Passive localization in the deep ocean based on cross-correlation function matching
Zhixiong Lei, Kunde Yang, and Yuanliang Ma
Citation: The Journal of the Acoustical Society of America 139, EL196 (2016); doi: 10.1121/1.4954053
View online: https://doi.org/10.1121/1.4954053
View Table of Contents: https://asa.scitation.org/toc/jas/139/6
Published by the Acoustical Society of America
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Lei et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4954053]
Published Online 14 June 2016
Passive localization in the deep ocean based on
cross-correlation function matching
1
Zhixiong Lei,1) Kunde Yang,1,a) and Yuanliang Ma2)
Key Laboratory of Ocean Acoustics and Sensing (Northwestern Polytechnical University),
Ministry of Industry and Information Technology, Xi’an 710072, China
leizhixiong@163.com, ykdzym@nwpu.edu.cn
2
School of Marine Science and Technology, Northwestern Polytechnical University,
Xi’an 710072, China
ylma@nwpu.edu.cn
Abstract: Passive localization of a sound source in the deep ocean is
investigated in this study. The source can be localized by taking advantage of a cross-correlation function matching technique. When a twosensor vertical array is used in the deep ocean, two types of side lobe
curves appear in the ambiguity surface of the localization. The side lobe
curves are analytically expressed and they are then used as indicators of
the localization result instead of the scanning point with the maximum
power. Simulation and experiment demonstrate the performance of the
proposed passive localization method.
C 2016 Acoustical Society of America
V
[DRD]
Date Received: January 5, 2016
Date Accepted: May 13, 2016
1. Introduction
In a deep ocean scenario, sound may propagate along different paths, such as direct
path, surface reflection, bottom reflection, and surface duct. When the sound source is
near the sea surface, receiving sensors can be set in deep water to reduce distant interference and relieve reflections from the bottom. This propagation path is referred to as
the reliable acoustic path (RAP).1 The existence of the RAP in the deep ocean environment enlarges the detection range when the acoustic sensor array is placed below the
critical depth, which indicates the depth at which the sound speed exceeds the sound
speed around the surface. The noise from distant sources below the critical depth is
10–25 dB (Refs. 2 and 3) lower than that at shallower depth. The diameter of the
surface coverage of the RAP is about several times the ocean depth,4 which is typically
20–35 km for a near-surface source. Techniques such as matched field processing
(MFP)5 and arrival structure matching6 can be utilized to localize the sound source in
the RAP scenario. However, for MFP in the deep ocean, the hydrophone array
[commonly a vertical line array (VLA)] requires a large aperture and a large number
of sensors to sample modes sufficiently. Arrival angles are not sensitive to depth, and
arrival time structures cannot be conveniently estimated when the prior information of
the source is not known.7 Depth-based signal separation (DBSS) technology2,8 has
recently been studied to estimate the depth of the source via the RAP; it uses the
coherent structure of the signals from the direct and surface-reflected paths. First, the
power output of the vertical beamformer is extracted along the time axis. The depth is
then recovered with a variation in the Fourier transform. The DBSS is not sensitive to
the sound speed profile (SSP) and is suitable for the scenario where a relatively long
time recording is available. In a multipath environment, the geometrical information
on the source location implied in the time delay and time delay difference of arrivals
can be utilized by using correlation-based array processing methods.9,10 A broadband
coherent matched-field processor was proposed and then applied to experimental
data by matching measured and modeled cross spectra and summing coherently over
frequency.11 The weighted least-square range and depth estimators for a vertical sensor
array in a two-path environment were developed with performance analysis.10 Much
research has demonstrated good performance using correlation-based methods in
passive source localization.12–14
In this study, the cross-correlation function-based passive localization (CCL)
method is investigated under the assumption that the signal from the source is broadband. Analytic expressions of two CCL trajectories are derived. The simulations show
that the trajectories indicate the maximum power point of the CCL, and may thus be
a)
Author to whom correspondence should be addressed.
EL196 J. Acoust. Soc. Am. 139 (6), June 2016
C 2016 Acoustical Society of America
V
Lei et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4954053]
Published Online 14 June 2016
treated as alternative indicators of the CCL. The method is verified through experimental data from an explosive sound source in the deep ocean environment.
