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2 REPORT DATE 

December 1993 


3 REPORT TYPE AND OATES COVERED 

Professional Paper 


4 title AND Subtitle 


VLF SOURCE LOCALIZATION WITH A FREELY DRIFTING ACOUSTIC 
SENSOR ARRAY 


6 AUTHORISI 

G. Chen and W. Ilodgkiss 


5 FUNDING NUMBERS 

PR; SUBS 
PE:0602314N 
WN. DN308105 


7 PERFORMING ORGANIZATION NAME(S| AND AOORESSIES) 

Naval Command, Control and Ocean Surveillance Center (NCCOSC) 

RDT&E Division 

San Diego. CA 92152-5001 


8 PERFORMING ORGANIZATION 
REPORT NUMBER 


9 SPONSORING/MONITORING AGENCY NAME(S| AND ADDHESS(ESI 

Naval Command, Control and Ocean Surveillance Center (NCCOSC) 

RDT&E Division 

San Diego, CA 92152-5001 


iTsPONSORIF^ 

AGENCY REll>RT,IIUM{ER I i 

f f: 

L- 



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t1 SUPPLEMENTARY NOTES 


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t2a DtSTRtBin’tON/AVAlLABlUTY STATEMENT 


Approved for public release; distribution is unlimited. 


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5 3 abstract (Maximum 200 worefsj 


This paper describes the source localization and tracking capability of a freely drifting volumetric array with matched- 
field processing (MFP) using experimental data. 


Published in IEEE Journal of Oceanic Engineering, July 1993, pp. 209-223. 


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14 SUBJECT TERMS 


environmental adaptation 
freely drifting sensor array 
matched-field processing (MFP) 


simulated annealing 
source localization 


t5 numBeF^ 




16 PRJCECODE 


17 SECURITY CLASSIFICATION 

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il.JI !()IK\\l < H (K{ AMC KN(;iNh:KKINC.. V( )| IS, \m • 


If I > :•**>; 


VLF Soul xe Localization with a 
Freely Drifting Acoustic Sensor Array 

George C. Chen, Member. IEEE, and William S. Hodgkiss, Member. IEEE 

(Invited Paper) 


Abstract —Source localization and tracking capability of the 
freely drifting Swallow float volumetric array is demonstrated 
with matched-field processing (MFP) technique using the 14- 
Hz cw data collected during the 1989 Swallow float experiment 
conducted in the northeast Pacific by Marine Physical Labora¬ 
tory. Initial MFP of the experimental data revealed difficulties 
in estimating the source depth and range while the source az¬ 
imuth estimate was quite successful. The main cause of the 
MFP performance degradation was incomplete knowledge of 
the enrironnient. An environment adaptation technique using 
a global optimization algorithm was developed to alleviate the 
environmental mismatch problem. With limited knowledge of the 
environment and a known location of the 14-Hz source during 
a selected time interval according to the source log, the ocean- 
acoustic environment can be adapted to the acoustic data in a 
matched-field sense. Using the adapted environment, the 14-Hz 
source was successfully localized and tracked in azimuth and 
range within a region of interest using the MFP technique at a 
later time interval. Two types of environmental parameters were 
considered, i.e., sound speed and modal wave number. While 
both approaches yield similar results, the modal wave number 
adaptation implementation is more computationally efficient. 

Index Terms — Matched-field processing, source localization, 
freely drifting sensor array, environment adaptation, simulated 
annealing. 


I. Introduction 

RADITIONALLY, source localization has relied on the 
processing of assumed plane-wave fronts received by 
spatially distributed sensors to estimate the source bearing 
or vertical angle of arrivals. In reality, the ocean acoustic 
channel is extremely complex due to refractive and multipath 
effects. Assumption of plane-wave arrivals in the processing 
scheme in some cases can lead to severe degradation of the 
estimate. Matched-field processing (MFP) has been proposed 
[I] to actually u.se the complex ocean acoustic properties 
to improve source detection and localization. MFP involves 
the correlation of the actual acoustic pressure field mea¬ 
sured at the array with a predicted field due to a source at 
an assumed location deriving from an acoustic propagation 
model. A high degree of correlation between the measured 
field and the predicted field indicates a likely source loca- 

Manuscript received January 20. 19*12. revised May 7. 199.2 This work was 
supported by the Oflice of Naval Techimlugv under NRI, Contract N000I4- 
88-K-2040 

G C Chen iv wnh the Nav.d i. i.i\'u.,iiKt Control and Ocean Surveillance 
Center. RDTVI. DiviMon, San Dice" ('\ '*2152 .2001 

W. S Hodgkiss IS with the Marine I'hv-ical l aboratory. Scripps Institution 
of Oceanograpliv liniversiiv of ( ilr m. i San Diego. CA 92152-6400. 
lliBL l.og Niiinbct 92IOI.''K 


tion. MFP of the acoustic wavciield has shown that when 
sufficient environmental characterizations (e.g., sound-speed 
profile, bathymetry, sediment properties) are available, rather 
remarkable detection and localization results can be obtained. 
Most available matched-field work has been for rather simple 
propagation situations (e.g., range-independent environment) 
and much of the work has been re.stricted to vertical-line arrays 
(!)-[91. Although matched-field processing offers an appealing 
approach to the underwater source detection and estimation 
problem, a common difficulty with this technique occurs when 
the environment information is inaccurate. A “mismatch" 
occurs between the measured data and the modeled pressure 
field, and the performance of the MFP is degraded and leads 
to errors in the e.stimation of the source location [10H141. 
Several previous studies such as self-cohering [15], envi¬ 
ronmentally tolerant beamfoiming (161, acoustic tomography 
(17], Realization 118). and MV beamformer with sound-speed 
perturbation constrains (19) have been proposed to combat 
the environmental mismatch problem so as to improve the 
localization performance. 

