Source depth estimation is an important yet very difficult task for passive sonars, especially for horizontal linear arrays (HLAs). This paper proposes an efficient two-step depth estimation scheme using narrowband and broadband constructive and deconstructive striation patterns due to interference between the direct (D) and sea surface reflected (SR) arrivals at an HLA on the bottom of deep water. First, the horizontal source-array ranges are derived from triangulation results of solid angle estimates by subarray beamforming. The applicable areas of the method in deep water are investigated through Mento Carlo simulations, assuming different subarray partitioning ways of a given HLA aperture. Second, cost functions are built to match the measured beam intensity striations with modeled ones. To mitigate the spatial smoothing effect of the beam intensity striations during beamforming, a criterion of the largest subarray aperture is established, and a computationally efficient way is presented to model the replicas by the D-SR time delay templates at a single element of the array calculated by ray theory. The performance degradation due to limited source range spans, the distortion of the beam intensity striations, and range estimation errors has been analyzed. Two experimental datasets verify the effectiveness of the proposed method.
REFERENCES
1.
Baggeroer
,
A. B.
, and
Kuperman
,
W. A.
(1993
). “
An overview of matched field methods in ocean acoustics
,” IEEE J. Oceanic Eng.
18
(4
), 401
–424
.2.
Bogart
,
C. W.
, and
Yang
,
T. C.
(1994
). “
Source localization with horizontal arrays in shallow water: Spatial sampling and effective aperture
,” J. Acoust. Soc. Am.
96
(3
), 1677
–1686
.3.
Carter
,
G. C.
(1979
). “
Passive ranging errors due to receiving hydrophone position uncertainty
,” J. Acoust. Soc. Am.
65
(2
), 528
–530
.4.
Cockrell
,
K. L.
, and
Schmidt
,
H.
(2010
). “
Robust passive range estimation using the waveguide invariant
,” J. Acoust. Soc. Am.
127
(5
), 2780
–2789
.5.
Conan
,
E.
,
Bonnel
,
J.
,
Nicolas
,
B.
, and
Chonavel
,
T.
(2017
). “
Using the trapped energy ratio for source depth discrimination with a horizontal line array: Theory and experimental results
,” J. Acoust. Soc. Am.
142
(5
), 2776
–2786
.6.
Duan
,
R.
,
Yang
,
K.
,
Li
,
H.
,
Yang
,
Q.
,
Wu
,
F.
, and
Ma
,
Y.
(2019
). “
A performance study of acoustic interference structure applications on source depth estimation in deep water
,” J. Acoust. Soc. Am.
145
(2
), 903
–916
.7.
Emmetière
,
R.
,
Bonnel
,
J.
,
Cristol
,
X.
,
Géhant
,
M.
, and
Chonavel
,
T.
(2019
). “
Passive source depth siscrimination in deep-water
,” IEEE J. Sel. Top. Signal Process.
13
(1
), 185
–197
.8.
Emmetière
,
R.
,
Bonnel
,
J.
,
Marie
,
G.
,
Cristol
,
X.
, and
Chonavel
,
T.
(2018
). “
Understanding deep-water striation patterns and predicting the waveguide invariant as a distribution depending on range and depth
,” J. Acoust. Soc. Am.
143
(6
), 3444
–3454
.9.
Flanagan
,
R. P.
, and
Weinberg
,
N. L.
(1980
). “
Effects of source motion on an acoustic signal in the frequency, time, and space domains
,” J. Acoust. Soc. Am.
67
(5
), 1532
–1544
.10.
Gavish
,
M.
, and
Weiss
,
A. J.
(1992
). “
Performance analysis of bearing-only target location algorithms
,” IEEE Trans. Aerosp. Electron. Syst.
28
(3
), 817
–828
.11.
Gorodetskaya
,
E. Y.
, and
Malekhanov
,
A. I.
(1999
). “
Deep-water acoustic coherence at long ranges: Theoretical prediction and effects on large-array signal processing
,” IEEE J. Oceanic Eng.
24
(2
), 156
–171
.12.
Hinich
,
M. J.
(1979
). “
Passive range estimation using subarray parallax
,” J. Acoust. Soc. Am.
65
(5
), 1229
–1230
.13.
Huang
,
Y. D.
, and
Barkat
,
M.
(1991
). “
Near-field multiple source localization by passive sensor array
,” IEEE Trans. Antennas Propagat.
39
(7
), 968
–975
.14.
Hunter
,
A. F.
, and
Kuperman
,
W. A.
(2021
). “
Range-coherent matched field processing for low signal-to-noise ratio localization
,” J. Acoust. Soc. Am.
150
(1
), 270
–280
.15.
Jensen
,
F. B.
,
Kuperman
,
W. A.
,
Porter
,
M. B.
, and
Schmidt
,
H.
(2011
). Computational Ocean Acoustics
(
Springer
,
Berlin
), pp. 17
–20
.16.
Kaplan
,
L. M.
,
Qiang
,
L.
, and
Molnar
,
N.
(2001
). “
Maximum likelihood methods for bearings-only target localization
,” in IEEE International Conference on Acoustics and Speech Signal Processes
, pp. 3001
–3004
.17.
Kim
,
J.
(2022
). “
Locating an underwater target using angle-only measurements of heterogeneous sonobuoys sensors with low accuracy
,” Sensors
22
(10
), 3914
.18.
Kim
,
K. M.
,
Yang
,
I. S.
,
Chun
,
S. Y.
, and
Oh
,
W. T.
(2002
). “
Passive-range estimation using dual focused beamformers
,” IEEE J. Ocean. Eng
27
(3
), 638
–641
.19.
