Use of Variable Threshold Detection in Time of Arrival Measurements
for SBL Underwater Acoustic Positioning Systems
SHINGO YOSHIZAWA
Faculty of Engineering,
Kitami Institute of Technology,
Koen-Cho 165, Kitami, 090-8507,
JAPAN
Abstract: - Underwater acoustic positioning systems (UAPSs) are used to know the positions of underwater
vehicles and sensors. In short baseline (SBL) acoustic positioning systems, the three-dimensional position is
localized by the measured distances, where the distance is obtained by estimating the time of arrivals (TOAs).
In underwater acoustics, the TOA measurement errors are caused by acoustic reflection and ambient noise. The
typical TOA measurement is done by detecting the time location of the maximum correlation peak. This peak
detection causes a measurement error when the first peak is not the maximum amplitude. We propose the
variable threshold detection to keep high positioning accuracy in highly reflective and noisy environments. The
results of our simulation and experiment have proved the effectiveness of the proposed method.
Key-Words: - Underwater acoustic positioning systems, short baseline, time of arrival, multipath interference,
acoustic reflection, variable threshold.
Received: May 14, 2024. Revised: October 17, 2024. Accepted: November 13, 2024. Published: December 27, 2024.
1 Introduction
Underwater acoustic positioning systems (UAPSs)
play an important role in knowing the positions of
underwater vehicles such as remotely operated
vehicles (ROVs) and autonomous underwater
vehicles (AUVs), [1], [2]. In addition, the UAPS is
essential for sensor nodes to be aware of their
positions in underwater acoustic sensor networks,
[3], [4]. The operation methods of UAPS are
generally categorized into three types, called as long
baseline (LBL), short baseline (SBL), and ultra-
short baseline (USBL), [5]. In LBL and SBL, the
three-dimensional position is localized by the
measured distance, where the distance is obtained
by estimating the time of arrivals (TOAs). USBL
estimates the time difference of arrivals (TDOAs)
with a small array of receiver elements.
In USBL, we tackled the improvement of
TDOA measurement under highly reflective and
noisy environments. A TDOA is computed from an
arrival time difference between received signals by
a correlation function, where generalized cross-
correlation with phase transform (GCC-PHAT) [6]
and matched filter (MF) [7] are typically used.
However, the TDOA measurement is strongly
influenced by the reflection of sound waves. In
underwater acoustics, many reflected waves are
caused by the reflection on the water surface,
bottom, and obstacles. This phenomenon is known
as multipath interference, which generates the
pseudo-peaks in the correlation function.
In our previous work, we presented impulse
response-based GCC-PHAT (IR-GCC-PHAT) to
cope with multipath interference, [8]. IR-GCC-
PHAT computes a time difference by taking a cross-
correlation between two impulse responses. We
demonstrated that IR-GCC-PHAT shows higher
position accuracy than GCC-PHAT and MF in the
evaluation of simulation and experiment.
The appropriate receiver element spacing in
USBL is less than several tens of centimeters. When
the element spacing is more than one meter in SBL,
we should consider the DOA estimation errors when
the sound waves arriving at the two receiver
elements cannot be assumed to be plane waves. In
SBL, the target of a sound source is localized by
multiple distances.
This paper focuses on improving the TOA
measurement algorithm. In typical TOA
measurements, the cross-correlation function
between received and reference signals is computed
and a TOA is detected by the maximum correlation
peak, [9]. This method sometimes induces
estimation errors in a highly reflective environment,
where some of the multipath signals are received
stronger than the line-of-sight (LoS) signal. The
fixed threshold detection is effective for highly
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
252
Volume 23, 2024
reflective environments [10], where the first peak
correlation is at least 50% of the maximum
correlation is detected.
The fixed threshold detection is robust with
acoustic reflections, however the detection
performance decreases under noisy environments. In
this paper, we propose a new method of using
variable threshold detection that the peak detection
is stable in both reflective and noisy environments.
The key idea is to use the TDOA measurement
algorithm such as IR-GCC-PHAT to check whether
a threshold is appropriate.
In this paper, we set a goal to locate two-
dimensional coordinates by the TOA measurement.