The focus of this paper is twofold: 1) to demonstrate the 
match-field source localization and tracking capability of the 
Swallow float freely drifting volumetric array using experi¬ 
mental data, and 2) to propose and demonstrate an environment 
adaptation technique that may minimize the effect caused by 
imprecise knowledge of the environment and thereby lead 
to MFP localization performance enhancement. This paper is 
organized as follows. Section II gives a brief description of 
the Swallow float system and a summary of the July 1989 
Swallow float experiment. Section III presents the results 
of initial matched-field processing on the 14-Hz continuous 
wave (cw) tone collected by the Swallow floats during the 
1989 experiment. Controlled simulations also are presented to 
aid in interpreting the experimental data priKessing results. 
Section IV proposes an environment adaptation technique to 
enhance the MFP localization performance The technique is 
illustrated using both simulation and experimental data. La.stly, 
a summary of Ihe paper is given 

11 1989 SWAl.I.OW l lO.XI H.XI’HRIMKNT 

A. Swallow Ebuir Svsiem l)i u "".'imi 

Over the last several yeais \li'l li.is designed and devel¬ 
oped a set of 12 acoustic scum ili.ii are neutrally buoyant 
and freely drifting when dejilov il m the ocean. The sensors 
are called Swallow floats m iimi.ii of J C. Swallow who 



0264 90.59/9.2$03 00 © 1992 IKBI 









ii i-i J(M K\ 


\\!( 1 \(.IM I KIN(;. VOI. IS, NO V JOl V 


nil N A 



Fig. I. Schematic drawing of a typical Swallow float. 

used freely drifting floats to measure deep ocean currents. The 
MPL Swallow floats are used to measure acoustic energy in 
the very low frequency (VLF) band from 1 to 25 Hz. The 
Swallow floats are designed to operate without tether so that 
their measurements are not contaminated by tether strumming 
noise and flow noise. As illustrated in Fig. 1 (20), (21), each 
Swallow float is a 17-in. diameter glass sphere containing 
three orthogonally oriented geophones used as the acoustic 
particle velocity sensor, a compass, the electronics, and power 
supply. External to the sphere are a hydrophone for measuring 
VLF acoustic pressure, an 8-kHz acoustic transducer for 
transmitting and receiving acoustic ranging signals, an optical 
flash, a radio beacon, and the relea.se ballast. In operation, 
the floats are deployed and ballasted to neutral buoyancy at 
the desired depths. While deployed, each float records signals 
from the three geophones and the hydrophone sampled at 50 
Hz, the compass, and the 8-kHz range puKse arrival times. 
The acoustic transducer with source strength 192 dB re I 
/iPa at 1 m generates and receives 8-kHz 10-ms pulses in 
a programmed sequence. A different float transmits every 45 
seconds. When 12 floats are deployed, each float transmits 
every 9 minutes. The floats are listening whenever they are not 
transmitting. They receive pulses transmitted by other floats 
as well as surface/bottom reflections of their own pul.ses. The 
interfloat and float-to-surface acoustic travel times can be used 
to determine the float positions as a function of time with a 
least-squares-based postprocessing procedure 120| 

B. 1989 Experiment Summary 

The 12 Swallow floats were deployed for a 24-h period on 
8-9 July 1989 near 34°50'N, 122'’20'W, about 150 km wc.si 
northwest of Pt. Arguello, CA (22). Of the 12 floats. 9 v.crc 
Irecly drifting in the water column, and } wore tethered to the 
ocean bottom by 3.05-m lines with lO- to 1.5-lb anchors The 


^ Ifue Nonh 

e * 


T Y 


9 -8 -7 6 5 -4 5 : 1 0 1 2 3 

Dtsunce (km) 

Fig. 2 Roa( honzontal displacement estimates using least-squares filter 
dunng the July 1989 experiment The circles mark the starting positions. 

I 

three bottom-tethered floats were positioned at the comers of 
a triangle with sides about 6.3 km long in order to provide an 
absolute reference for the float localization The nine midwater 
floats were deployed in a quasi-vertical line array geometry | 
with a vertical float separation of about 400 m, starting at : 
about 600-m depth to about 3800 rn. The midwater floats 
were put into the water at about the geometric center of 
the bottom-float triangle. Fig. 2 shows the horizontal position 
estimates of the midwater floats from the least-squares method 
between 00:00-13:58 PST, 9 July 1989 (records 1003 and 
2120). The position estimates indicates that the freely drifting 
floats dispersed away from the center of the float triangle with 
floats 0 and 1 (the shallower floats) moving to the northwest, 
floats 2 and 3 to the west, float 4 to the southwest, and floats > 
5, 6, 7. and 8 (the deeper floats) to the southeast. The drifting 
pattern was probably due to the complex water movement 
near the experiment site. The float depth estimates from the i 
least-squares Alter are also plotted in Fig. 3. The estimate of 
rms float position error is less than 4.6 m [23). The float j 
localization procedure appeared to be capable of estimating 
float positions to within the desired accuracy of one-tenth of 
a wavelength at the highest frequency of interest 25 Hz (6 m) 
in order to effectively beamform the VLF acoustic data. ; 