2. Passive localization based on cross-correlation matching
When the signal emitted from the source is broadband and the waveform is known, a
matched filter can be used to estimate the time delay, which can be used to localize the
source. However, the assumption of a known waveform is not realistic in practice. An
alternative approach is to extract the information contained in the cross-correlation
between two hydrophones. In this way, the time delay does not need to be estimated
directly. The CCL method has been well established in previous work.10–14 A simplified description of this method is given in the following paragraphs.
A VLA with two hydrophones is assumed to be deployed in the deep ocean
[Fig. 1(a)]. The depth of the two sensors are z1 and z2 (z1 < z2 ). The depth of the
source is zs , and the horizontal distance between the vertical array and the source is r.
The signal emitted from the source is sðnÞ [discrete samples of sðtÞ]. Therefore, the
received signal can be expressed as
xp ðnÞ ¼ hp ðr; zs Þ sðnÞ þ ep ðnÞ;
(1)
where p 2 f1; 2g is the subscript denoting a specific hydrophone, and hp ðr; zs Þ
¼ +i gp;i ðr; zs Þdðn np;i ðr; zs ÞÞ is the transfer function between the source and the pth
receiver. Here, gp;i ðr; zs Þ and np;i ðr; zs Þ are the amplitude and the time delay of the ith
eigen ray of the pth receiver, respectively. dðnÞ denotes the unit sample function, and
ep ðnÞ denotes the noise. If the signal and the noise are not correlated, then the crosscorrelation function between the received signals is
N
1X
x1 ðnÞx2 ðn mÞ
N n¼1
X
g1;i g2;j Rss ðn1;i n2;j mÞ þ R1 ðmÞ ;
¼
R ðm Þ ¼
(2)
i;j
N
N
where Rss ðmÞ ¼ ð1=NÞ+n¼1 sðnÞsðn mÞ, and R1 ðmÞ ¼ ð1=NÞ+n¼1 e1 ðnÞe2 ðn mÞ. The
noise is assumed to be independent and identically distributed; accordingly, R1 ðmÞ 0.
If the signal is broadband, the cross-correlation function will have peaks at
m ¼ n1;i n2;j . In the deep ocean scenario, the direct and surface-reflected paths dominate the arriving wave. Equation (2) can then be approximately rewritten as
RðmÞ g1;D g2;D Rss ðn1;D n2;D mÞ þ g1;D g2;S Rss ðn1;D n2;S mÞ
þ g1;S g2;D Rss ðn1;S n2;D mÞ þ g1;S g2;S Rss ðn1;S n2;S mÞ ;
(3)
where the subscripts D and S denote the direct and surface-reflected paths, respectively.
Equation (3) indicates that the cross-correlation function has four distinct peaks. Let
peaks A and D represent the peaks appear at n1;D n2;S and n1;S n2;D in the crosscorrelation function, respectively. Peaks B and C correspond to the other two peaks in
the function. The peak structures can be used for passive localization by matching
them with the replica. For a scanning position ðr; zs Þ, the transfer function on each
hydrophone can be computed using an ocean acoustic model, such as Bellhop.15 The
normalized replica wðm; r; zs Þ is then derived through cross-correlation between the
Fig. 1. (Color online) (a) Sound source localization in the deep ocean with two hydrophones. (b) Numerical
localization result of the CCL. The function values are normalized to the maximum value and the color scale is
in decibels.
J. Acoust. Soc. Am. 139 (6), June 2016
Lei et al. EL197
Lei et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4954053]
Published Online 14 June 2016
transfer functions of the two hydrophones. Selecting a sufficiently large point number
N and truncating the terms out of N can yield the objective function for the CCL as
N
1 X
wðn; r; zs ÞRðn mÞ:
(4)
f ðr; zs Þ ¼ max
m N
n¼1
Compared with traditional passive localization methods, the CCL does not need to
estimate the multipath time delay and the prior information of the source waveform,
and it can work with only two hydrophones. Figure 1(b) shows the localization result
when the replica is numerically computed by the Bellhop with r ¼ 10 km, zs ¼ 200 m,
z1 ¼ 4410 m, and z2 ¼ 4910 m. The SSP is supposed to be the Munk profile, and the
ocean depth is 5400 m. The sound source emits a wideband random signal with a
frequency of 50–500 Hz. The signal-to-noise ratio is 10 dB. The sampling frequency is
10 kHz, and the length of the extracted signal to compute the cross-correlation function is 0.1 s.