Kniffin
,
G. P.
,
Boyle
,
J. K.
,
Zurk
,
L. M.
, and
Siderius
,
M.
(2016
). “
Performance metrics for depth-based signal separation using deep vertical line arrays
,” J. Acoust. Soc. Am.
139
(1
), 418
–425
.20.
Le Cadre
,
J.-P.
(1995
). “
Performance analysis of wavefront curvature methods for range estimation of a moving source
,” IEEE Trans. Aerosp. Electron. Syst.
31
(3
), 1082
–1103
.21.
Li
,
H.
,
Xu
,
Z.
,
Yang
,
K.
, and
Duan
,
R.
(2021
). “
Use of multipath time-delay ratio for source depth estimation with a vertical line array in deep water
,” J. Acoust. Soc. Am.
149
(1
), 524
–539
.22.
Li
,
H.
,
Xu
,
Z.
, and
Yang
,
K. D. R.
(2020
). “
Analysis on effective propagation range of reliable acoustic path with experimental demonstration
,” in Global Oceans 2020: Singapore – U.S. Gulf Coast
, pp. 1
–4
.23.
McCargar
,
R.
, and
Zurk
,
L. M.
(2013
). “
Depth-based signal separation with vertical line arrays in the deep ocean
,” J. Acoust. Soc. Am.
133
(4
), EL320
–EL325
.24.
Pereira
,
A.
,
Harris
,
D.
,
Tyack
,
P.
, and
Matias
,
L.
(2020
). “
On the use of the Lloyd's Mirror effect to infer the depth of vocalizing fin whales
,” J. Acoust. Soc. Am.
148
(5
), 3086
–3101
.25.
Porter
,
M. B.
(1991
). The KRAKEN Normal Mode Program
(
SACLANT Undersea Research Center
,
La Spezia, Italy
).26.
Porter
,
M. B.
(2011
). “
The BELLHOP manual and user's guide: Preliminary draft
,” http://oalib.hlsresearch.com/Rays/HLS-2010-1.pdf (Last viewed July 8, 2023).27.
Premus
,
V. E.
, and
Helfrick
,
M. N.
(2013
). “
Use of mode subspace projections for depth discrimination with a horizontal line array: Theory and experimental results
,” J. Acoust. Soc. Am.
133
(6
), 4019
–4031
.28.
Qi
,
Y.
,
Zhou
,
S.
,
Liang
,
Y.
,
Du
,
S.
, and
Liu
,
C.
(2020
). “
Passive broadband source depth estimation in the deep ocean using a single vector sensor
,” J. Acoust. Soc. Am.
148
(1
), EL88
–EL92
.29.
Reeder
,
D. B.
(2014
). “
Clutter depth discrimination using the wavenumber spectrum
,” J. Acoust. Soc. Am.
135
(1
), EL15
–EL21
.30.
Turgut
,
A.
,
Orr
,
M.
, and
Rouseff
,
D.
(2010
). “
Broadband source localization using horizontal-beam acoustic intensity striations
,” J. Acoust. Soc. Am.
127
(1
), 73
–83
.31.
Weiss
,
A. J.
, and
Friedlander
,
B.
(1993
). “
Range and bearing estimation using polynomial rooting
,” IEEE J. Oceanic Eng.
18
(2
), 130
–137
.32.
Weng
,
J. B.
, and
Yang
,
Y. M.
(2018
). “
Experimental demonstration of shadow zone localization using deep water interference patterns measured by a single hydrophone
,” IEEE J. Oceanic Eng.
43
(4
), 1171
–1178
.33.
Wu
,
J. N.
,
Zhou
,
S.-H.
,
Peng
,
Z.-H.
,
Zhang
,
Y.
, and
Zhang
,
R.-H.
(2016
). “
Bearing splitting and near-surface source ranging in the direct zone of deep water
,” Chin. Phys. B
25
(12
), 124311
.34.
Wu
,
Y. Q.
,
Zhang
,
W.
,
Hu
,
Z. L.
,
Zhang
,
W. H.
,
Zhang
,
B. B.
,
Wang
,
J.
,
Guo
,
W.
,
Xu
,
G. J.
, and
Zhu
,
M.
(2022
). “
Directional response of a horizontal linear array to an acoustic source at close range in deep water
,” Acoust. Aust.
50
, 91
–103
.35.
Xie
,
L.
,
Sun
,
C.
, and
Kong
,
D.
(2020
). “
Matched-phase weighting beamformer to improve the gain of a long linear array in the range-dependent ocean waveguide
,” IEEE Access
8
, 177437
–177446
.36.
Yang
,
T. C.
(2003a
). “
Beam intensity striations and applications
,” J. Acoust. Soc. Am.
113
(3
), 1342
–1352
.37.
Yang
,
T. C.
(2003b
). “
Motion compensation for adaptive horizontal line array processing
,” J. Acoust. Soc. Am.
113
(1
), 245
–260
.38.
Zheng
,
G.
,
Yang
,
T. C.
,
Ma
,
Q.
, and
Du
,
S.
(2020
). “
Matched beam-intensity processing for a deep vertical line array
,” J. Acoust. Soc. Am.
148
(1
), 347
–358
.39.
Zhou
,
L.
,
Zheng
,
G.
, and
Yang
,
T. C.
(2022
). “
Target depth estimation by frequency interference matching for a deep vertical array
,” Appl. Acoust.
186
, 108493
.© 2023 Acoustical Society of America.
2023
Acoustical Society of America
You do not currently have access to this content.