As part of a companion experiment, a VLF source was being j 
towed approximately 2500 km west of the Swallow float array 
at an average speed of 8 knots and depth of 90 m. Fig. 4 shows 
the VLF source relative to the Swallow float deployment site. 
The VLF source was to transmit 14 Hz for a half-hour, then j 
8 Hz for a half-hour, then 14 Hz, then 11 Hz and then repeat 
the pattern. The power spectral estimates from data collected i 
by float I's hydrophone during records 1040 to 1680 (00:28- } 

08:28 PST, 9 July 1989) are presented in Fig. 5 in spectrogram 
format. Evidently, the Swallow floats can see quite clearly the j 
14-flz line projected by the VLF source and, at times, the 
11 Hz line 

A large volume of environmental data such as AXBT, XB3 . 
and CTD measurements was collected by the companion c\ 
IH'iimeni during 8-10 July 1989 beiween ,34"r)0'N, 122°2{l'W 


Fig 3. 
The hor 
number 


z 

U 

1 

■a 

J 


Fig. 4. 
of mar 


and 3'. 
profilt 

111 . 

Thi 
Hz-to’ 
float ( 
The fi 
the sc 
vector 
the CO 
surfac 
array 
(7), I 
that L' 
conve 


\vhere 
-ure f 













H k , ( I ( H \l 1 / M K >N 


‘illcr 

ons 

rs of 
Je an 
•vater 
netry 
ng at 
Hoals 
■:r of 
>ition 
Mhod 
and 
ifting 
with 
west, 
floats 
ifting 
ment 
n the 
ite of 
float 
ating 
ith of 
6 m) 

Teing 
array 
hows 
site 
then 
cpeai 
ccted 
0:28- 
■gram 
V the 
.. the 

\BT. 
II ex 
-’O'W 


9 . 10.11 


JSOO.. i.. 1 .: 

900 ICO'' !iX) 1600 1800 300 C 2200 

K-v Surrifx’f 


I ig ^ I'loal depth estimates uMfig least ^quarcs filter. July 1989 expcnmeni 
The ht'ri/onlal axis <'l'the figure gixoN the time m units of Swallow fh^al record 
numher l ights records represent one tmui 



Fig 4 VLF source—Swallow float arras gesmietry. 9 July 1989 The line 
of triangles marks the AXBT measurements taken between H-IO July 1989 


and 32°00'N. 150°0()'SV. Fig. 6 is the summary of sound speed 
profiles derived from the measurements. 


III. Source Locai.i/.ation SVith Swai.i.ow Ft.OAT Array 


This section presents the results from initial MF'P of the 14- 
Flz-tone propagation eolleeied during the July 1^)8^ Swallow 
float experiment. There are three steps involved in the MFP. 
The first step is the estimation of array covarianee matrix at 
the source frequency, the second is the prediction of replica 
vectors for all assumed source locations; and the Iasi step is 
the computation of amhiguiis surfaces a peak m the ambiguity 
surfaces indicates a likely source location In this studs, three 
array processing structures commonly reported m the literature 
|7|, |24| are used to compute the amhicmts surfaces ,o 
that their results can he compared I he It u': -;; method is a 
conventional technique that is rohusi h :' . lesoliiiion’ 

l \ unun {'. .. «) /';"///■; (I) 


where r is the beamformer output power. I-' ■ -phea pres¬ 
sure field vector due to a narrow band smiic ■ H). II - 


X k 7 k 


V. ■ 

i i.HunwiUSM 


1! ! Y 



l-mjueocy ill;' 


l-ig 5 VLF acouMic spcclrograni ol lloal I. (XI 2S--0S F’S I. u .lul> IVSn 
The vertical aris of ihc figure goes ihe limc m iinils ol S^.iHow lloat record 
number Eighty records icpreseni one Ik'ui 



E\XX^] is the cross-spectral densit; matrix or array covan- 
ance matrix of the sensor outputs,' nd X is vector ot the array 
Fourier coefficients computed at me frequency of interest. The 
minimum variance method is a data adaptive technique that 
yields higher resolution 




ff| = -^7 - 

k" n 




( 2 ) 


and the eigenvector methtid exploits ihe orihogou.iliis princi¬ 
pal that achieves even higher resolution 


/’vii sictr. ; 'I 




1.^) 


where R\ is the noise cov:in.mce m.iiiiv 


A. Estimating the Arnn CinniKinn Mann 

Although each .Swallow iloat colicvo ' 
geophone data and one channel oi In.i 
the omnidirectional hydrophone dai.i !!.•■ 
floats are studied and analyzed m this p.ipe 
contains its own clock for timing, the In 
the acoustic data is to align the time Ic! ■ 
path travel times arc combined to estim.i: 


uinels of 
i.ii.i. only 
■ ilrifting 
c.ieh float 
'■I'Cessing 
leeipriKal 
dive clock 







>•» <M } Wll- I N(ilM-,KKIN(J. VOL IS. \() L Jl LV I'sr, 




Fig 7 Acoustic pressure 





3 too 

\ 

Fto»l7 

• 40 

■ S A 

1 ■ 

H 

\ A A 


Z » 