When the positioning target is an underwater robot,
an accurate z-coordinate position is available by
employing a depth sensor. For example, we
demonstrated that the use of a single TDOA and
depth information provides higher positioning
accuracy than multiple TDOAs in USBL, where we
evaluated positioning accuracy by the condition of
one source and two receiver elements.
This paper is organized as follows. Section 2
introduces the methods for calculating positioning
coordinates and compares positioning accuracy
between TDOA and TOA measurements in UBSL.
Section 3 explains the conventional detection
methods in the TOA measurement. Section 4
presents the proposed detection method. Section 5
reports the experimental results in acoustic
positioning. Section 6 discusses the proposed and
conventional methods given the simulation results.
Section 7 summarizes our work.
2 Calculation Methods of Positioning
Coordinates
2.1 Two-dimensional Localization
We assume that the two-dimensional coordinates are
calculated assuming that the height positions of the
sound source and the receiver elements are the
same. When the height position of the sound source
is known, as measured by the depth sensor, the
conversion from two-dimensional to three-
dimensional coordinates is straightforward.
There are two methods to calculate the
positioning position of a target using two receiver
elements. The first method calculates with one angle
of arrival and one distance, and the second method
calculates with two distances.
The two methods of calculating positioning
coordinates are illustrated in Figure 1. Note that the
angle of arrival and the distance are estimated by
TDOA and TOA measurements, respectively. When
the coordinates of the sound source and receiver
elements are represented by and
, the coordinates of source in Figure 1(a)
are calculated as: (1)
(2)
, (3)
where is the angle of arrival and is the distance
between the sound source and the first receiver
element. The underwater sound speed and receiver
element space are expressed by [m/s] and [m].
As for the localization by the measurement of
TOAs in Figure 1(b), the coordinates of source are
calculated as:
(4)
, (5)
where and are the distances between the sound
source and the first and second receiver elements.
Fig. 1: Methods of calculating positioning
coordinates
2.2 TDOA Measurement
Although most of the explanations in TDOA
algorithms have been made in [8], we describe some
of them again for readability.
Two received signals and can be
modeled by using a transmitted signal and
impulse responses and that express a
propagation path from a transmitter to a receiver as
(6)
(7)
where indicates a discrete time index and shows
a convolution operation. and are noise
x
y
x
y
(a) Measurement of a TDOA (b) Measurement of TOAs
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
253
Volume 23, 2024
components uncorrelated with the transmitted
signal. The received signals can be expressed in
frequency domain as:
) (8)
(9)
indicates the discrete Fourier transform for
samples and denotes a discrete frequency index.
GCC-PHAT algorithm [6] is given by the
following equation:
(10)
The time difference is detected by the highest peak
detection as:
(11)
The estimated time difference is converted into
the angle of arrival as explained in (3).
IR-GCC-PHAT algorithm is the improved
version of GCC-PHAT [8]. In UAPS, an artificially
generated signal such as a pseudo-noise (PN) code
sequence can be utilized as a sound source. It
indicates that ( in frequency domain) can
be treated as a known parameter. IR-GCC-PHAT
directly computes the two impulse responses by the
frequency-domain division that is expressed as
(12)
. (13)
The time difference can be detected by the
cross-correlation function after taking absolute
values for the two impulse responses:
(14)
(15)
(16)
(17)
IR-GCC-PHAT is robust with noisy and
reverberant environments and provides higher
positioning accuracy than GCC-PHAT and MF.
2.3 TOA Measurement
There are two methods of distance measurement in
UAPS. One is to measure a round trip time (RTT)
by an acoustic transponder. The other is to measure
one-way propagation time assuming that a sound
source and a receiver have the same clock time. For
example, time synchronization has been achieved by
integrating a chip-scale atomic clock (CSAC) into
an acoustic modem [11]. The latter is addressed in
this paper.
When the signal start times are identical among
the sound source and receivers, we can take the two
cross-correlations as:
(18)
(19)
(20)
(21)
The TOAs are converted into the distances by
(22)
(23)
In (20) and (21), each TOA can be detected by
the maximum correlation peak. We call it the
maximum value detection. The maximum value
detection is sensitive to acoustic reflections, which
is to be explained in Section 3.
2.4 Positioning Accuracy in TDOA and TOA
Measurements
The TDOA measurement is mainly used for USBL,
where the receiver spacing is less than several tens
of centimeters. It assumes that the sound source is
located farther from the receiver and that the plane
wave reaches the receiver elements.
