mid-night in order to
reduce traffic interference during recording. A Nissan Cabstar
lorry is used as a source for all vehicle tests.
10
Infrasound PSD
10
5
Background PSD
0
5
0
-5
-5
-10
-10
0
50
100
150
Distance (m)
200
250
Background PSD
0
50
150
100
Distance (m)
200
250
Fig. 3. Vehicle detection using PSD based on 10 m test recorded by (a) the
microphone and (b) the infrasound sensor.
note that the PSD for the data collected by the microphone
shown in Fig. 3 (a) reduces to background noise level when
the vehicle is more than 50 m away from the sensor. The
PSD of the infrasound is also found to be significantly higher
than that of the microphone. This implies that the infrasound
sensor is expected to achieve a longer detection range than the
microphone.
C. Vehicle Detection Using QPC
Although the correlation-based power estimation discussed
in Section IV-B provides valuable information of the recorded
data in terms of vehicle detection, its limitations are evident.
As such we propose the use of QPC analysis for the identification of CFs for vehicle detection. The preprocessing of data
for QPC analysis follows the same as in Section IV-B except
that the received signals are filtered with a low-pass filter with
a cut-off frequency of 100 Hz since the CF is a low frequency.
In the implementation, we have selected the maximum number
of third-order moment lags as 1000 with p=600. We have also
used L=500 with a frame size of 100 and an overlapping factor
893
2010 Asia Pacific Conference on Circuits and Systems (APCCAS 2010)
6 – 9 December 2010, Kuala Lumpur,Malaysia
TABLE I
QPC ANALYSIS OF MICROPHONE DATA AND INFRASOUND DATA IN
VEHICLE DETECTION .
100
80
Dist. (m)
CPA(=10)
50
100
150
200
250
2
f (Hz)
Peak for Microphone Data
60
40
20
0
0
20
40
60
80
100
Maximum Amp.
Microphone Infrasound
44718
71359
466
352
584
754
417
2449
492
632
2453
1118
Peak Location(f1 ,f2 )
Microphone Infrasound
(25, 25)
(25, 25)
(49, 13)
(28.6, 26)
(26, 23)
(26, 26)
(26, 26)
(28, 25)
(26, 26)
(27, 26)
(5, 5)
(26, 26)
f1 (Hz)
Fig. 4. Vehicle detection using QPC based on 50 m test recorded by the
microphone.
100
80
2
f (Hz)
Peak for Infrasound Data
60
40
20
0
0
20
40
f1 (Hz)
60
80
(+1◦ 26 42.02 , +103◦ 42 27.93 ) in a forested area where
the acoustic energy is obscured by the surrounding thick
vegetation. We therefore expect this detection range to
increase significantly for vehicular detection in open areas.
Comparing results obtained in Table I and that obtained by
PSD in Section IV-B, the QPC is more effective than PSD for
vehicle detection. The QPC analysis has shown to be more
robust for vehicular detection over longer distance for the
infrasound sensor.
V. C ONCLUSION
100
Fig. 5. Vehicle detection using QPC based on 50 m test recorded by the
infrasound sensor.
of 50%. We note that since the amplitude of the bispectrum
is highly related to the parameters, they have to be equivalent
for both experiments before the scales of the bispectrum can
be compared meaningfully.
Figures 4 and 5 show the QPC analysis plots for the
microphone and infrasound data respectively when a stationary
lorry is positioned at 50 m from the sensors. As can be seen
from Fig. 4, the maximum amplitude of the QPC for the
microphone data is located at (49, 13) Hz. This implies that the
second harmonic CF is phase coupled with its half frequency
13 Hz. The maximum peak for the infrasound data in Fig. 5
is located at (25, 25) Hz as before.
Applying above method to the recorded data at different
distances, the maximum bispectrum magnitudes and their
corresponding frequencies are listed in Table I. It can be
seen that the peaks of the QPC are mostly located in the
neighborhood region of (25 ± 2 Hz, 25 ± 2 Hz). This implies
that the 25 ± 2 Hz frequency is phase-coupled with itself. It is
also found that the maximum magnitudes of the QPC obtained
from the infrasound sensor are larger than those obtained from
the microphone except for the 50 m and 250 m test cases.
These deviations could be due to the presence of interference
contributed by environmental factors. This suggests that the
infrasound sensor has a larger detection range than that of the
microphone. Based on the high QPC values obtained from the
infrasound sensor compared to that of the microphone, it is
expected that the infrasound sensor can detect vehicles as far
as 250 m.
Although this detection range is not excessively
high, we note that this experiment was conducted at
The QPC analysis has been applied to multiple data sets
including background and stationary vehicle tests at different
source-sensor ranges. Results show that QPC is more effective
than PSD for vehicle detection. It is also shown that an
infrasound sensor provides a higher detection range over
a microphone from either PSD or QPC analysis. Although
limited improvement on the signals can be observed for the
QPC analysis, QPC analysis has shown to be more robust
for vehicular detection over longer distance for the infrasound
sensor.
ACKNOWLEDGMENT
The authors would like to thank Mr. Xiang Li and Mr. KaiEn Yap for their contributions in terms of data collection.
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