^ X, 




0 S 10 IS 20 25 

Frequency (Hi) 


specira for mjdwaier floais 


acceleration, clock rate, and the offset between two floats (25|. 
The lime bases are then aligned by choosing one float as 
a reference whose time base is not shifted and shifting the 
time base of the rest of the floats’ time series. To ensure 
the quality of the array covariance matrix estimate, the data 
records need to be qualified and selected with care. Two 
criteria used in selecting the data record are S/N and spatial 
coherence at the frequency of interest. Fig. 7 is the power 
spectra obtained by processing 3 min of data (records 1143 
to 1146). The power spectra are derived from incoherently 
averaging 28, 50% overlapped, 512-point FKls (97-mHz bin 
width). A Kaiser-Bessel window with a parameter of 2.5, 
yielding a sidelobe level of -57 dB (26), weights the data 
prior to each FFT. Power values are calibrated in decibels re 
1 fiPa. The 90% confidence level in these spectra is about 
±1 dB. The 14 Hz was being transmitted during the time 
when data records 1120 through 1160 (01:27-01:57 PST, 9 
July 1989) were collected. A line at 14 Hz, about 10 to 15 
dB above the background noise, can be clearly scon in all 
freely drifting floats’ pressure spectra. The high S/N at 14 Hz 
observed in the power spectra illustrates the good quality of the 
1989 Swallow float data sets. The second criterion in selecting 


the data is to estimate the spatial coherence between floats. The 
spatial coherence or the magnitude-squared coherence (MSC) 
is defined as 


|7xv(/)|" 


\Sry{f)\^ 

5xx(/)5„(/) 


(4) 


where Szy{f) is the cross-spectral density at frequency / 
between x{t) and y{t) with power spectra S^xif) and Syy{f). 
The MSC function evaluated at / is a real value, conveniently 
normalized to lie between zero and unity. High coherence 
of a line frequency harmonic among all float pairs not only 
indicates the signals originate from the same source but 
assures high array gain when the individual sensor outputs are 
combined to form a beamformer. Fig. 8 shows the magnitude- 
squared coherence and the phase difference between floats 
0 and 2 during 00:27-02:57 PST, 9 July 1989 (records 
1040-1240). The MSC functions are calculated by averaging 
over 40.96 s of data, 128-point FFT’s with 50% overlap, 
providing 31 averages. The high coherence during records 
1120 to 1160 is a confirmation that the signal originates 
from the same source, and the smooth measure of the phase 
differential suggests that beamforming of this data would be 
successful. 


1 


,L 


I 



•2 - 

I04( 


Fip 8 


Estin 
three f 
estimat 
Hz wic 
FFT’s . 


windov 


I 

j 


a 40.9< 
{XX” 
In prai 
reliable 
the nui 
will su 


proces; 
well ki 
to ensu 
31) use 
invertil 
numbe 
the lai 
is requ 
loadin) 
by add 
is the ■ 
systen- 
sensor 


B. Act 

The 
replicc 
by a 5 


















vi*.J \ 


i HI \ Wl) HOlHiKlSs \\ \ S(tlk(| l(N \ 1 I/Alt(*\ 




1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 

Record Number 



acduslit.- iMnni'aii .:i! ''riu cl-ii the .iiiil the vciimm I le 

<■> IS .1 sciics oi -.pi'L'il piolik's ileriNi’il ti'im ilie t, I D s, 

the XHI's. .Hill liiL’ A.XlJT's taken alone the a|ipro\iniaie 
path between the souree ;inj the Swiilluu lloat ;ina> uithin 
4X h ol' the .Sv^allov^ lloat experiment All of the proliles 
along the propagation path exhibit a depth excess that is a 
necessary condition for long range-propagation. The itteso 
scale change in the ocean temperature structure across range 
on the order of several thousand kilometers results in range- 
dependent variations in the sound-speed profile as shown in 
Fig. 6. The slow varying sound speed structure variation, 
especially in the upper water column between 120°W and 
l.T'5‘'W. is believed to be influenced by the cold waters of the 
California Current coming dowm from the north. The sound 
speed structure between 140°W and 15()°W remains relatively 
stable; this pan of the ocean is known to be environmentally 
benign. 

We use the adiabatic mode theory to model the acoustic 
pressure field. The adiabatic mode theory solution in a 2-D 


environment is: 


1040 1060 10*0 1100 1120 1140 1160 1180 1200 1220 1240 

Record Number 


Fig. 8 (a) Spaiial coherence al 14 Hz and (b) Phase difference beiween 

floats 0 and 2 at 14 Hz during records 1040-1240 


Estimating the array covariance matrix is required by all 
three processors. The array covariance ntatrix R can be 
estimated from the measurement data. Frequency bins of 0.4- 
Hz width centered at 14 Hz were extracted from 128-poini 
FFT's (2.56 s of data) using a Kaiser-Bessel (with a = 2.5) 
window and 50% overlap for each of the nine floats over 
a 40.96-s data record. This results in a 31 dyad produefe 
(XX^) being averaged for the covariance matrix estimate. 
In practice, the number of averages required to produce a 
reliable covariance matrix estimate is about two to three times 
the number of sensors in the array. In our case, 31 averages 
will suffice. Since the matrix must be inverted for the MV 
processor, it should be well conditioned and of full rank. It is 
well known that as many dyads as sensors must be averaged 
to ensure full rank. Although a large number of snapshots (i.e.. 
31) used to compute the array covariance matrix R ensures the 
invertibility of the covariance matrix in theory, the condition 
number of the matrix given by the ratio of the smallest to 
the largest eigenvalue is below 10“^’. and additional effort 
is required. We use the white-noise slabili/alion or 'diagonal 
loading" method (27J. The covariance matrix R is stabilized 
by adding to the main diagonal the quantity 10 ' (ir/f/\/)(tr 
is (he trace operator) which corresponds to intrxKlucing m the 
system an uncorrelated .sensor noise 10 dB below ihc average 
sensor power level (9). 