The positioning accuracy in the TDOA and
TOA measurements are compared by our simulation,
where the simulation results are shown in Figure 2.
This simulation condition is close to being ideal,
where a signal-to-noise ratio (SNR) of 30 dB with
non-acoustic reflection is set. Please see the other
conditions such as sound source and receiver
locations in Section 5. The positioning coordinates
in the TDOA and TOA measurements are computed
by (1), (2), (4), and (5).
The positioning results for the small array
spacing (R=0.1) are plotted in Figure 2(a). The
averages of positioning errors are 0.58 m and 0.34
m for the TDOA and TOA measurements. The
positioning accuracy of the two measurements is
approximately the same.
The positioning results for the large array
spacing (R=1) are plotted in Figure 2(b). The
averages of positioning errors are 0.37 m and 0.04
m for the TDOA and TOA measurements. The TOA
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
254
Volume 23, 2024
measurement can improve positioning accuracy,
whereas the TDOA measurement does not. The
angle estimation in (3) assumes that a plane wave
reaches the two receiver elements. This assumption
is no longer valid for the large spacing. When the
receiver spacing is more than one meter, the TDOA
measurement cannot provide high positioning
accuracy anymore.
Fig. 2: Comparison of TDOA and TOA
measurements
3 Conventional Methods
3.1 Maximum Value Detection
The maximum value detection is widely used for the
TOA measurement. Each TOA is detected at the
point of having the highest value in the cross-
correlation, [9]. The maximum value detection has
the disadvantage of being sensitive to acoustic
reflections.
Figure 3 shows an example where the maximum
value detection induces a measurement error under a
reflective environment. Note that the cross-
correlation functions of and are
normalized so that the value of maximum peak
becomes 1. As shown in Figure 3(a), the correct
TOAs can be detected under the non-reflective
environment.
Fig. 3: Influence of acoustic reflection in maximum
value detection
Multiple correlation peaks are observed in
Figure 3(b). These peaks are caused by acoustic
reflections, where the sound wave reflects on water
surface, bottom, and surrounding walls. When we
look at the graph of , the maximum value
detection cannot find the point of the first peak,
which outputs an incorrect TOA.
The situation that the first peak does not have
the highest value can be explained by the
relationship between propagation path and impulse
response as illustrated in Figure 4.
When a sound wave reaches the receiver
following a direct or reflected path, its arrival time
and reception intensity are expressed as an impulse
response. The impulse response can be observed by
measuring the cross-correlation functions as
examples in Figure 3. When the path lengths of the
two paths are identical, the signals are combined on
the same arrival time. The magnitude of the
synthesized reflected path surpasses that of the
direct path.
Another factor is the directivity of the receiver
hydrophone. The directivity of the receiver is not
completely omnidirectional, even if it is noted in the
specifications. Due to the sensitivity variations
depending on the location on the surface of the
hydrophone, the received intensity for the direct
path may be small.
(a) Positioning results for array spacing of 0.1 m
(b) Positioning results for array spacing of 1 m
Receiver elements
Receiver elements
(a) Non-reflective environment
(b) Reflective environment
Maximum correlation peak
Maximum correlation peak
Maximum correlation peak
Maximum correlation peak
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
255
Volume 23, 2024
Fig. 4: Relationship between propagation path and
impulse response
3.2 Fixed Threshold Detection
The fixed threshold detection can find the first peak
even if the first peak does not have the maximum
magnitude, [10]. The procedure of threshold
detection is illustrated in Figure 5, where a threshold
is set to 0.5 for the maximum value of 1 in the
cross-correlation functions.
Figure 5(a) shows how the threshold detection
can get correct TOAs even in a reflective
environment. The detected points correspond to the
propagation time in the direct path.
Although the fixed threshold detection is
effective for reflective environments, the detection
degrades under noisy environments. Many pseudo
peaks appear on the correlation function under the
low SNR condition of Figure 5(b). Since the
magnitude of their pseudo peaks surpasses 0.5, the
threshold detection cannot find the true peak derived
from the direct path.
