HIGH RESOLUTION BEAMFORMING TECHNIQUES APPLIED TO A DIFAR SONOBUOY CAPT

CAPT DANIEL DESROCHERS
B.Sc. Collège Militaire Royal de St-Jean, 1988
A thesis submitted in partial füllfilment of the requirements For the Degree of Master of Science at
Royal Military College of Canada, July 1999.
Approved
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Abstract
The hydrophone in a DIFAR sonobuoy consists of an omnidirectional bender element and
two directionai sensors, in a crucifonn-shaped wobbkr assembly, providing data as three
separate channels. These channels contain the acoustic directional information, which is
typicaily extracted as a single bearing value for each fiequency bin. When this bin contains
energy from more than one source, or if strong directional noise is present, this single value
results in an erroneous direction estimate.
High-resolution beamforming techniques, developed to produce directional spectra from
a small number of sensors, have been applied successfully to DIFAR data. A cornparison
of the results provided by Maximum Likelihood [Capon, 19693 and Eigenvectors [Johnson
and DeGraaf, 19821, as well as iterative improvements of these techniques [Pawka, 19831
and [Marsden and Juszko, 19871 will be presented. When applied to real data, it was found
that two sources contained in a single fiequency bin could be simultaneously and accurately
identified. By averaging the directionai spectra over a range of fkequencies, a simple polar
plot was obtained, containing peaks which correctly tracked three ships in the vicinity of the
sonobuoy.
Acknowledgement s
-4 project of this magnitude requires support from many sources- Merci à mon épouse Line
et à mes enfants, Patrick et Sophie, qui m'ont aidé au cours de ces demu années par leur
support, leur présence et leur amour.
Thanks to Dr Rick Marsden for taking the time to assist and to provide clear directions
during these 1 s t two years. 1 am also gratehl to Dr Mike Stacey and LCdr David Williams
for their comrnents and suggestions to improve this work, and to Dr Joe Buckley for his
assistance wit h my numerous computer related questions.
This thesis would have been difficult without the support from persons and agencies
outside of WIC, which allowed me to present results based on reality. In particular, the
information about DLFAR sonobuoys received from Mr Ken Walker, Hermes Electronics Inc,
was very appreciated.
Finally, special thanks are extended to Ron and his hard working habits which were a
constant source of motivation during this challenging experience-
Contents
1.1.1 Sound sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Passive acoustics 4
. . . . . . . . . . . . . . . . . . . 1.2.3 D IF'.. R O v e ~ e w and Ernployment 5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Processing techniques 5
1.3.1 Fourier transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
. . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Directional information 6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Objective 7
2 Theory 9
2.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2-2 Data presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3 Conventional Beamforming . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Simulation 24
3.2 Directional energy distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Single source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.5 'Ibo sources with different power . . . . . . . . . . . .. . . . . . . . 32
3.3 WAE vs angular spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.1 Single source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.5 Two sources with different power . . . . . . . . . .. . . . . . . . . . 39
3.4 WAEvsSNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4.5 Two sources with diEerent power . . . . . . . . . . . . . . . . . . . . 46
3.5 Discussion on validity of each technique . . . . . . . . . . . . . . . . . . . . . 48
4 Field data 50
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Processing 53
4.2.3 Directional energy distribution display . . . . . . . . . . . . . . . . . 61
4.2.4 Averaged Directional Spectra (Polar plots) . . . . . . . . . . . . . . . 67
5 Discussion 71
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 PassiveASW 72
5.2.3 Directional arnbient noise from DIFAR . . . . . . . . . . . . . . . . . 73
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Summary 74
List of Figures
1.1 Representation of Broadband and Narrowband noise abng the fiequency spec-
trum of a typical ship or submarine [Urick, 19751. . . . . . . . - . . . . . . .
2.1 Schematic of a DIFAR hydrophone showing the omni bender element and two
of the four armç of the wobbler assembly. [Hermes Electronics] . - - - . . . .
2.2 Illustration of the lobe patterns of a DIFAR and their relationship wïth source
arriva1 angle and buoy orientation relative to magnetic north. . . . . . . . .
2.3 Example of a gram display, showing frequency on the honzontd axis and time
on the vertical. . . . . . . . - . - . . . . . - . - . - . . . . - . - . - . . - . - 2.4 Example of a directional dispiay, showing frequency on the horizontal axis
and bearing, relative to tme north, on the vertical. . . . . . . . . . . . . . .
2.5 Same as previous figure, but with a threshold applied to show only the stronger
sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Directional Spectra for one source (power 1.0) at 180". . . . . . . . . . . . .
3.2 Directional Spectra for two identical sources (power 1.0) separated by 180". .
3.3 Directional Spectra for two identical sources (power 1.0) separated by 120". .
3.4 Directional Spectra for two identical sources (power 1.0) separated by go0. .
3.5 Directional Spectra for two different sources (potver 1.0 and 0.5) separated by
3.6 Directional Spectra for two different sources (power 1.0 and 0.5) separated by
120 " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Directionai Spectra for two different sources (power 1.0 and 0.5) separated by
90 O . . . . . . . . . . . . . . . . . . . . . . . . . . . * . . . . . . . . . . . . . .
3.8 WAE vs Angular Spread (Std Dev) for one source (power 1.0) a t 180" . . . .
3.9 WAE vs Anguiar Spread (Std Dev) for two identical sources (power 1.0) s e p
arated by 180" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.10 WAE vs -4ngula.r Spread (Std Dev) for two identical sources (power 1.0) sep-
arated by 120" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.11 WAE vs Angular Spread (Std Dev) for two identical sources (power 1.0) sep-
arated by 90" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 WAE vs Angular Spread (Std Dev) for two different sources (power 1.0 and
0.5) separated by 120" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 WAE vs Angular Spread (Std Dev) for two dXerent sources (power 1.0 and
0.5) separated by 90" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 WAE vs SNR for one source (power 1.0) at 180"- . . . . . . . . . . . . . . .
3.15 WAE vs SNR for two identical sources (power 1.0) separated by 180'. . . . .
3.16 WAE vs SNR for two identicai sources (power 1.0) separated by 120" . . . . .
3.17 WAE vs SNR for tmo identicai sources (power 1.0) separated by 90" . . . . . .
3.18 WAE vs SNR for two different sources (power 1.0 and 0.5) separated by 120" .
3.19 WAE vs SNR for two different sources (power 1.0 and 0.5) separated by go0 .
4.1 Map of the area showing three ships around the sonobuoys . . . . . . . . . . .
4.2 Gram showing both sonobuoys, from 5 to 100 Hz . The data updates upwards
from time 1956 to 2036 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
BScan a t 2023 (minute 27) showing the directional information as a single
value for each fiequency bin. . . . . . . . . . . . .. . . . . . . . . .. . . . .
Directional Spectra calculated by CB at t h e 2023, covering a frequency range
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . of 5 to 100 Hz.
Directional Spectra calculated by ML and IML at time 2023, covering a fre-
quency range of 5 to 100 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Directional Spectra calculated by EV and IEV at time 2023, covering a fre-
quency range of 5 to 100 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bscan at time 2023, covering a frequency range of 150 to 250 Hz- . . . . . .
Directional Spectra calculated by ML and L\IL at time 2023, covering a fre-
quency range of 150 to 250 Hz, . . . . . . . . . . . . . . . . . . . . . . . . .
Directionai Spectra calculated by EV and IEV at time 2023, covering a fre-
quency range of 150 to 250 Hz. . . . . . . . . . . . . . . . . . . . . . . . . .
Directional Spectra for kequency bin 25.1 Hz, calculated at time 2023. The
four High-Resolution techniques identified two sources in the same Çequency
brn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Directional Spectra for the fiequency bin 46.9 Hz, calculated at time 2023.
The strong narrow band source outpowers a weaker source to the North, picked
up by the high-resolution beamforming techniques. . . . . . . . . . . . . . .
Directional Spectra for the frequency bin 42.5 Hz, calcuiated at time 2023. A
combination of ML and EV techniques identified the three known targets in
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . the same frequency bin.
Directional Spectra for frequency bin 202.4 Hz, calculated at time 2023. Spu-
rious peak estimates that do not match the surface picture were identified by
vii
4.14 Directional Spectra for frequency bin 240.5 Hz. calculated a t time 2023 . The
double peaks were created by IEV at a few fkequency bins . . . . . . . . . . .
4.15 Directional Spectra for frequency bin 18.8 Hz, calculated a t time 2023 . Spu-
rious peak estirnates that do not match the surface picture were identified by
EVandIEV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17 -4veraged Directional Spectra calculated at t h e 2009 . . . . . . . . . . . . . .
4.18 Averaged Directional Spectra cdculated a t time 2018 . . . . . . . . . . . . . .
4.19 Averaged Directional Spectra calculated at time 2023 . . . . . . . . . . . . . .
4.20 -4veraged Directional Spectra calculated at time 2029 . . . . . . . . . . . . . .