li. Acoustic Propagation Modeling 

Tlic second step toward MFP is the calciilaiion >1 
replica vectors. To predict the acoustic pressure field reccnc.l 
by a .sensor due to an assumed source, one mu.si model ihe 


/)(r. = ,-1 ^ !/,,,(0)u, 


j(c. r j . ■— 


The modal sum is over the number of propagating modes. 
A/, that exist between the source and the receiver The 
modal function involves the depth eigenfunctions at the source 
u„,(Zo; 0). the receiver u,„(z: r). and the horizontal wave 
numbers function (,n(-^) reflecting the range dependence of the 
mediurr along the path between the source and the receiver. 
The implementation strategy for (,„(■•<) ds is to divide the 
full range into a number of segments; the horizontal wa\e 
numbers are calculated at a di.screie sets of ranges where sound 
speed measurements are available. To determine the number of 
propagating modes. M, for the oceanic waveguide formed by 
the source and the Swallow float array, we need to examine the 
modal depth eigenfunctions. The modal depth eigenfunctions 
at a frequency of 14 Hz for the environment near the VLF 
sourcc and the Swallow float deployment site are computed 
with the ATLAS normal mode model (28), [29], The first 30 
modal depth eigenfunctions are gray-leveled and displayed 
in Fig. 9. Examining the upper portion of the figure that 
corresponds to the environment where the .source is ioeaied. 
we see that there are about 22 modes trapped in the water 
column and are non-bottom interacting; also, for the voutee 
depth at 90 m, the first 6 modes arc very weaklx exviied 
For the low-order modes to be strongly excited, the Mmive 
would have to be placed between its turning points vDH'ie the 
mode peaks up. The lower portion of the figure eonv'poiuis 
to the environment at the array site; given the water d. pih .n 
this liKation, non-bottom interacting modes are limited fo iIk- 
first 16 modes. Note that the depth functions entei le ■ > 
pressure field calculation in (5) as product u ,Oo 
where the one depth function is evaluated at source dc 
the other depth function is evaluated at the receivei , ; ' 
As result of the product j ), and .i-.- 

the bottom interacting modes arc unable to propagate 
long range due to bottom attenuation, only the first lo u : - ■ ■ i 









CIU-.N 


u i-l lOUkNAl. OF CKTANKM.NGtNH RtNCi. VOL IH NO ^ l 


sSf ,?t S.Hjfce 



USO i!^ 1520 1 540 

Sound Speed ( ir /« c ) 


0 5 10 15 20 25 '0 

Mode Nunbcf 




Sound Speed (m/sec) 


S 10 IS 20 25 

Mode Nmnber 



00 02 04 06 Of 10 

Unevtcik 


Fig 9 Modal eigenfunctions at frequency of 14 Hz. 


modes were used in the calculation of the acoustic pressure 
field. Also, in the mode calculation, earth curvature correction 
was incorporated due to the propagation distance of 2500 km. 
In this paper, the 3-D replica pressure field was approximated 
by evaluating the adiabatic model along a series of N bearings 
in the range-dependent environment assuming the environment 
is a^imuth-invariant, to give an /V x 2-D description of the 
field [30]. 


C. Experimental Results 

After aligning the float time bases and performing data 
quality checks, the array covariance matrix for record 1145 
(01-.47 PST, 9 July 1989) was estimated. The problem of 
grating lobes in beamforming using a sparse array was not 
addressed; we therefore limited our focus to a region of 
interest. The replica vectors were computed using (5) for a 
hypothetical source in a spatial window extending in range 
from 2300 km to 2700 km, in depth from 0 to 300 m, and 
in azimuth from 166° to 176° (refer to Fig. 2, we use the 
mathematical convention with -X pointing 0° as reference and 
rotating counterclockwise). The sampling intervals in range, 
depth, and azimuth were 1000 m, 10 m, and 0.1°, respectively. 
MFP was performed with all three processors; Bartlett, MV, 
and MUSIC. The peak value in the region of interest was 
recorded and normalized to yield power in dB re /rPa. Table 1 
summarizes the results of MFP on the experimental data along 
with the true source location and the expected bcamformer 
output power. Note that power levels were reported for the 
Bartlett and MV processors onlv since (he MUSIC method 
does not yield the true power l ip. 10 present the Bartlett 


TABl.F. I 
MFP Rf.si i IS 



Banleli 

MV 

MUSIC 

1 ',. ■ ' 