Fig. 5: Influence of acoustic reflection and noise in
fixed threshold detection
4 Proposed Method
We apply the variable threshold that a threshold can
be changed according to surrounding environments.
Since the magnitude of the first peak is unknown,
the threshold should be as small as possible.
However, a small threshold tends to have false
detection due to the pseudo-peaks derived from
background noise.
The key idea is to check whether a threshold is
appropriate in some way. We employ the TDOA
measurement using IR-GCC-PHAT for checking a
threshold, where the cross-correlation functions of
are shown in Figure 6. The arrival time
difference is detected according to (17). Unlike the
results of Figure 3 and Figure 5, the expected time
differences detected are similar. IR-GCC-PHAT is
robust with both reflective and noisy environments
[8].
Fig. 6: Cross-correlation functions in TDOA
measurement
Although the TDOA measurement with a small
receiver array does not provide an accurate arrival
time difference (see Section 2.4), it is suitable for
only verifying that the threshold is appropriate. We
compare the arrival time differences estimated by
the TDOA and TOA measurements as:
(24)
(25)
. (26)
Reflected path
Reflected path
(a) Propagation path
Direct path Direct
path Reflected
paths
(b) Impulse response
Sound
Source Receiver
Water surface
Water bottom
(a) Reflective environment with a SNR of 30 dB
(b) Reflective environment with a SNR of 7 dB
First point for
First point for
First point for
First point for
(a) Non-reflective environment with a SNR of 30 dB
(b) Reflective environment with a SNR of 30 dB
(c) Reflective environment with a SNR of 7 dB
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
256
Volume 23, 2024
If is within a certain range, the time
difference obtained from the TOA measurement is
reasonable and the threshold is also appropriate.
The flowchart of the proposed method is shown
in Figure 7, where the variable threshold is given by
. The initial threshold is set to 0.3 and increased by
each iteration loop processing. The two TOAs are
finalized when the conditions of deg. or
are satisfied. The small threshold can
detect the first peak in a reflective environment and
the large threshold cope with a noisy environment.
Fig.7: Flowchart of variable threshold detection
5 Evaluation
5.1 Experimental Conditions
Our underwater acoustic positioning experiment
was conducted in the swimming pool. The
experimental scenery is shown in Figure 8.
Table 1 presents the specifications of the
transmitted signal and the experimental conditions.
We generate the transmit signal (corresponding to a
sound source) by using PN code sequences. The
frequency band of the transmitted signal is 12 kHz
to 32 kHz, and it is a flat spectrum with
approximately within the band. The
acoustic field size is 25 × 15 × 1.35 m for length,
width, and height.
The locations of the transmitter (TX) and
receiver elements (RX1 and RX2) are shown in
Figure 9. TX is moved every 2 m along the x-axis
(2.5 to 22.5 m) and the y-axis (8 to 12 m). RX1 is
fixed at =12.5 m and =0.5 m with an interval of
1.4 m between the receiver elements. The height of
the transmitter and receiver elements is set to the
same 0.8 m.
Fig. 8: Experimental scenery
Table 1. Specifications of transmitted signal and
simulation conditions
Fig. 9: Locations of transmitter and receiver
elements
We compare positioning accuracy in the two
conventional methods and the proposed method, i.e.,
the maximum value detection, the fixed threshold
detection, and the variable threshold detection.
Three measurements are taken per TX location and
the two-dimensional coordinates are calculated
according to (4) and (5). We adjust the amplitude of
noise signals and add them to the received signals to
evaluate various SNR conditions.
5.2 Experimental Results
The experimental results in a high SNR condition
are shown in Figure 10. The maximum value
detection tends to have large positioning errors
when the sound source is near the wall. The sound
Start
Yes
Compute
Measure and by threshold detection
or
Compute
End
No
Sound Source
Receiver Elements
Sampling frequency
200 kHz
Frequency
band 12 kHz - 32 kHz
Transmitted
signal Pseudo-noise (PN) sequence
Signal length
81.9 ms
Number of signal points
16,384
Number of receivers
2
Receiver
array spacing 1.4 m
Acoustic field
25 15 1.35 m
TX ( )
RX1 (12.5, 0.5) RX2 (13.9, 0.5)
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
257
Volume 23, 2024
waves reflected from the side walls interfere
strongly in the swimming pool. The error average of
maximum value detection is larger than those of the
fixed threshold detection the variable threshold
detection.