4.21 Averaged Directional Spectra calculated at time 2035 . . . . . . . . . . . . . .
List of Symbols
Acoustic time signal as a fmction of t h e (analog)
Signal angle of amival from the main response axis of cosine hydrophone
Alignrnent of main response axis of cosine hydrophone from magnetic north
Signal angle of arrival Çom magnetic north
Discrete acoustic time signai sampled at equal increments (omni-directional)
Discrete acoustic time signal sampled at equal increments (sine channel)
Discrete acoustic t h e signal sampled at equal increments (cosine channel)
Number of time increments used for Fast Fourier Tramform. .Us0 used to r e p
resent constant noise in beamforming
Fast Fourier Transfom of x,k
Omni-directional power spectra: 00 - 0,
Cross spectra between ornni-directionai and sine channel: @: - a,
Cross Spectral Matrix estimate
Look of Direction Vector
Directional energy distribution estimate
Vector of filter coefficients in Data Adaptive techniques
Lagrange's undetermined multiplier with respect to ML technique
mlh Eigenvalue mith respect to EV technique
mth Eigenvector
Iterative improvement with respect to ML and EV techniques a t step i
Parameters for Iterative improvement techniques
Number of sources for simulation
Power of source n
Standard deviation (angular spread) of source n
List of Abbreviations
AD-AC
AStV
Bscan
CB
CP-!
CSM
DFT
DIFAR
DRE-4
EV
FFT
Gram
IDL
IEV
Acoustic Data -4oalysis Center, located in Halifax (NS) and Victoria (BC)
Ant i-Su bmarine Warfare
Defence Research Establishment Atlantic (Halifax)
Eigenvalue and Eigenvector Analysis (data adaptive technique)
Fast Fourier Transform
Interactive Data Language, fiom Research Systems Inc.
Iterative Eigenvdue and Eigenvector Analysis (data adaptive technique)
xi
LOF'AR Low Frequency Analysis and Recording
ML Maximum Likelihood (data adap t ive technique)
SDev Standard deviation
SNR Signal to Noise Ratio
W,4E Weighted Average Error
1.1.1 Sound sources
Ships and submarines, like any other vehicle, require large amounts of energy for propulsion
and for potvering various mechanical and electronic equipment. Some of this energy radiates
outwards as acoustic energy in the form of both broadband and narrowband noise, in a
pattern similar to figure 1.1.
The sources of noise on a vessel can be grouped into three major classes: machinery noise,
propeller noise and hydrodynarnic noise [Urick, 19757. The spectral shape defines broadband
and narrowband disturbances. The broadband component , seen here as a continuous curve,
is produced mainly by propeiler blade cavitation, radiated flow noise from the hull and fluid
flow turbulence frorn pipes inside the vessel [Urick, 19751. Although it is possible to detect
and localize a target using only this component, little other information can be determined.
In addition, passive sonar systems operating in the frequency domain utilize automatic gain
control algorithms and other fiitering methods, which may result in an emphasis on the
narrowband signals only.
Narrow band Sources
Figure 1.1: Representation of Broadband and Narrowband noise along the frequency spec- tmm of a typical ship or submarine [Urick, 19751.
The narrowband components, or the tonals, are generally produced by the rotation of
shafts, motor armatures, and other components of the submarine [Urick, 19751. These are
the narrow peaks associated with specific fkequencies as shown in figure 1.1.
When the source is moving relative to a stationary receiver, its radiated fkequencies \vil1
appear to shift up or down depending on the geometry. This frequency shift is proportional
to the relative speed between the target and a receiver, and is c d e d the Doppler effect.
Doppler information can be readily interpreted to provide target position, course and speed
to a good degree of accuracy, especidly when the source is held on multiple sonobuoys a t
one time. h i d e from target speed, the strength and frequency of these components depend
on V ~ ~ O U S factors. Two examples are source depth, and environment parameters such as
water temperature and surface weather. A thorough analysis of the frequency spectrum can
provide the operator with important information on the target identity, mode of operation,
location and rnovements.
1.1.2 Noise
In the ocean, noise from many different sources also contributes to the total spectrum. Noise
is usudly defined as the residual sound background in the absence of individua.1 identifiable
sources [Urick, 19751. It includes distant shipping, wind, waves and biological sounds, which
can also be in the form of broadband and narrowband energy- Different types of noise pre-
dominate in specific parts of the spectrum, depending on the source. Shipping, for example,
appears below 100 Hz while rain occurs a t higher fiequencies, in the 1 to 10 kHz region
[Urick, lW5j -
The presence of noise hinders detection and may create confusion in distinguishing be-
tween target and non-target related contacts. Noise may also have a horizontal directiond
distribution depending on
used
1.2.1 Active sonars
Active acoustics is a branch of underwater acoustics that is very similar to radar. It requires
the production of a pulse of energy by the transmitter, and the detection of the signal
reflected by the target a t the receiver. In a mono-static configuration, the receiver is co-
located with the transmitter while a bi-static system uses completely separate units. With a
knowledge of the transmitted pulse parameters, the received signal can provide the operator
with the target range, bearing and Doppler speed. These systems axe carried by numerous
naval vesseh and submarines-
-4irborne units use active sonar in the fonn of expendable active sonobuoys which can
be dropped at chosen locations. The signal received by the sonobuoy is transmitted back to
the unit through a transmitter iocated in the floating portion of the buoy. Some helicopters,
like the Canadian Forces CH-146 Sea King, ca ry an active sonar which can be lowered in
the water while the aircraft is hovering.
The main disadvantage of active sonars is the requirement for the transmission of energy
in the water which can alert the target, and provide counter-detection opportunities. Long
range detections can be obtained by using lower fkequency systems, but the increased tram-
mitter size and the considerable amount of energy required result in further limitations for
these systems.
1.2.2 Passive acoustics
Passive acoustics is a method used for the locdization and tracking of surface and submarine
contacts which relies on the source-generated acoustic signal for detection. On naval vessels,
passive acoustic operations are accomplished mainly through an axray of receivers towed
behind the ship. This type of array usually offers increased sensitivity for a number of reasons.
The high number of receiver elements results in a high array gain, or signal amplification.
In addition, operators can choose the depth at which the towed array is deployed, and can
therefore take advantage of propagation paths such as convergence zones and deep sound
channels which trap radiated sounds.
These systems are large and a deployed array places many constraints on the ship's
position, speed and manoeuvers. Since the towed array is linear, the initial contact consists
of ttvo bearings, the tme direction and its mirror image, relative to the array heading.
The arnbiguity is resolved by altering the ships course, resulting in one bearing remaining
constant, and a large shift on the other. In addition to carrying s i d a r towed arrays,
submarines are equipped with a number of passive receivers, including hull mounted receiver
arrays.
Airbome units rely solely on expendable sensors for passive acoustics operations. One of
the main tools used to gather tactical acoustic information, also used by naval units, is the
&Irectional Bequency Analysis and Recordhg (DIFAR) sonobuoy.
1.2.3 DIFAR Overview and Employment
The DIFAR sonobuoy is an expendable three sensor array employed by anti-submarine war-
fore (MW) units operating from airborne platforms, like the CP-140 Aurora and CH-146
Sea King, and from naval vessels.
The two main components of a DZFAR sonobuoy are the hydrophone and the floatation
bag/upper electronics. Upon deployment, the hydrophone reaches a pre-determined depth
and measures acoustic energy, which is transmitted continuously by the upper electronics.
This analog signal is received by an ASW unit, and is digitized before processing. These data
can then be analyzed onboard the units using various tools and dispIays, and are recorded
for further analysis in centers such as the Acoustic Data Analysis Center (ADAC) in Halifax,
or Victoria. The DIFAR sonobuoy can also be used as the receiver component for bi-static
active systems, for the detection of the original and the returned energy pulse sent by a
transmitter at a different location.
1.3 Processing techniques
1.3.1 Fourier t ransform
The main processing technique used for acoustic signals employs the Discrete Fourier Trans-
form (DFT) . Processing these data with DFTs breaks the coLlected signal into its constituent
frequencies, providing the operator with criticai information about an acoustic target such
as its identity, speed, mode of operation, etc.
1.3.2 Directional information
The three-element construction of the DIFAR hydrophone makes it possible to obtain di-
rectiond acoustic information from a single instrument. The main technique employed has
been in use for many yeam and relies on a combination of DFTs to provide directional infor-
mation through an arctangent calculation. The result is a Bscan display which consists of a
single directional value for each frequency bin [14 SES, l98Oj. The analysis of the directional
spectrum in the frequency domain makes it possible to discriminate targets based on the
bearing information presented.
1.3.3 Limitations of the Directional information
The data used to determine bearings are integrated over a relatively long perïod, and are
subject to significant bearing errors. To provide a bearing estimate in a real- the system,
only past information can be used, and for a rapidly moving target, this wiii cause the
bearing to lag behind the source.
Furthermore, this technique may introduce errors when two sources a t the same fiequency
are received from different directions. The resulting bearing estimate will lie somewhere
between the actual targets, usually closer to the stronger one, an effect known as bearing b i a s
[Collier, 19841. Bearing debiasing algorithms have been devised to reduce these effects. In
essence, these dgorithms remove non-signal components, determined fiom adjacent bins from
the bea.ring calculation, under the assumption that the signal of interest is narrowband [14
SES, 19801. This method only addresses the bias that is introduced by relatively broadband
interference over discrete tonals- With two sources producing narrowband signals in the
same hequency bin, bearing errors are still Lïkely to occur [Collier, 19841.