Pr(Kesst>r 

l^roccssor 

ProcossDf 


IV pill t't 

Max 

10 m 

1.70 m 

10 ni 


Range 

Max 

26.S9 km 

2659 km 

2659 km 

2-i^t ' km 

A/imuih 

Max 

172.r 

172 1° 

172.r 

1717 

l\»ucf 

Max 

82.7 dB 

73 2 dB 

- 

.S7 dB 


matched-field ambiguity surfaces. The upper panel was the 
range-azimuth ambiguity surface evaluated at the depth where 
the highest peak occurred while the lower panel was the 
range-depth ambiguity surface evaluated at the azimuth where 
the highest peak occurred. The surface was normalized to 
its highest peak and was marked with this symbol. *. For 
comparison, the true source location was marked with a A. 
While mismatch existed, all three processors were in good 
agreement except for their depth estimates. In fact, all three 
lacked the depth resolving power [31]. The highest peak 
in the ambiguity surface differs from the true location by 
0.6° in azimuth and 166 km in range. The large number of 
sidelobes observed in the ambiguity surfaces was thought to 
be due to imperfect modeling and the sparseness of the array. 
The MV and MUSIC processors suffered large losses due to 
mismatch since the replica were imperfect [31]. Ambiguities 
(or sidelobes) in range were the result of the repetitive structure 
of the acoustic field in a convergence zone environment. ' 

D. Controlled Simulation 

' While source localization in azimuth was somewhat sue- , 
cessful, localization in range and depth seemed to be a 
problem. Simulations are presented here in an effort to under¬ 
stand the experimental ambiguity surfaces. Three simulation 
cases were studied; the ideal simulation, uncertainty in float | 
positions, and uncertainty in sound speed structure. j 

1) No Mismatch Simulaton: Assuming there was no mis¬ 
match and input S/N was 10 dB, the simulated "acoustic data” 
and replica vectors were generated using the same environment 
model. A 14-Hz source was simulated at a range of 2493 km, 
an azimuth of 171.5°, and a depth of 90 m, which is the 
true source location at record 1145 according to the source 
ship log. The Bartlett ambiguity functions were evaluated at a 
depth of 90 m and an azimuth of 171.5° degrees and plotted in 
Fig. 11. As expected, the source was correctly localized. The 
high sidelobes found predominately for the ambiguity surfaces 
produced by the Bartlett processor were believed to be due 
to the nature of the processor and the array geometry. Also,' 
the pressure field calculated using the adiabatic normal mode 
model was composed of only the first 16 low-order waterborne 
modes. Thus, the acoustic pressure field was less complex or 
less unique at the simulated source liKation. The poor depth 
resolution observed in the ambiguity surfaces was thought to 
be due to the combination of few propagating modes and the 
low source depth (90 m) to wavelength (105 m) ratio. 


Fig. 1 


2 ) 
posit 
no p 
the 5 
simu 
array 
sensi 
over 
had i 
The 
the s 
posit 
case 
in Fi 
are s 
Th 
simu 
proa 
[31]. 
the h 
SUCCl 

The 

rang! 

simu 

less 


















CH1-:N AM) HOlKiKISS Ml S(>|!R(| i « k M;.'\U()\ 


Kange-A/iniuih anthigmr. sum.*. 


led 

U 


km 


IB 


IS the 
where 
IS the 
where 
ced to 
For 
I a A. 

good 
I three 
. peak 
lon by 
iber of 
ight to 
• array, 
due to 
(guities 
ructure 
nl. 



Kange-.A/iniutii a;nhik:t< 


2700 26S0 2^ 2SS0 2500 2450 2400 2350 2300 

fUsseOaa) 





flSO 

& 


250 

300 


RA&ge-Oepth ambiguirv surface at izunutfa 171.5 degree (Banlen) 

. M i 4 . ^ - ^ . 


2700 2650 2600 2550 2500 2450 2400 2350 1300 

Rjuge 0cm) 


•3 -2 

Rc1m«c Pawn (dB) 


Fig. 10. Matched-field processing results using the Bartlett method for the Fig. 11. Matched-field processing simulation result.s (no mismatch) using 


14-Hz source during record 1145. 


the Bartlett method. 


at suc- 
) be a 
under- 
lulation 
in float 

lo mis- 
ic data” 
onment 
f93 km, 

^ is the 
; source 
ited at a 
lotted in 
'.ed. The 
surfaces 
■ be due 
y. Also, 
lal mode 
iterbome 
nplcx or 
lor depth 
■ought to 
> and the 
o. 


2) Uncertainty in Float Positions: The sensitivity to sensor 
position mismatch was next investigated. Assuming there were 
no position errors, the replica field were generated using 
the same conditions as in the real data case. However, the 
simulated “acoustic data” was computed using a perturbed 
array geometry where the amount of perturbation to each 
sensor position had been drawn from a uniform distribution 
over (4 m, 10 m), similarly the perturbation related to direction 
had also been drawn from a uniform distribution over (0, 2n). 
The rms position error for the particular realization used in 
the simulation was 7 m. The impact of mismatch due to float 
position error was investigated again in a 10-dB input S/N 
case. The Bartlett range-azimuth ambiguity surface is plotted 
in Fig. 12(a) and the all three matched field processing results 
are summarized in Table II. 

The sidelobe structures were very similar to those of ideal 
simulation, but the peak value for the MV and for the MUSIC 
priKessor was much reduced from that of the ideal simulation 
(31). Although the mismatch reduces the dynamic range of 
the MV and MUSIC processors tremendously, the source was 
succes,!ully located in range and azimuth with reduced power. 
The ONiiin.iied source range was identical to the “true” source 
range with a minor discrepancy in the azimuth estimate. These 
simui.i.. ; results suggest that slight float position error, i.e., 
less than one tenth of the wavelength (10.7 m) might be the 


cause of the mismatch in azimuth but cannot be responsible 
for the mismatch in range. 