Fig. 10: Experimental results in a high SNR
condition
The error averages between the fixed threshold
detection and the variable threshold detection are
similar. It indicates that a threshold of around 0.5 is
appropriate in this SNR condition.
The experimental results in a low SNR
condition are shown in Figure 11. While the
variable threshold detection keeps high positioning
accuracy, the fixed threshold detection increases the
error average. Since the fixed threshold was set to
0.5, some TOA measurements failed due to the
pseudo peaks derived from background noise.
Table 2 summarizes the experimental results for
all SNR conditions. The maximum value detection
shows larger positioning errors for the SNR
conditions of 5 dB and 0 dB.
Fig. 11: Experimental results in a low SNR
condition
The fixed threshold detection degrades
positioning accuracy for the SNR conditions of 5
dB and 0 dB. The variable threshold detection can
keep the highest positioning accuracy even for all
SNR conditions.
(a) Maximum value detection with a SNR of 5 dB
(b) Fixed threshold detection with a SNR of 5 dB
(c) Variable threshold detection with a SNR of 5 dB
Error average: 1.61 m
Error average: 0.28 m
Error average: 0.28 m
(a) Maximum value detection with a SNR of 5 dB
(b) Fixed threshold detection with a SNR of 5 dB
(c) Variable threshold detection with a SNR of 5 dB
Error average: 1.40 m
Error average: 0.73 m
Error average: 0.31 m
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
258
Volume 23, 2024
Table 2. Average positioning errors [m] for all SNR
conditions
6 Discussion
We evaluate positioning accuracy for various
conditions in simulation. We use a sound wave
propagation simulator that tracks sound waves by
the mirror image method. The sound wave
propagation simulator reproduces acoustic
reflections where a user specifies the size of
acoustic field space, reflectance ratios on six
boundaries, and sound source and receiver positions.
The locations of the sound source and receiver
elements and the signal specifications are the same
as those in the experiment.
Table 3 shows the results of average positioning
errors under a non-reflective environment, where all
reflectance ratios are set to 0. Since only the peak in
derived from the direct path appears in the
correlation function as shown in Figure 3(a), the
maximum value detection gives the highest
positioning performance for the low SNR conditions
of less than 10 dB.
While the variable threshold detection slightly
decreases positioning accuracy at the SNR of 10
dB, the fixed threshold detection significantly
degraded its performance. The threshold of 0.5
would be insufficient in this SNR condition.
Table 4 shows the results of average positioning
errors under a reflective environment. The
reflectance ratios are set to 1 for the water surface
and 0.7 for the water bottom and the surrounding
walls. The maximum value detection shows large
positioning errors due to acoustic reflections. The
variable threshold detection shows better
performance than the fixed threshold detection for
the low SNR conditions of less than 5 dB.
We confirmed that the variable threshold
detection can cope with noisy and reflective
environments.
Table 3. Simulation results under a non-reflective
environment
Table 4. Simulation results under a reflective
environment
7 Conclusion
This paper has presented a method of variable
threshold detection for SBL underwater acoustic
positioning systems. We explained the three
methods in the TOA measurement. The maximum
value detection and the fixed threshold detection
suffer from noise interference and acoustic
reflections. The variable threshold detection can
find an appropriate threshold by using the estimated
angle in the TDOA measurement. The experimental
and simulation results have proved that the proposed
method outperforms the conventional methods in
positioning accuracy.
Our future work will focus on the improvement
of positioning accuracy when a source target is
moving at high speed. The countermeasure of
Doppler shifts will be discussed.
Acknowledgement:
The authors would like to thank Mr. Shuhei Habu
for his support and assistance with this research.
Declaration of Generative AI and AI-assisted
Technologies in the Writing Process
During the preparation of this work the author used
Grammarly and DeepL services in order to correct
and improve the quality of English writing. After
using this tool/service, the author reviewed and
edited the content as needed and takes full
responsibility for the content of the publication.