Ocean noise can also greatly affect incoming target signds. When the noise originates
from specific directions and is of high enough amplitude, it may introduce significant bearing
errors or mask the target of interest entirely, despite the debiasing algorithms. The operator
is then provided with directional information fkom the stronger signal, which may be the
noise. A similar error may also occur in the presence of two broadband signais hom different
origins.
Standard beamforming is ineffective in producing directional information in systems with
few degrees of fieedorn such as DIFAR buoys. New data adaptive beamforming techniques
have been developed [eg. Johnson and DeGraaf, 19821 that improve bearing resolution.
These high-resolution beamforming techniques involve the design of Eiters that emphasize
the signal. They were developed initiaily as signal detectors used when the number of
sensors in the array was small. Early developments made use of these techniques to study
seismic data from a large aperture array to provide high-resolution directional information on
propagated seismic waves [Capon, 19691. Other areas have also benefited from this research
such as radar, sonar and radio astronomy, where sensors aIso consist of distributed arrays.
One example for which there is extensive documentation, is the pitch, roll and heave
buoys used in ocean wave measnrements. This fioating buoy measures the vertical motion,
as well as the slope of the water surface in orthogonal directions. There is a mathematical
equivalence to the DIF'AR sonobuoy described earlier, indicating that the application of the
same data adaptive techniques could provide improved results over curent methods.
1.5 Objective
The objective of this thesis is to demonstrate that data adaptive beamfonning can be applied
to DIFAR data to detect two sources transrnitting at the same frequency, and hence alleviate
some of the problems common to the standard Bscan processing.
The theory will be presented in chapter 2, starting with a comprehensive description of
the DIFAR sensor and the format of the data provided- The second haif of chapter 2 WU
describe the underlying theory of each high-resolution beamforming technique in detail for
the case of a three-sensor array of the DIFAR configuration.
Chapter 3 describes simulations that were carried out to test the vaLidi@ of the differ-
ent schemes studied. The simulated signai and its resulting cross-spectral matrix dl be
described, as weil as the method chosen for error rneasurement. Different algonthms were
tested for one and two sources, using a combination of variables such as background noise
level and target separation. The angular spread, or the width of the signal a t the receiv-
er, were also varied. Plots of directional energy distribution are provided for the difFerent
combinations of signais.
The high-resolution techniques were then tested using field data in chapter 4. The data
consisted of three digitized time series, with the corresponding positional data of known
surface ships. Possible applications are discussed in chapter 5, in terms of how to use these
techniques in the different cornponents of the ASW community.
Chapter 2
2.1.1 Description
The SSQ 53D(2) DIF'AR sonobuoy is a s m d array which uses three acoustic sensors to
provide omnidirectional and directional information. Figure 2.1 shows a schematic of the
DIFAR sonobuoy. The omni bender element, on the bottom of the hydrophone, measures
only the amplitude of the acoustic pressure waves, regardless of the direction of arrivai. To
measure the direction of the signal, two sensors are combined in a totaLly separate crucifonn-
shaped wobbler assembly, which rests on four ceramic discs. Acoustic pressure waves reach
the hydrophone and induce vibrations. The pressure applied on the four ceramic discs
produce voltages induced by the piezo-electric properties of the material. The orthogonal
arrangement results in patterns similar to dipole response patterns, referred to as the sine
and the cosine lobes, based on the geometry of the assembly [Hermes Electronicsl. The
combination of signals fiom the three receivers contains the power spectral density and the
directional information of the incoming acoustic waves.
TO Suspension II
Omni en der Element
Figure 2.1: Schernatic of a DIFAR hydrophone showing the omni bender e1ement and two of the four arms of the wobbler assembly. [Hermes Electronics]
2.1.2 Data Format
Acoustic data sensed by a DL.4R buoy consist of separate time series fiom the three channels.
The incoming acoustic signal, x(t), reaches the sensor and is detected by the omni-directional
bender element . The other two orthogonal sensors, mentioned in 2.1.1 measure the respective
components of the same signal determined using basic trigonometry. Figure 2.2 shows the
geometry of a DZFAR buoy, and illustrates the lobe patterns created by each of the two
orthogonal receivers. This geometry ailows for the detection of signai components based on
an angle of arriva1 p relative to the main response axis of the cosine hydrophone, or the
cosine channel. A flux gate magnetic compass, located on the sensor, is used to provide the
alignment a! of that axis with respect to magnetic north.
Signais from the three analog channels and the magnetic compass are multiplexed and
are transmitted through the upper electronics located under the floatation bag. The receiver
inputs this signal in the acoustic processor where it is demultiplexed. The Sine and Cosine
channels combined with the compass uiformation provide the acoustic processor with the
N Main Response Axis of Cosine Hydrophone
+ and - Lobes of
/
Figure 2.2: Illustration of the lobe patterns of a DIFAR and their relationship with source arriva1 angle and buoy orientation reIative to magnetic north.
angle of arrival 8, by essentidy adding the angles a and cp, where cp is the angle between the
axis of the buoy and the target direction, as shown in figure 2.2. The three resulting time
series used as input for omni and bearing caicuIations are then:
x,k = xOksin8 East-West (Sine) Channel
x d = xokcos~ North-South (Cosine) Channel
2.1.3 Basic Acoustic Processing
A typical acoustic processor samples the digitized omni-directional time series x,k, N points
at a time, representing a set period of time of usually a few seconds. The number of data
points N is determined by the frequency resolution required by the system. The fiequency
spectra is provided by a,, the Discrete Fourier Transform (DFT) of the sample, from
equation 2.1, which is computed through a Fast-Fourier Transform (FFT),
where xok is the data for the ornni channel at time step k and a, is its DFT at fiequency
n.
Simila. transforms can be calculated for the sine and cosine channels, resulting in the
DFTs a,, and G, respectively.
The intensity QO0 of the omni-directionai perîodogram is found from
where the asterisk (*) indicates complex conjugation and the frequency index (n) has been
dropped for convenience. The power spectral density 6, is then obtained from
where the brackets indicate some form of averaging. The caret ( ) indicates that the
averaging resulted fiom band limited sampling to prevent aliasing. Similady, periodograms
and power spectral density for the sine and cosine channels are given by
A
Finally, the cross-periodograms and cross-spectra between channels are obtained from
To ensure adequate statisticaï coddence and to increase the probabiliv of detection of a
weak signal over noise, these values are averaged over tirne. This running average, a process
also called time integration, is often used in difFerent displays, for the average spectra and
directional (Bscan) displays described in the next section. Weights can be appiied when
performing this integration to give more importance to recent samples, and less to older
ones. The direction of the sound source is then obtained from the quotient of the averaged
values of equations 2.5 over 2.6, using the simple trigonometry relation 2.8.
The value 0 provides a single direction estimate, from O to 27r for each fiequency bin,
assuming signs for the numerator and denominator are considered. This angle is relative
to magnetic north and requires a further correction, for magnetic vanation, before being
displayed to the operator.
Passive acoustic information is displayed in many formats, which typically include frequency
spectrum as a function of time, and bearing and power spectral density as a function of
frequency. The frequency spectra versus time is traditionally referred to as a LOw Frequen-
cy Analysis and Recording (LOF.4R) gram or skply, a gram, shom in figure 2.3. Each
horizontal line on the gram consists of the power spectral density calculated from equation
2.2, displayed as a line on a screen with power spectrd density translated as brightness.
Successive samples are displayed sequentially, progressing in the y direction to form a con-
tinuously updating w a t e r f ' display. The operator is provided wïth a three-dimensional
representation of the acoustic spectrum with frequency dong the x M s , t h e along the y
suis and power spectral density as brightness. Figure 2.3, shows a number of narrowband
sources displayed as narrow vertical Iines, and a surface interference pattern, seen here as
the broad curved lines between 80 and 100 Hz. This pattern is produced by the constructive
and destructive interference of sound rays arriving fiom direct and surface reflected paths.
The information displayed in the gram is used for detecting and identimng the source of the
acoustic signatures and requires a significant amount of operator analysis-
The directional spectrum is currently obtained Tom the combination of individual FFT7s
described by equation 2.8. By using the omni channel in conjunction with the sine and cosine
channels, directional information can be determined and displayed in the form of bearings as
a function of frequency, illustrated in figure 2.4. This is referred to as a Bscan display with
frequency along the x axis, and bearing along the y axis. A threshold is usuaily applied to
prevent clutter, and to show only the strongest narrow band sources, as in figure 2.5. A low
threshold wïll allow nearly al1 of the fiequency bins to display a direction value, resulting in
large clusters of dots. if the broadband signais are strong enough, these clusters may appear
grouped horizontally and can be interpreted as the broadband noise direction, for specific
LOFAR Gram
O 20 40 60 80 1 O0 120 1 40 Frequency (Hz)
Figure 2.3: Example of a gram display, showing kequency on the horizontal axis and time on the vertical.
frequency ranges.
O .. . . . . . - . - I . - . - - - I . . - - . - - I - - . -- i - - .%--. .-;, .. . . . .
O 20 40 60 80 1 O0 1 20 140 frequency (HZ)
Figure 2.4: Example of a directional display, showing frequency on the horizontal axis and bearing, relative to true north, on the vertical.
Some modern processors combine this bearing information into color on the gram display.