The scanning point with the maximum power in Fig. 1(b) (red point in the
rectangular box) corresponds to the true location of the source. Two types of side lobe
curves occur. After considerable numerical simulations with different parameters, we
find that two types of curves appear all the time, of which the intersection point always
lies on the scanning point corresponding to the true position of the source. If this
feature structure is stable, then the source location can be indicated by the intersection
of the two curves instead of the maximum power point, and it may reduce the ambiguity of the localization process.
3. Side lobe curve analysis
Suppose that t1;D , t1;S , t2;D , t2;S [Fig. 1(a)] represent the arrival times that correspond
to the samples n1;D , n1;S , n2;D , n2;S , respectively. When environmental parameters and
positions of hydrophones are given, the arrival times are functions of the range r and
the depth zs . In the range-depth plane, equations of these arrival times represent
curves. For brevity, we omit variables r and zs in the notations where time arrivals are
involved. The side lobe curves in Fig. 1(b) can be represented by Eqs. (5) and (6),
respectively,
ðt1;D t2;D Þ ðt1;S t2;S Þ ¼ ðt01;D t22;D Þ ðt01;S t02;S Þ;
ðt1;D t2;S Þ ðt1;S t2;D Þ ¼
ðt01;D
t02;S Þ
ðt01;S
t02;D Þ;
(5)
(6)
where t01;D ; t01;S ; t02;D ; t02;S are the values that correspond to the true location of the
source ðr0 ; zs0 Þ. Here, constant SSP
is used to simplify the derivation.
By using image
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
theory,16 we obtain tp;D ¼ r2 þ ðzp zs Þ2 =c, tp;S ¼ r2 þ ðzp þ zs Þ2 =c, t0p;D
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼ r0 2 þ ðzp zs0 Þ2 =c, and t0p;S ¼ r0 2 þ ðzp þ zs0 Þ2 =c, where p 2 f1; 2g, and c is the
sound speed. Each equation is difficult to solve because the four square roots complicate the simplification. The true location ðr0 ; zs0 Þ lies on both curves and becomes one
of the obvious, possible intersections of the curves. Let l1 ðr; zs Þ ¼ ðt1;D t2;D Þ ðt1;S t2;S Þ and l2 ðr; zs Þ ¼ ðt1;D t2;S Þ ðt1;S t2;D Þ. Considering that the depth of the sources is smaller than the depth of the hydrophones, l1 and l2 can be approximated with
the Taylor series expansion up to the third order at point zs ¼ 0, which yields
0
1
2z1
2z2
l1 ðr; zs Þ @ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiAzs
(7)
r2 þ z21
r2 þ z22
and
0
1
2z1
2z2
l2 ðr; zs Þ @ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiAzs :
r2 þ z21
r2 þ z22
(8)
Inserting Eqs. (7) and (8) into Eqs. (5) and (6), respectively, and solve the two simultaneous equations, we get
r2 r20 :
(9)
Given that the range cannot be negative, r ¼ r0 . Inserting r ¼ r0 into Eq. (5) or Eq. (6)
derives zs ¼ zs0 . So the intersection point denotes the true location of the source.
EL198 J. Acoust. Soc. Am. 139 (6), June 2016
Lei et al.
Lei et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4954053]
Published Online 14 June 2016
Although the preceding derivations are under image theory, they can give us
insights into the reason for the appearance of the side lobe curves. The curves that correspond to Eqs. (5) and (6) are computed using the arrival time generated by Bellhop
with the Munk profile to verify the compatibility in different environments (parameters
are the same with the simulation in Sec. 2). The curves computed by Eqs. (5) and (6)
are represented in Fig. 1(b) using pink dashed curves C1 and C2 . It is noted that C2 is
also centered in the bundles of other stripes. But these stripes are weaker than the side
lobe curve which is covered by C2 . These stripes are caused by other arrivals, such as
the arrival from bottom reflection. In the deep ocean, these arrivals have larger transmission losses and they are less important in our case.