SNR
[dB] Maximum value
detection Fixed threshold
detection
Variable threshold
detection
5 1.61 0.28 0.28
0 1.65 0.28 0.28
5 1.40 0.73 0.31
10 1.87 6.97 1.16
SNR
[dB] Maximum value
detection Fixed threshold
detection
Variable threshold
detection
5 0.02 0.02 0.02
0 0.02 0.02 0.02
5 0.02 0.02 0.02
10 0.02 3.36 0.08
15 22.87 10.74 6.12
SNR
[dB] Maximum value
detection Fixed threshold
detection
Variable threshold
detection
5 2.48 0.02 0.02
0 3.91 0.04 0.03
5 4.62 9.62 1.94
10 26.83 10.86 10.26
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
259
Volume 23, 2024
References:
[1] L. Paull, S. Saeedi, M. Seto and H. Li, "AUV
navigation and localization: a review," IEEE
Journal of Oceanic Engineering, vol. 39, no.
1, pp. 131-149, Jan. 2014, doi:
10.1109/JOE.2013.2278891.
[2] D. Thomson and S. Dosso, "AUV localization
in an underwater acoustic positioning
system," MTS/IEEE OCEANS-Bergen,
Bergen, Norway, pp. 1-6, June 2013, doi:
10.1109/OCEANS-Bergen.2013.6608140.
[3] I. Ullah, J. Chen, X. Su, C. Esposito and C.
Choi, "Localization and detection of targets in
underwater wireless sensor using distance and
angle based algorithms," IEEE Access, vol. 7,
pp. 45693-45704, Apr. 2019, doi:
10.1109/ACCESS.2019.2909133.
[4] J. Luo, Y. Yang, Z. Wang and Y. Chen,
"Localization algorithm for underwater sensor
network: a review," IEEE Internet of Things
Journal, vol. 8, no. 17, pp. 13126-13144, Sep.
2021, doi: 10.1109/JIOT.2021.3081918.
[5] Otero P, Hernández-Romero Á, Luque-Nieto
M-Á, Ariza A, "Underwater positioning
system based on drifting buoys and acoustic
modems," Journal of Marine Science and
Engineering, vol. 11, no. 4, pp.1-9, Mar 2023,
doi: 10.3390/jmse11040682.
[6] J. Choi, J. Park, Y. Lee, J. Jung, and H. Choi,
"Robust directional angle estimation of
underwater acoustic source using a marine
vehicle,” MDPI Sensors, vol. 18, issue 9, pp.
1-14, Sep. 2018, doi: 10.3390/s18093062.
[7] B. Kouzoundjian, F. Beaubois, S. Reboul, and
J. B. Choquel, and J. Noyer, "A TDOA
underwater localization approach for shallow
water environment," MTS/IEEE OCEANS-
Aberdeen, Aberdeen, UK, pp. 1-4, June 2017,
doi: 10.1109/OCEANSE.2017.8085030.
[8] S. Yoshizawa, "Underwater acoustic
localization based on IR-GCC-PHAT in
reverberant environments,'' International
Journal of Circuits, Systems and Signal
Processing, Vol. 15, pp.164-171, Mar. 2021,
doi:10.46300/9106.2021.15.18.
[9] Y. Wu, Y. Liu, S. Yan and L. Yang, "The
improvement of acoustic positioning of
underwater vehicles based on synthetic long
baseline navigation," MTS/IEEE OCEANS
2017-Aberdeen, Aberdeen, UK, pp. 1-5, June
2017, doi:
10.1109/OCEANSE.2017.8084593.
[10] W. A. P. van Kleunen, K. C. H. Blom, N.
Meratnia, A. B. J. Kokkeler, P. J. M. Havinga
and G. J. M. Smit, "Underwater localization
by combining time-of-flight and direction-of-
arrival," MTS/IEEE OCEANS 2014-Taipei,
Taipei, Taiwan, pp.1-6, Apr. 2014, doi:
10.1109/OCEANS-TAIPEI.2014.6964309.
[11] M. V. Jakuba, J. W. Partan, S. E. Webster, D.
Giaya and C. Ramirez, "Performance of a
low-power one-way travel-time inverted ultra-
short baseline navigation system," MTS/IEEE
OCEANS 2021-San Diego, San Diego, CA,
USA, pp. 1-10, Sep, 2021 doi:
10.23919/OCEANS44145.2021.9705795.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.25
Shingo Yoshizawa
E-ISSN: 2224-266X
260
Volume 23, 2024