To accomplish this, every kequency bin in the power spectrum is assigned a color depending
O 20 40 60 80 100 1 20 140 frequency (Hz)
Figure 2.5: Same as previous figure, but with a threshold applied to show only the stronger sources.
on its calculated bearing and its intensity. Broadband noise direction can be easily distin-
guished from the color of the gram background, whiie the thresholded bearing display can
provide the precise bearing rneasurements for narrowband sources.
2.3 Beamforming techniques
Bearnforming was developed in parallel with frequency spectral estimators for estimation in
the directional domain. Methods have been developed using time delays between signals at
different sensors and various correlation techniques.
The development of these techniques have also been perfonned in the frequency domain,
where directional spectra can be obtained for each frequency bin. Passive acoustic analysis
relies heavily on nmowband signatures, and the ability to associate an identîfied target
tonal with a specific direction is crucial for the localization and tracking of that target.
Furthemore, the analysis for a point sensor is preferred since the DIFAR sonobuoy contains
three sensors in one location.
2.3.2 Cross Spectral Matrhc
Beamforming techniques rely on the Cross Spectral Matrix (CSM) estimate 0, calculated
£rom al1 the channels available. In the fiequency domain, Fast Fourier Transforms (FFTs)
can be used to build this matrix efficiently, which has the form of equation 2.9 for the specific
case of a three-sensor DIFAR sonobuoy, giving
where the subscripts O, s and c indicate the omni, sine and cosine channels.
2.3.3 Conventional Beamforming
Consider an input sinusoidal signal from a direction 8, in the presence of noise. For a DIFAR
sonobuoy, the Fourier Traasforms can be calculated as the vector
- a + E,
a sin 8, + E,
a cos 8, + 6, - where the subscripts n denoting frequency have been dropped, a is the amplitude at frequency
w and E,, E , , and E, are the Fourier Transfonns of the noise fiom the three channels. The
direction of look vector, in the horizontal plane, is determined from the buoy geometry as
gT(e) = (1, sine, COS 0 ) (2.10)
The conventional beam power estimate a t any arbitrary direction Êcs ( O ) [Burdic, 19911
is given by
where ( ) denotes an ensemble average, and CB indicates Conventional Beamforming.
The cross-spectral matrix may be partitioned into a signal (S) and a noise (N) component
Then, substituting in equation 2.11:
Êc* ( O ) = pTssT/3 + p T ~ / 3 (2.12)
The beam pattern of the buoy for the signal component is given by the f is t term in 2.12:
B (0) = (1 + sin 0 sin O, + COS e COS o , ) ~ a*
The array gain of the buoy is given by the ratio of signal-to-noise ratio (SNR) of the
array divided by the SNR of the omni channel at the target direction
N /3=sST/9 array gain = -
a* P N B
Assuming that the noise components of the three channels are independent and equal in
amplitude (that is N=NI, where N is a constant, and I is an identity matnu) then
N 4a2 array gain = -- - - 2
a 2 N - 2
Thus, analysis of a h e a r point array (e-g. Burdic, 1991) can be applied dïrectly to
the DIFAR configuration with the direction of look vector defined by 2.10, the beampower
defined by 2.11 giving the bearnpattern of 2.13 and an array gain of 2.
.A major disadvantage of the conventional beamformer is that i t has very low resolution,
particularly for arrays with a srnall number of elements, such as the DIFAR configuration.
It can be readily s h o m through inverting equation 2.13 that the beamwidth a t half power
is 131".
In the past 30 years, however, techniques have evoIved that greatly increase resolution
for small data arrays. These high-resolution methods have been used successfully in geology
[Capon, 19691 for seismic array processing and in passive sonar arrays [e-g. Johnson , 19821.
Of particular interest is the oceanographic application of Marsden and Juszko [19871 to the
heave, pitch and roll buoy as this instrument is the exact mathematical analogue of the
DIFAR buoy.
2 -4.1 Maximuni Likelihood Technique
The Maximum Likeiihood Technique (ML) was orïginally developed by Capon [19691 in the
wavenumber domain for the estimation of seismic data. The ML technique was extended
to the frequency domain by Lacoss [19711 and used by Marsden and Juszko [19871 for the
estimation of ocean wave spectra.
An estirnate of the omni-directiond amplitude a, can be calcdated as a h e u combina-
tion of the data elements
a, = yt@ (2.16)
where y is a vector of fîlter coefficients, or weights, to be determined and the dagger denotes
the Hermitian transpose. The beamformer is given by
To determine y, we minimize equation 2.17 subject to the condition that the filter pro-
cesses a pure sinusoid unaltered in amplitude and phase. Following Kanasewich (19811, it
can be shotvn that this results in the condition that
We can use the Lagrange undetermined multiplier technique with equation 2.17 and
condition 2.18 to minimize
with respect to 7, where X is the Lagrange undetermined multiplier. The result is standard,
given by
Methods such as these are usually referred to as data adaptive, as the choice of weights
Vary wit h direction of look and the characteristics of the sound field measured a t the sensors
[Johnson, 19821.
2.4.2 Eigenvector Technique
The eigenvector (EV) technique is similar to the ML technique, except that we assume that
the matriu 0 can be separated into signal and noise components
The partitioning is achieved through an eigenvector-eigenvalue decomposition of the
cross-spectral matrix, which is then truncated so as to retain only those terms which best
contribute to increase bearing resolution [Johnson and DeGraaf, 19821. The Eigenvalues (A)
and Eigenvectors (4) of matrix 4 are determined, and for an array consisting of M sensors,
we can arbitraxiiy assign the p largest eigenvalue/eigenvector pairs as spanning the signai to
obtain equation 2.21.
The remaining M-p eigenvalue/eigenvector pairs are assurned to span the noise (IV) and
can be determined by equation 2.22.
We can now minimize only the noise component, following closely on the ML derivation
(equation 2-19), using the noise matrix N instead of the cross-spectral matrix Q.
The directional spectrum is then caiculated with equation 2.23.
Note that if we assign al1 the eigenvalue/eigenvector pairs to span the noise, the result is
identicaI to the one obtained for ML. For the specific case of a three-element array DIFAR
sonobuoy, onIy the largest eigenvalue, and the corresponding eigenvector, is dropped. The
EV directional spectrum is calculated with equation 2.24, to give
2.4.3 It erat ive Improvement Technique
Pawka [1983] proposed a scheme to improve the results of the ML technique used to ana-
Iyze the directional ocean wave spectra. In essence, the original ML spectnun is iterative-
ly modified to move closer to a possible true spectrum by examining the behavior of ML
[Oltrnan-Shay and Guza, 19841. Marsden and Juszko [1987] successfully applied this tech:
nique to results obtained by the ML and the EV method for a heave, pitch and roll buoy-
The technique improves the estimates determined by equations 2.19 and 2.23 using the fonn:
The improvement Ji (0) is calculated at each iteration, with
where
ÊO (0)
Ti-' ( O ) is the estimated spectrum calculated from the cross spectral mat& of @-' (0). The
parameters used by Pawka [19831 are = 1.0 and $ = 5.0, and the iterations were stopped
after 50 iterations. Marsden and Juszko [1987] used 11 = 20.0. Pawka found that the final
solution spectrum was not strongly dependent o n the various parameters, as long as Ji was
srnall relative to &-' (O) [Pawka, 19831.
This improvement can be applied to both methods of spectral estimation in this thesis.
The resulting estimates will be labeled IML for Iterative ML, and IEV for Iterative EV.
Chapter 3
Simulation
The data adaptive algonthms outlined in Chapter 2 were tested using simulations described
in Marsden and Juszko [19871. This process involves the construction of a simulated direc-
tional energy distribution fiom pre-detennined parameters, and from this, the calculation
of the simulated cross-spectral matrix. This resulting matrk was then used in the calcula-
tion of the different directional spectra estimates using CB, ML, EV as well as the iterative
techniques IML and IEV.
After a detailed description of the construction of the signal and its cross-spectral matrk,
the measure used to describe the error wiU be presented. The last sections of this chapter
contain the results and plots obtained, and an analysis of the effectiveness of each data
adaptive technique.
3.1.1 Simulated source and noise
The directional test spectnun is calculated as a sum of n, separate sources using the following
expression [Oltman-Shay and Guza, 19841:
In this equation, the simulated signal E(9) consists of n, peaks of maximum power P,
at angle of amval On, and represents the received signal. The standard deviation a, is a
measure of the width of each peak which wïll also be called angular spread when used in a
more general form. The noise was added as a constant over the sum of ail signals and
represents isotropic background noise in the horizontal plane. This noise correspmded to
the predetermined signai to noise ratio (SNR), defined by using
In the following simuIations, the test spectra contain combinations of only one or kvo
signal sources. We first have to ensure an accurate estimate for one source in the presence of
isotropic noise a t various levels, before we can attempt to discern multiple sources. Further
simulations using two sources are then required to determine the effects of angular separation
between the two sources, again with various noise levels. Different sources, in terms of peak
power and angular spread, can also provide interesting results, as it may represent more
realistic cases.
Power levels (P,) were set a t 1.0 for the single source and for the two identical sources.
For the cornparisons using different sources, P2 was set to 0.5 while Pl remained a t 1.0. The
simulations were performed for various angular spreads and SNR combinations, as labelled
on each plot. The simulated scenarios were chosen to be one source at bearing 180°, and
two sources with separation angles (O,) of 180, 120, and 90".