3) Uncertainty in Sound-Speed Structure: We then Studied 
the simulation of sound speed mismatch. For simplicity, the 
sound-speed profiles collected during the experiment were 
modified by adding a linear function of the form (2}: 

m/s (6) 

to the sound-speed profiles collected between 140°W and 
1 j 0°W. In this simulation, we used 6 = -3 and D = 2000 
m so that at the surface, the sound speed was decreased by 3 
m/s. while below 2000 m. there was no change. The specific 
form (6) is justified for two reasons; 1) The sound-speed 
profiles collected in this track during the experiment were 
south of ihc signal propagation path (refer lo Fig. 4) and 2) 
The general climatic change as one goes from south to north 
is such ihai the sound speed in the upper part of the water 
column l.creases. The replica vectors were generated using 
the ongiii.il profiles while the simulated “acoustic data" were 
generated using the modified sound speed profiles reflecting 
(fi) lii. iiarilett range-azimuth ambiguity surfaces for the 
sound speed mismatch simulation are plotted in Fig. 12(b) and 












n i l- JOUkNM Oh (K h.ANIC I N(.IM I Kl\< 


(. lU N AN 


U nccna inty in Sensor Po&iuons 


|.j 

i 

I- 


/Ml 


2700 2650 2600 2550 2500 2450 2400 25^0 2300 

Range (kis) 


(a) 


166 

168 

|,70 

-e 

J- 

174 

176 

2700 2650 2600 2550 2500 2450 2400 2350 2300 

Range (kn) 

(b) 


Uocenainty in Sound Speed Stnicture 


/ 1 I 


f / f » 


I I 


Fig. 12. Maiched-field sitnulaiion using the Bartlett Method (a) uncertainty 
in sensor positions and (b) uncertainty in sound-speed structure. 


TABLE II 

Matched-Field Si.mulation of Sensor Position Errors 



Bartlett 

Processor 

MV 

Processor 

MUSIC 

Processor 

Depth of Max. 

no m 

110 m 

110 m 

Range of Max. 

2493 km 

2493 km 

2493 km 

Azimuth of Max. 

171.7° 

171.7° 

171.7° 

Power of Max. 

-0.16 dB 

-7.25 dB 

- 


the MFP results are summarized in Table III. The results show 
the source peak shifted in range with much reduced power for 
the MV and MUSIC processors [31]. The estimated source 
range is off by 117 km from the "true” source range, and the 
source azimuth is slightly shifted by 0.1°. These simulated 
results confirmed that uncertainty in sound-speed structures 
can be responsible for the large mismatch observed in the 
real-data ambiguity surfaces, particularly the range error. The 
environmental mismatch problem will be further investigated 
in Section IV. 


IV. Environment Adaptation 
Matched-Reld Processing 

MFP has been proposed and developed for localizing un¬ 
derwater acoustic sotirces by comparing acoustic data with 
predicted replica pressure fields [Ij. The inputs to MFP are 
the acoustic parameters of the ocean for predicting the replica 


U T -1 


';•! I 


TAIil I. Ill 

M-m'i iii.ti iTiiii .SiMiT Arms m s,,. 



Banleii 

iV'vL - 

Sl( 

IX‘pth ol Max 

no 

1 il 

;n 

Range ol Max 

2610 


■f.in 

A/.imuth of Max 

171 4° 

i:i 1 

■ 1 1 

Power ('f Max 

-0 5 dB 

- in 7 .iH 



pressure fields and the acoustic data rcceiscd h> an arras 
of hydrophones. In order to compute the rcplic.t sectors 
for the MFP, the knowledge of sound-speed structure and 
bottom characteristics as a function of depth and range are 
required. As shown in the previous section, if the available 
environmental information is not sufficiently accurate, MFP 
can be degraded even if the signal-to-noise ratio is high. 
Thus, calibration of the environmental parameters so as to 
improve the matched-processing performance is of special 
interest. In this section, we propose an environment adaptation 
technique which has the potential to enhance the matched-field 
localization performance. This technique is illustrated using 
both simulation and experimental data. 

A. Environment Adaptation Technique 

We envision that the way that the environmental mismatch 
can be reduced is a two-phase process [15). 1) Adaptation 
phase: During this phase, a narrowband signal with frequency 
of interest at a known location is transmitted to probe the 
oceanic waveguide. The signal could be a surface ship of 
opportunity or a broadband source with good S/N at the 
frequency of interest such as air-deployed shots [17], The 
matcned-field processor is configured in a feedback loop 
fashion as in Fig. 13 to adjust the environmental parameters 
with the goal of causing the predicted pressure field to match 
the measured pressure field, i.e., 

maximize P(r„, ^o) (7) 

r 


Monte 
minimi 
many t 
of exp 
problet 
of new 
allow t 
by a t 
tempet 
less ar 
Our in 
uses tl 
(becau 
cost ft 
algorit 
procec 
1 ) 

2 ) 


3) 

4) 

5) 


where F is the environmental parameter set, and Zg, 6„) 
is the matched-field processor output power due to source at 
a known location (tq, Zo, Oo). 2) Localization phase: When 
the environment adaptation phase is completed, the optimized 
environmental parameter set Fopt is then used to compute the 
replica pressure fields and normal matched-field processing 
can resume to search for an unknown target of interest in the 
vicinity of the reference source. In this study, two types of 
environmental parameters, sound-speed structure, and modal 
horizontal wave number, are considered. We use matched-field 
processor output as a performance function or cost function, 
since the cost function P is nonlinear and may have many 
focal maxima (or local minima if we use the negative of P as 
the cost function); a global optimization technique is required 
for searching the optimum environmental parameters. 