The side lobe curves above imply that the cross-correlation matching has two
structures that dominate the ambiguity. Four distinct peaks exist in the crosscorrelation function, as stated in Sec. 2. Note that the peaks appear at n1;D n2;S and
n1;S n2;D in Eq. (3) are denoted by peaks A and D, respectively. The other two peaks
are denoted by peaks B and C. A comparison of Eqs. (5) and (6) indicates that curve
C1 represents the point set in which the corresponding distance between peaks B and
C equals a specific constant value. Similarly, curve C2 represents the point set in which
the corresponding distance between peaks A and D equals a specific constant value.
The intersection point of C1 and C2 then satisfies the two distance conditions. The two
curves are always accompanied by the maximum power point, and can thus be indicators of the localization result. As shown in Fig. 1(b), curve C2 has a larger power and
a shallower width than curve C1 . In general, if the distance between peaks B and C
increases, the width of C1 decreases. For a specific range, the distance between peaks
B and C increases as the depth of the sound source and the spacing between the hydrophones increase. Figure 2 shows the simulation when the range is 16.8 km and the
depth of the deeper hydrophone is 4218.6 m. The sampling frequency is 25 kHz (the
parameters are selected to be consistent with the following experiment). The distances
between peaks B and C are generated for different source depths and hydrophone
spacings under homogeneous water column assumption (using image theory). Thus,
when the CCL is used in practice, a large spacing between the two hydrophones yields
good localization performance.
4. Experiment
Localization performance was determined via an experiment. In the experiment, a
VLA consisting of 16 elements with 4 m spacing was deployed in the deep ocean. The
depth of the first hydrophone (the shallowest) was 4158.6 m. The bottom depth of the
ocean was 4390 m. The SSP is shown in Fig. 3(a). An explosive charge [100 g
Trinitrotoluene (TNT)] was used as the wideband sound source, 16.83 km away from
the VLA. The explosive charge was automatically triggered when it reached the depth
of 50 m. The sampling frequency was 25 kHz. Signals received by the 1st and 16th
hydrophones, represented by s1 and s16, respectively, were used to localize the explosive
source, as shown in the top and middle panels of Fig. 3(b). Although the secondary
pressure pulses caused by gas globe oscillation would appear in the underwater explosion,17 we did not take specific steps to eliminate these pulses in the time domain
because no distinct degradation occurred in passive localization performance. The
Fig. 2. Distribution of distance (unit in samples) between peaks B and C for different source depths and hydrophone spacings when the range is 16.8 km.
J. Acoust. Soc. Am. 139 (6), June 2016
Lei et al. EL199
Lei et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4954053]
Published Online 14 June 2016
Fig. 3. (Color online) (a) SSP in the experiment. (b) Received signals (top and middle panels) and absolute value
of the cross-correlation function (the bottom panel). (c) Localization of the explosive source (estimation denoted
by the intersection of two dashed lines). The function values are normalized to the maximum value and the color
scale is in decibels.
absolute value of the normalized cross-correlation sequence is shown in the bottom
panel of Fig. 3(b). In the localization computations, the scanning depth points started
from 10 to 500 m with intervals of 2 m, and the scanning range points started from 2 to
20 km with intervals of 0.1 km. The matching result shown in Fig. 3(c) suggested that
the estimated depth and range were 55 m and 17 km, respectively (the intersection of
two dashed lines denotes the estimation). Curve C2 is more distinct than C1 . The
enhancement of C1 needs further research to make the localization robust.
5. Conclusion
In this study, a passive localization method based on the matching of cross-correlation
functions of two hydrophones in the deep ocean is investigated. The localization
method needs no prior information about the source, provided it is broadband. Two
side lobe curves accompanying the maximum power point of the CCL are analytically
expressed under image theory. The simulation and experiment show that the two
curves can be represented exactly using two equations, and the intersection of the
curves indicates the location of the sound source.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant
No. 11174235), and the Fundamental Research Funds for the central Universities (Grant
No. 3102014JC02010301).
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