3.1.2 Calculation of cross-spectral matrix
The cross-spectral mat& can be calculated Erom the simulated directional spectrum E ( O )
constructed above using
[Marsden and Juszko, 1987
sectors of 6" each-
described by equation 2.10, and p* is its compiex conjugate
'1. A look vector of 60 elements was dehed, resulting in 60
In the case of DIFAR, the result is a 3x3 matrix, which contains the actual parameters of
the signal. This simulated cross-spectral mat+ can now be used to test our data-adaptive
techniques and obtain an estimated directional spectrum mhich can be compared with the
original simulated spectrum E(0).
3.1.3 Provide statistics for cornparison
The first series of simulation plots shows the five estimated directional spectra dong with the
original simulated spectrum to provide a visual appreciation of each method. The fidelity
of the estimated directional spectrum obtained can then be determined using a weighted
average error (WAE) , calculated by equation 3.4, ais0 used by Marsden and Juszko [l9871.
The validity of the analysis techniques for a DIF'AR can be assessed in part by using
this error measure, and by varying parameters such as SNR and angular spread for each
simulation run. The resulting plots obtained are WAE versus SNR, and WAE versus Angular
spread. The different combinations used for the simulations are described in the foilowing
sections in order to provide an overall assessrnent of each technique.
3.2 Directional energy distribution
The simulation plots showing the directional energy distribution for the different algorithms,
are complemented by the WAE plots of the next sections. These particular plots allow
comparison of the shapes of the estimates in t e m s of peak width, location and relative
height. Each page contains four plots shonring the effect of both SNR and angdar spread
on the estimated spectra. SNR values were set to 1.0 and 2.0, and angular spreads to 2 and
4". These values were chosen as being representative of red acoustic signals.
In each plot, the original simulated spectra is displayed as a solid Iine, wïth the narrowest
and highest power spectral density peak(s). The plots have been truncated for ease of
comparison between the different estimates, but peaks reach a maximum of 1.0 or 0.5, as
noted in the plot descriptions. The estimates for CB are also represented by solid lines, but
the much broader peaks and lower power spectral density should prevent any confusion. The
line styles used for ML, IML, EV, and LEV are labelled in every plot.
Plots are provided for a single source a t 180°, and two sources separated by 180, 120,
and 90". When desc~bing estimates quantitatively, the actual values quoted will be those
for SNR of 2.0 and angular spread of 4", located a t the bottom left of each page, unless
othenvise specified.
DIR. SPEC. SOev=4/SNR= 1,00000
O 45 90 135 180 225 270 315 360 LOOK ECTOR (deg)
DIR. SPEC. SDev=4/SNR=2.00000 0.60 1 1'1 C 8
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
DIR, SPEC. SDev=Z/SNR= 1 -00000 v - . - - a - , -
C E - - - - - - - -ML - , , IML
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
DIR- SPEC. SDev=2/SNR=2.00000
, , - IML œ
0.20
0.10
0.00 O 45 90 135 180 225 270 315 360
LOOK VECTOR (deg)
Figure 3.1: Directional Spectra for one source (power 1.0) at 180".
Figure 3.1 shows the resuits for a single source. EV provides the closest match to the
original spectra, with a perfect match for SNR of 2.0 and angular spread of 4". ML and IML
result in wider, hence lower peaks, only up to 0.25 for the latter. CB offers the broadest
estimate, with a peak power almost reaching 0.1 a t the proper direction.
IEV splits the single signal into two narrow peaks, within the width of the original peak.
This effect is magnified for a narrower signal, or for higher SNR, resulting in extremely high
energy double maxima which becomes not useable.
3.2.2 Two sources (180")
,-, - -- - L v
0.00 1 O 45 90 135 180 225 270 315 360
LOOK VECTOR (deg)
DIR. SPEC. SDev=4/SNR=2.00000
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
DIR- SPEC. SDev=2/SNR= 1 -00000
O 4 5 90 135 180 225 270 315 360 LOOK VECTOR (deq)
DIR. SPEC. SOev=2/SNR=2.00000 C B . - . . - - , -ML , , , IML --,-,Ev - - - - -lm
O 4 5 90 135 180 225 270 315 360 LOOK VECTOR (deg)
Figure 3.2: Directional Spectra for two identical sources (power 1.0) separated by 180".
Figure 3.2 shows two sources separated by 180°, all five algorithms resulted in Mder and
lower peaks, including CB. The maxima location of each estimate matched the input signal
exactly. As expected, the results improved fiom CB, ML, EV, IML then IEV with peaks
maxima going from 0.1 to 0.25.
-4 narrower separation of 120" results in changes different for each of the algorithms in figure
3.3. CB results in only one broad peak, centered between the two original peaks. ML shows
barely two peaks with only a small energy difference between the peaks and the trough. EV
shows a slightly higher level of energy overall, but as in ML, the energy difference between
DIR. SPEC. SDev=4/SNR= 1.00000 DIR. SPEC. SDev=2/SNR= 1 -00000
o . o o F . . . . . . - . O 45 90 t35 180 225 270 315 360
LOOK VECTOR (deg)
DIR. SPEC. SDev=4/SNR=2.00000
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
O 45 9 0 135 180 225 270 315 360 LOOK VECTOR (deg)
DiR. SPEC. SDev=2/SNR=2.00000
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
the peaks and the trough is small. In addition, an obvious drawback of EV is a bias in the
direction estimates, producing peaks closer together than those of the original signal. In this
case, an error of 15" is measured for each peak. This effect has aiso been noted for other
direction values.
Both iterative methods showed improved results. IML increased the difference in energy
between the peaks and the trough, at the cost of a slight bias in direction. IEV significantly
improved both the peak level and the direction accuracy.
- - - - - - - - - - -- -
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
DIR. SPEC, SDev=4/SNR=2.00000
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
DIR- SPEC. SDev=2/SNR=?-00000
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
DiR. SPEC. SDev=2/SNR=2.00000
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg)
At 90" separation, only IEV provided enough directional resolution to result in two peaks
in al1 four plots of figure 3.4. IML barely produced two peaks for a SNR of 2.0 in the two
bottom plots. Finally, EV and ML only resolved one source, with a direction estimated
exactly betrveen the originai peaks. Although IEV resolved the two sources, a significant
bias is present, again pulling the peaks together by about 15".
Other simulations included narrower source separation which provided results similar to
the 90" case, but where o d y IEV discerned both peaks.
3.2.5 Two sources with different power
3.2.5.1 Two sources - Merent power (180")
DIR. SPEC, SDev=4/SNR= 1.00000 DIR- SPEC. SDev=2/SNR= 1.00000
O 45 90 135 180 225 270 315 360 O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg) LOOK VECTOR (deg)
Figure 3.5: Directional Spectra for two different sources (power 1.0 and 0.5) separated by ISOO.
DIR. SPEC. SDev=4/SNR=2.00000 DIR. SPEC. SDev=2/SNR=2.00000
In figure 3.5, we can see that CB and ML produced two distinct peaks at the 180"
- - - - - - - - M L - , - IML ,,,-,EV , -, , ,IN
separation, and although it was weaker, it maintahed the relative strength of each source.
C B ...-.---ML , - , IML -----fZv - - - - - IO/
17 -.- C
For EV, the peak of the weaker source was barely distinguishable while providing a very
.JL .y -- . - - . __ - - .
strong estimate of the stronger source a t 80% of the original power.
IML greatly increased the power levels for the estimates, with peak maxima a t 0.2 and
0.1, and maintained the original two-to-one power ratio. Although the iterative algorithm
seerns to correct the power estimation of EV, the creation of a double peak for the stronger
source indicates a problem with IEV for acoustic waves with the chosen parameters.
3.2.5.2 Two sources - different power (120°)
DIR. SPEC. SDev=4/SNR= 1 -00000 DIR. SPEC. SDev=2/SNR= 1 -00000
O 45 90 135 180 225 270 315 360 LOOK VECTOR (deq)
O 45 90 135 180 225 270 31 5 360 LOOK VECTOR (deg)
DIR. SPEC- SDev=4/SNR=2-00000 OIR. SPEC. SDev=2/SNR=2.00000
O 45 90 135 180 225 270 315 360 O 45 90 135 180 225 270 315 360 LOOK VECTOR (deg) LOOK VECTOR (deq)
Figure 3.6: Directional Spectra for two different sources (power 1.0 and 0.5) separated by
With sources separated by 120" in figure 3.6, CB and EV did not maintain the two-source
resolution while ML was only slightly better, with a very weak second peak. Both iterative
met hods provided some improvements wit h IML matching the sources relative power more
closely again.
3.2.5.3 n o sources - different power (90")
DIR. SPEC. SDev=4/SNR= 1 .O0000 DIR, SPEC. SDev=2/SNR= 1 .O0000 c e - - - , , - - -ML - , - IML ,,,--EV - * - * -1Ev
O 45 90 135 180 225 270 315 360 O 45 90 135 180 225 270 315 3 6 0 LOOK VECTOR (deg) LOOK VECTOR (deg)
DIR. SPEC. SDev=4/SNR=2-00000 DIR, SPEC. SDev=2/SNR=2.00000 7 - 1
C E . - - . . .-.ML - , - IML --, -,Ev - - - - -IN .\
Figure 3.7: Directional Spectra for two different sources (power 1.0 and 0.5) separated by 90".
In this 1 s t case displayed in figure 3.7, only IEV provided an indication of more than one
source, although the direction of the source associated with the weaker peak vvas in error by
40".
3.3 WAE vs angular spread
This set of simulations shows the effect of angular spread on the WAE for the different
algorithms. The angular spread was vaxied from 0.5 to IO0, in 0.5" increments, dong the x
axis. At each increment, the simulated signal was constmcted, and spectrum estimates were
determined for each of the techniques. The WAE were then calculated and plotted at each
increment.
The input signal was further tested for SNR values of 0.5, 1, 2 and 4, resulting in four
plots per page, allowing a cornparison of the techniques a t difFerent signal strengths. In the
WAE equation (eq. 3.4), the Lower tenu acts as a normalizing factor. The absolute value of
the WAE is not important
This whole process was done for a single source at BO0, and two sources separated by
180, 120, and 90". The values for CB are omitted as their WAE was consistentiy higher than
ML and EV techniques. The CB technique &O failed to discem two signai peaks unless they
were Mdely separated, close to 180" apart. Additional simulations were perforrned using two
signals of different strengt hs, for the same angular sepaxations.
3.3.1 Single source
1 source: 180 de O.ML AIML .O% , X!W , 1
O 2 4 6 8 10 Std Dev (Sigma)
1 source: 180 de 0 4 . AIML ,O%' x!EV , .
O 2 4 6 8 10 Std Dev (Sigrnu)
O 2 4 6 8 10 O 2 4 6 8 10 Std Dev (Sigma) Std Dev (Sigma)
Figure 3.8: WAE vs Angular Spread (Std Dev) for one source (power 1.0) a t 180".
Figure 3.8 shows the first results of the simuiation. ML, IML and IEV follow a similar
path for an SNR of 0.5. The WAE decreases steadity as the source angular spread (midth)
is increased. EV shows good results for a spread higher than 5", but the WAE increases
significantly for narrower sources.
For a SNR of 1.0, the overall W m increases slightly, but the shape remains simlar. EV
is the exception again, being markedly better for spreads between 3.5 and 9". For higher
SNR, the curves show sirnilar results, with lower WAE obtained by EV for spreads up to
6.5, and IEV above 6.5". For a SNR of 4.0, IEV becomes unstable for angular spreads under
7 O , giving extremely high errors. This is seen in the bottom right plot, where the x symbols
do not appear in the plot area.
SNR=0.500000 SNR= 1.00000 1.5 - 1 -5
Figure 3.9: WAE vs Angular Spread (Std Dev) for two identical sources (power 1.0) separated by 180".
SNR=2.00000 SNR=4.00000
The curves in figure 3.9 show little variation other than increased WAE as the SNR
i i
i e P w ~ 8 g , 0 0 0 0 ~ 0 1 0 0 0
1.0 - - W
0.0
is increased. For each plot, WAE steps d o m when the angular spread reaches 2". This
- r ' " ' ' ' ~ a ~ ~ a e s g e 0.5 - ' - Q Q Z ~
- 2 sources:180deq sep. - 2 sources: 180deg sep. 0.0
- oML AlML , ON x!EV . , 0.0 .- ,ML ,IML . oEV x!EV
W '-O:r
- 0 P P ~
- 1.0 - W s
- 0.5 - - 2 sources: 1 80deq sep. 2 sources: 180deq sep. - .ML AIML x!RI 0.0 OML, &IML , 0EV .,II3
phenornenon appears throughout the simulations, and is caused by the choice of a sector
- 0 1 C o o s
0.5
width, for the look vector, much wider than the source(s) width. A narrower sector will
move this step-dom towards the left. Above 2.5", IEV shows the lowest WAE, followed by
IML, then EV and ML respectively.
O 2 4 6 8 1 O Std Dev (Siqmo)
2 sources: 1 20deq sep. 0.0 oM& -,!ML . oEV x ! N . .
O 2 4 6 8 10 Std Oev (Sigma)
2 sources: 1 20deg sep. 0.0 0 ML ,ML , oEV x!EV
Figure 3.10: WAE vs Angular Spread (S td Dev) for two identical sources (power 1.0) separated by 120".
The results in figure 3.10 are similar to those of 3.9, with the same stepdown in WAE for
angular spreads above 2.5". Although the order remains the same as in the 180°case, with
IEV showing the Iowest error, the difference between the WAE of each method is smaller.
This is an indication of simiiar performance for al1 four techniques, until higher SNR levels
are reached.
O 2 4 6 8 1 O Std Dev (Sigma)
O 2 4 6 8 10 Sta Dev (Sigma)
Figure 3.11: WAE vs Angular Spread (Std Dev) for two identical sources (power 1.0) separated by 90".
When the sources are separated by only 90°, EV becomes the method with the higher
WAE for al1 SNR levels. The shape of the c u ~ e s displayed in figure 3.11 is still sirnilar to
the previous cases, with the same stepdown in WAE as the angular spread gets above '2.5".
The error for EV is higher than the other three techniques for a SNR of 0.5 and 1.
3.3.5.1 Two sources - dinerent power (180")
The high double peaks seen for IEV in figures 3.1 and 3.5 (left source) resulted in very
high WAE. In this particdar case, IEV caused the IDL program to stop before completion,
indicating a stability problem with the technique. The exact cause could not be isolated,
but the IEV double peaks seem to appear with a higher SNR, and/or with a smaller angular
spread. No plots are available.
3.3.5.2 Two sources - different po-r (120")
L - 2 sources (diff. pwr -120deg sep- 0.0
- oML *!ML , ri-d- x!EV
2 sources (diff. pwr .120deg sep, 0.0 *Mc .IML .!EV
0-0
- 2 sources (diff. pwr :120deg sep. - . oML . A ~ M L . x!m i
Figure 3.12: WAE vs Anylar Spread (Std Dev) for two dinerent sources (power 1.0 and 0.5) separated by 120".
In figure 3.12, IEV and EV showed the lowest WAE and were almost identical for higher
SNR values, with the same overall shape as before. The use of IML resulted in oniy a slight
improvement over ML, but unlike the previous case with two s i d a r sources, its error was
higher than EV.
SNR=O-500000 SNR= 1 -00000 1.5 - 1.5 -
Figure 3.13: WAE vs -hgular Spread (Std Dev) for two different sources (power 1.0 and 0.5) separated by 90".
1.0 - - W W
1 .O - 1.0 - W W s <
L
Figure 3.13 shows a higher WAE for EV in low SNR. IEV resulted in definite improve-
- 0 0 0 , y *-o:*a** =
0.5
0.0
rnents, showing Iower WAE, especidy in a higher SNR environment. For a 90°separation,
s - 0 0 0 0 s *Wuna 0.5 0.5 -
- 2 sources (diff. pwr :gode sep. 0) x $ - , - - - 2 sources (diff- pwr :gode
0.0 - - - oM4 _ , 0- 0-0 ' OMC .[ML , .E?
,
O 2 4 6 8 10 O 2 4 6 8 10 Std Dev (Siqmo) Std Dev (Sigma)
ML and IML were nlmost identical for all values of SNR.
- -
0.5 -
This set of simulations shows the efFect of SNR on the WAE for the different algorithms.
Simulations were performed for SNR of 0.5 t o 5, in increments of 0.25 along the x M s . At
each increment, the simulated signal was constructed, and spectnrm estimates were deter-
mined for each of the techniques. The WAE was calcuiated and plotted for each. Further
- 2 sources (diff. pwr :gode sep. - 2 sources (diff. pwr :90dy& sep. ES : oML AIML , O f 0.0 1 alML , od x.
tests were performed for angular spread (Std Dev) values of 4, 6, 8 and IO0, resulting in four
plots per page.
This process was done for a single source at 180°, and two sources separated by 180, 120,
and 90". Again, the graphs for CB are omitted as their bVi4.E v a s consistently higher than
ML and EV techniques. Additional simulations were performed using two signals of different
strengths, for the same angular separations.
3.4.1 Single source
O 1 2 3 4 5 Signal/Noise Ratio
Figure 3.14: WAE vs SNR for one source (power 1.0) at 180".
For one source oniy, the EV and IEV behave quite differently depending on the SNR and
the angular spread, as shown in figure 3.14. IML results in much lower WAE than ML, and
shows a steady improvements as the SNR increases to 5. EV is better for a narrow source
at high SNR, but IEV results in lower WAE on a wider spread and SNR at mid-range.
Figure 3.15: W.4E vs SNR for two identical sources (power 1.0) separated by 180".
For two sources, the results are smoother and easier to interpret. Figure 3.15 shows the
smallest WAE for the iterative methods. IEV is markedly better for SNR values above 1.5,
followed by IML, then EV and ML. For lower SNR values, al1 four methods result in similm
WAE.
O 1 2 3 4 5 Signal/~oise Ratio
* * @ 6 1 % s B P H . ~ ? x x x x x x x x x
p l x
0.2 . 2 ~ o u r y ~ ~ 1 wegx I i ip . 0.0: 0 . A n
O 1 2 3 4 5 O 1 2 3 4 5 Signol/Noise Ratio Signal/Noise Ratio
Figure 3.16: WAE vs SNR for two identical sources (power 1.0) separated by 120°.
Figure 3.16 shows very similar results those in figure 3.15.
g 8 1 e o O O n A ~ ~ ~ d ~ a ~
O 1 2 3 4 5 Signol/Noise Ratio
Figure 3.17: WAE vs SNR for two identical sources (power 1.0) separated by 90".
Figure 3.17 shows similar shape curves again, exept for EV which shows higher WAE
than ML. IEV and IML retained the same order, indicating good performance for al1 SNR
tested.
3.4.5.1 Two sources - different power (180')
Again, the estimate from lEV resulted in two very high power spectral density peaks, as
described in section 3.3.5, resulting in a stability problem. No plots are available.
3.4.5.2 Two sources - different power (120")
, ( d g 1 20deg sep rl
O 1 2 3 4 5 ~ignal/Noise Ratio
- - - -
O O O O Q O O O O A A A A A A A ' I A A
o % a P ~ ~ . p B
~7&120deg sep
Figure 3.18: WAE vs SNR for two different sources (power 1.0 and 0.5) separated by 120".
For the peaks at different power levels in figure 3.18, the lowest WAE is achieved by
the EV and the IEV method, which follow an nlmost identical curve. The other techniques
resulted in a sipXcantly higher error, especially ML.
3.4.5.3 Two sources - different power (90°)
, s a m ~ I i a s s s a s i i a i 4 a x ~ x ~ ~ ~ ~ x ~ ~ j
o p ~ ~ x X X X x X x X X x x X
, ( d g p&90deg sep. j p~&90deg sep. n
O 1 2 3 4 5 O 1 2 3 4 5 Signol/Noise Ratio Signol/Noise Ratio
Figure 3.19: WAE vs SNR for tvvo different sources (power 1.0 and 0.5) separated by 90".
In figure 3-19? the WAE for the IEV technique is significantly lower than the other three
methods.
3.5 Discussion on validity of each technique
From the WAE plots, both ML and EV consistently showed higher errors levels than their
iterative counterparts. However, the error level differences were often relatively smail and
the directional energy plots may offer a better representation of the results. Both techniques
have very similar results for two identical sources, with only a s m d energy level difference
between the peaks and the trough, and the ability to resolve sources down to 120" apart.
For sources with different parameters, ML is slightly better, for both peak-to-trough energy
48
difference and relative maximum energy of each peak.
-4fter considering al1 the sixnuiations, IML seems to be the most promising data adaptive
technique. The directional estimates are accurate under almost all conditions, and it can
consistently resolve two identical sources separated by 120". It also gives acceptable resuits
for angular separations down to 90°, although lower SNR may affect the results significantly.
When dealing with different sources, the angular resolution was attainable only for separation
of 120" or more. The amount of computing required to produce this estimate is also of
concern. The improvement over kf L for estimating sources directions rnay not be worth the
intensive iterations.
IEV seemed to have a good potential, but stability probIems occurred in some cases. The
precise cause is unknown, but problems seem to appear for sources with high SNR, or when
the angular spread was below 4". Peaks in the directional spectra produced by IEV were often
estimated as two very high power spectral density narrow peaks. A large part of the ASW
acoustic detection problem has to do with discrete sources, and these simulations indicate a
potentid reliability problem for what may be common conditions. When estimating multiple
peaks separated by less than 180°, IEV also introduced significant biases in the order of 15"
for each peak. The bias was more significant for sources with different maximum power.
Chapter 4
Field data
4.1 Known targets in area
The high-resoiution beamforming methods were applied to real DIFAR data to evaluate the
performance of each algorithms. Figure 4.1 shows the surface plot with three ships present
in the viciniw of the sonobuoys. The first sonobuoy, DIFAR channel 03, was Iaunched at
19:47 and provided data until approximately 20:ll. Another DIF'AR 03 was launched at
20:13, which provided data until 20:36. Contact 1 is traveling from west to east at over 20
kts, and should result in a bearing shift from northwest to northeast. Contact 2 is moving
at over 15 kts in a southwest direction, a t about twice the range of contact 1. Due to its
slower speed, the extra distance fiom the sonobuoy and the heading difference, the bearing
shift for contact 2 is =pected to be smalIer than the one for contact 1. Contact 3 launched
the sonobuoys and is traveling to the southeast. An underwater sound projector was towed
by the launching ship, contact 3, and produced strong narrowband tonals a t fiequencies 15,
17, 47, 50 and 147Hz. Its bearing relative to the sonobuoy will be nearly constant as the
ship is traveling directly away from it.
The gram shown in figure 4.2 was processed localiy, and presents acoustic information
Figure 4.1: Map of the area showing three ships around the sonobuoys.
from the two sonobuoys, with a frequency range of 5 to 100 Hz. This particular display
shows the first buoy from 1956 to 2011 (minute O to 15), updating from the bottom. After
about 3 minutes without signals, the second buoy is processed fkom 2014 to 2036 (minute 18
to 40). The intensiw of the image indicates the power spectral density, with brighter bins
indicating stronger contacts. This monochromatic gram is representative of older acoustic
displays, many of whkh are still in use- The Bscan in figure 4.3 is also similar to current
system displays, and shows the directional information a t 2023 (minute 27). A more modern
processor can incorporate directional informaion as color on the gram. Each frequency bin
would be assigned a color to indicate the direction of the acoustic source. The intensity of
the frequency bin would then be translated into a shade of the chosen color, with stronger
contacts displayed as brïghter bins. Variations of this type of display are already in use on
various acoustic processors, offering different choices of sector number, and colors. More
precise bearings are available through a Merent display such as a Bscai;.
LGFAR Gram
40 60 Frequency (HZ)
Gram showing both sonobuoys, fiom 5 to 100 Hz. The data updates upwards from time 1956 to 2036.
The only data provided were the three time series fiom the DIFAR, with no individuai
acoustic signatures or anaIyses. Further analysis will not be performed, nor is it required for
the purpose of comparing the beamforming techniques. The directional spectra calculated
from the raw data are ail based on magnetic north, hence a correction of 20°W was applied
to al1 plots in order to present the results relative to tme north.
40 60 frequency (Hz)
Figure 4.3: BScan a t 2023 (minute 27) showing the directional information as a single value for each frequency bin.
Directional Processing and Display
4.2.1 Processing
The techniques discussed in Chapter 2 were used to construct the directional spectra of the
data a t various times, using cross-spectral mat M estimates calculated for each kequency bin.
To provide a statistically valid cross-spectral matrix estimate Q, 16 samples were averaged,
requiring about one minute of data based on the sampling rate. For this thesis, a simple
average was used, with 8 samples before and 8 samples after the chosen time. This method
is adequate for applications such as post-ftight andysis where the complete t h e series can
be made available for computing. Simple modifications to the D L programs used for this
thesis could allow for other types of averaging, resulting in slightly different cross-spectral
matrix estimates. The estimate of Q is then used as a starting point for processing by aU
techniques. After the directional spectra estimates have been cdculated for a Çequency
bin, they are normalized to the omni power value to provide proper power scaling and
allow compaxison amongst methods. This nomalization is necessary because data-adap tive
techniques determine directions of maximum power, not actual energy levels.
4.2.2 S haded Surface Display
The results are displayed using dinerent forms of directional plots. The first m e of plot is
provided by a shaded surface, as in figure 4.4, which spans a selected fkequency range on
the x avis (horizontal), from 5 to 100 Hz in this case. For each frequency bin, the energy is
distnbuted dong the y axis (left), providing directional information hom O to 360" relative
to true north. Because the radial information is displayed as a 0at surface, a maxima to
the north would appear both at the top near O", and a t the bottom near 360". The vertical
axis shows the normalized power spectral density and the maxima dong the Y axis provide
the direction(s) of the incoming signd(s). Again, we are only interested in the shape of the
estimates as absolute power values are not available from these techniques.
f r o p ange: ch 5-190 1 S;ime=20:23:00 z Res:0.244141 Hz Conventional Beamforming 1
Figure 4.4: Directional Spectra caiculated by CB at time 2023, c o v e ~ g a frequency range of 5 to 100 Hz.
Figure 4.4 shows the directional spectra caiculated by the CB technique a t t h e 2023,
with only two peaks being more obvious. The first peak, a t 25 Hz, has a ma..Omw power
spectral density a t 340" matching with contact 1, and the other, a t 47 HZ, indicates a source
at 110" corresponding to contact 3. Similar maxima are visible in figures 4.5 and 4.6 for
estimates calculated by the ML, M L , EV and IEV techniques, showing the same directions,
but with narrower peaks.
Brg from ch 1 Time=20:23:00 Re~:0.244141 Hz Frequency Range: 5- 100Hz 4 Moximum Likeiihood
-11
lterative Maximum Likelihood
Figure 4.5: Directional Spectra calculated by ML and IML a t time 2023, covering a frequency range of 5 to 100 Hz.
Bra frorn ch 1 T i rne=20:23:00 Reç :0 .244141 Hz ~ r e & e n c ~ Range: 5-1 00Hz
Eiaenvector
lterotive Eigenvector
Figure 4.6: Directional Spectra calculateci by EV and IEV at tirne 2023, covering a frequency range of 5 to 100 Hz.
In addition, the data adaptive techniques produced small peaks at 42 and 51 Hz, visible
just below and on either side of the 47 Hz peak, corresponding with two diffuse lines from
contact 2 at bearing 195". A closer inspection of the 25 Hz directional spectra reveals a
second maximum, also at bearing 195", for these techniques. At this point, we note that
the normalization discussed in 4.2.1 results in an obvious drawback for this type of plot, as
strong sources with high peaks tend to make the weaker directional spectra flat, and difficult
to assess.
160 180 200 220 240 frequency (Hz)
Figure 4.7: Bscan at time 2023, covering a frequency range of 150 to 250 Hz.
The ability to provide accurate directional information from broadband signal is also a
desired feature for target detection and localization. The fkequency spectrum between 150
and 250 Hz contains no narrowband sources and was used to compare the performance of
the techniques.
Figure 4.7 is a Bscan display with a threshold of zero, showing a bearing point for each
frequency bin, with no other procesçing or corrections applied to the data. This display
shows a concentration of dots dong bearing 180°, with a wide bearing variation from dot
to dot. To a lesser extent, another concentration of points, grouped dong bearing 340°, can
be identified. The rest of the bearing dots seem to be distributed in a somewhat random
fashion between the two main directions. In fact, this is expected as the Bscan is calcuiated
as an average of the stronger bearing values, resulting in estimates between the real targets.
Brg from ch 1 Time=20:23:00 Res8:0.244141 Hz Frequency Range: 150-250Hz
Moximum Likelihood
iterative Maximum Likelihood
Figure 4.8: Directional Spectra calculateci by ML and IML at t h e 2023, covering a frequency range of 150 to 250 Hz.
Figures 4.8 and 4.9 show the sarne part of the frequency spectrum, where no obvious dis-
cre te t arget signals are present. Wit h high-resolution beamfodng techniques, t his broad-
band noise is separated as two distinct contacts correspondhg to contact 1 to the North and
contact 2 to the South. The direction estimates show very little variation between fiequency
bins, much less than in the Bscan display discussed above.
Brg from ch 1 Time=20:23:00 Resb:0.2441 41 Hz Frequency Ronge: 150-250Hz
Eig envec tor
iterative Eigenvector
Figure 4.9: Directional Spectra calculated by EV and IEV at time 2023, covering a frequency range of 150 to 250 Hz.
Although EV and IEV result in narrower directional peaks, some anomalies were ob-
served. At 202 Hz, EV provided two peaks, exactly 180 degrees apart, with no corresponding
surface contacts in the vicinity of the buoy. The iterative improvement of EV maintained
and amplified the two peaks. As obsewed during the simulations, IEV created double peaks
for two frequency bins, between 240 and 250 Hz, seen in this plot at bearing 180.
4.2.3 Directional energy distribution display
Brg from ch 1 Time=20:23:00 Res:0.244141 Hz 3.5 j
Freq: 25.1 465 Hz
O 45 90 135 180 225 270 315 360 Bearing (deg)
Figure 4.10: Directional Spectra for frequency bin 25.1 Hz, calculated at time 2023. The four High-Resolution techniques identified two sources in the same frequency bin.
To alleviate the visualization problems due to power scaling, a second type of plot, as in
figure 4-10, isolates specific fiequency bins as a two dimensional plot similar to those used
to illustrate the simulations. The vertical dashed line represents the single bearing value
provided by current acoustic processors, using the arctangent method (Bscan). Based on
the power spectral density of the spectra, the 25 Hz bin appears to contain acoustic signals
from two sources, a strong one at 340" (contact 1) and a weaker one at 195O (contact 2) from
all the techniques except CB.
3 O II-
O 45 90 135 180 225 270 315 360 Bearing (deg)
Figure 4.11: Directional Spectra for the frequency bin 46.9 Hz, calculated at time 2023. The strong narrow band source outpowers a weaker source to the North, picked up by the high-resolution bearnfonning techniques.
Figure 4.11 (46.9 Hz) shows the effect of a strong narrowband source from contact 3 over
a weaker source in the same frequency bin. Aithough much weaker, and not visible from
the gram, or Bscan, a second source to the north is identified by the four high-resolution
methods. The weaker peaks direction estimate matches contact 1, indicating approxïmately
330°, Mth the iterative techniques providing better results again.
O 45 90 135 180 225 270 315 360 Bearing (deg)
Figure 4.12: Directional Spectra for the frequency bin 42.5 Hz, calculated at time 2023. A combination of ML and EV techniques identified the three known targets in the same frequency bin.
Figure 4.12 shows a fiequency bin located within a strong but d a s e fi-equency tonal,
seen on the gram at 42.5 Hz, Contact 2 is correctly identified to the south by ML and
IML along with a weak indication of contact 1 to the North. EV indicates a contact at
bearing 110, which could be contact 3, with a smaller hump for contact 2. IEV separates
those two contacts more completely, resulting in a strong bearing for the possible contact 3,
and a weaker one for contact 2. These last two methods could not discern contact 1. The
limitation of data-adaptive techniques with respect to power estimation is highlighted in this
figure. What appears as the strongest source in the gram, CB, ML and IML is estimated as
a weak contact in EV and IEV. In terms of directional information, it is interesting to note
that three sources can be isolated with a combination of techniques.
O 45 90 135 180 225 270 315 360 Bearing (deg)
Figure 4.13: Directional Spectra for frequency bin 202.4 Hz, calculated at time 2023. Spu- rious peak estimates that do not match the surface picture were identified by EV and IEV-
The anomaly at 202 Hz, discussed in 4.2.2, is shown in figure 4.13. A few other frequency
bins showed simiiar patterns, where EV and IEV provided detection on spurious directions
not related to known contacts in the vicinity- In this case, CB, ML, and IML al1 show
contacts 1 and 2 at about the same strength, with the arctangent bearing indicating an
erroneous estimate of 275". This error is expected in the presence of sources with similar
power, as the average of directiond energy wiil fall somewhere between the actual sources.
Freq: 240,479 Hz
135 1 80 225 270 315 360 8earing (deg)
Figure 4.14: Directional Spectra for fiequency bin 240.5 Hz, calculated at time 2023. The double peaks were created by LEV at a few fiequency bins.
The double peaks created by IEV, shown in figure 4.14, also appeared at other fiequencies,
as seen in the simulations. No clear explanation can be given, but it seems that these peaks
only appear for specific combinations of SNR and angular spread.
Brg from ch 1 Tirne=20:23:00 Res:0.244141 Hz J I
:'t
Figure 4.15: Directional Spectra for kequency bin 18.8 Hz, calculated a t time 2023. Spurious peak estimates that do not match the surface picture were identified by EV and IEV.
-4nother anomaly appears in the 18.8 Hz bin, shown in figure 4.15, with the lower overall
power spectral density indicating broadband signal, CB, ML and IML correctly identi&
contact 1 to the North, also matching the arctangent value. The results from EV and IEV
show two sources separated by about 90°, with no correlation to surface data.
Over the observed range of 2048 hequency bins, less than five bins contained erroneous
data for EVIIEV. Although this may represent a high percentage in some systems, the
spurious peaks can usuaJiy be discarded visuaiiy based on appearance. The other methods,
namely ML and IML appeared to be very stable and provided consistent results in all cases.
4.2.4 Averaged Directional Spectra (Polar plots)
The last type of plot is the averaged polar plot, as in figure 4.16, where the directional
spectra are averaged over a selected frequency range, Erom 5 to 250 Hz in this case. Note,
the spectra are implicitly weighted by the total spectral power density in each fkequency
bin, determined by the omnidirectional processing. A strong source will therefore have more
weight in the final result.
-4lthough the result of a very simple operation, this tool showed good potential to display
multiple contacts on one plot. The resulting plots provide a quick visual reference, showing
targets as peaks on a rosette, with each plot contabïng the five high-resolution estimates.
The line patterns are the same as in section 4.2.3 for the identification of each technique.
Figures 4.16 to 4.21 show the progression of the three lobes, which cioseiy match the
three different contacts described in figure 4.1- CB provided the worst results with no
distinct peaks at au, showing an elongated circle at best. ML was better, showing a definite
bearing for contact 3, but fairly wide lobes for contacts 1 and 2. IML, EV and IEV were
similar in shape and provided narrower lobes with three definite contacts in most cases.
Brg from ch 1 Time=19:57:00 Res:0.244141 Hz
Figure 4-16: Averaged
Brg from ch
Figure 4.17: Averaged Directional Spectra calculated at time 2009.
Figure 4.18: Averaged Directional Spectra calculated at tirne 2018.
Brg from ch 1 Time=20:18:00 Res:O-244741 Hz 40
20
- - - - - - -
I I I
-40 -20 40 - - - - - - -
Brg from ch 1 Time=20:29:00 Res:0.244141 Hz
Bra from ch 1 Time=20:35:00 Res:0.244141 Hz
20
IO
c - - - - - - - - - - -
In general, the high-resolution methods provided good directional estimates for the observed
target separations. The reçdts from the ML technique were equivaient to, and often better
than, the EV method in terms of bearing accuracy and the detection of a second weaker
target. In one case, we observed that EV provided the stronger source with only little, or
no information about the presence of a second contact.
The power spectral density difference from trough to peak was increased with the iterative
methods, providing similar results for both IML and IEV- The bearing estimation bias
experienced with EV during the simdations, was al

Documents

HIGH RESOLUTION BEAMFORMING TECHNIQUES APPLIED TO A DIFAR SONOBUOY CAPT