/) Global Optimization Method: In this Study, we use the 
fa.st annealing mcthiHl (IS], [32] for searching the envi¬ 
ronmental pariimcier spaces. The method is based on the 
conventional simulated annealing technique [33], a heuristic 


6 ) 


7) 


2 ) 
rial c 
cient 
lead 

i [18], 

inter 
way. 
; princ 

\ find 












I'Wl 


array 
;ctors 
; and 
■e are 
ilable 
MFP 
high, 
as to 
pecial 
lation 
1-field 
using 


match 
)tation 
jUency 
Te the 
nip of 
at the 
|. The 
loop 
meters 
match 


(7) 


urce at 
When 
imized 
ute the 
;essing 
in the 
pes of 
modal 
;d-field 
nction, 
■ many 
)f P as 
^uired 

use the 
; envi- 
on the 
euristic 


CHI N AMI IIOIKIKISS Ml SOl'KCI I ( K' Al 1 / \ I H 


Sensor Dat* f ' 1 \ .. 1 

-^ i-f-T J- •“[l-. 1 \N I 



Fig. 13. Environment adaptation technique bltKk diagram 

Monte Carlo search method for the determination of global 
minimum of combinatorial optimization problems involving 
many degrees of freedom. Its basic feature is the possibility 
of exploring the parameter search space of the optimization 
problem allowing “hill climbing” moves, i.e., the generation 
of new states (or parameter sets) which increase the cost to 
I allow escape from local minima. These moves are controlled 
I by a dynamic variable called temperature, in analogy with 
I temperature in annealing process. The hill climbing moves are 
! less and less probable as the temperature decrea.ses or cools. 
Our implementation of the fast simulated annealing algorithm 
uses the negative of the MUSIC matched-field output power 
(because of its high resolution capability) as the energy or 
cost function to be minimized. The fast simulated annealing 
algorithm for this study is encapsulated in the following 
procedure. 

1) Set the initial temperature T„ to a large value. 

2) Determine the number of parameters needed to be per- 

' turbed using a random number generator with Poisson 

distribution and select the parameter to be varied using 
a random number generator with uniform distribution. 

3) Generate the perturbations for the selected parameter(s) 
using a random number generator with Cauchy distribu¬ 
tion [32]. 

I 4) Perturb the current parameter set and compute the new 
: cost, f is the iteration number. 

5) If E, < £,-i, then accept the new parameter set and 
i proceed to (7). 

I 6) If £, > £._i, then accept the new parameters with 
a probability given by the Boltzmann distribution, 
e\p{-AE/kT), the quantity /c is a constant and its 
dimension depends on the dimensions of A£ and T. 

7) Decrea.se the temperature according to the fast cooling 
schedule [32] which is inversely linear in time, i.e., 
= 7'„/?, and repeat the procedure, terminate the 
procedure when no new parameters are accepted for a 
large number of interactions. 

2) Reducing the Parameter Search Spaces: For combinato¬ 
rial optimization problems of very many parameters, an effi¬ 
cient characterization to reduce the parameter search space will 
lead to fast convergence and more uniqueness in the solution 
[18]. Thus we wouki like to characterize the environment of 
intere.st in as few parameters as possible yet in a meaningful 
way. A common method from statistics for analyzing data is 
principal component analysis. The essence of this method is to 
find a set of K onhogonal vectors in data space that account 


loi HA much as possible of the dai.i's '..ui.hkc l’iii|c>,liiig the 
tlat.i trom their original A'-dimension.il sp.i, c mito ihc A 
dimensional subspace spanned by these vciHU' ilien peiiornis 
a dimensionality reduction that often leitmis most of the inirm 
sic infomiation in the data. Typically. A' <t. .\ . thus making 
the reduced data much easier to handle. Similar to the principal 
component analysis method, oceanographers have developed 
a method for deriving efficient basis functions, known as 
empirical orthogonal functions (EOF’s), for measured physical 
quantities such as temperature, salinity, or sound speed as a 
function of depth [17], [18], [34], [3.“)]. In an effort to reduce 
the ocean-acoustic parameter spaces, one can describe the 
parameter set as a sum of EOF’s. The EOF's are defined as 
the eigenvectors V, of the parameter covariance matrix R: 

RV, = X,V, (8) 

where A, is the ith eigenvalue or the variance associate with 
V,. The covariance matrix for the environmental data R is 
defined as 


R = iJlf F] (9) 

where F I' - £[r], and F is the measured environmental 
parameter values. E\ ] is the expectation operator. The pa¬ 
rameter search spaces can then be represented or spanned as 
a linear combination of appropriate EOF's. 


A’ 

Ein-t-^QnV'n (10) 

n = l 


where N is the total number of eigenvalues, the V^„'s are 
indexed so that A^ > A„ + i, and rt„’s are the EOF coefficients. 
In practice, a high degree of accuracy can be achieved with 
only two or three EOF’s for representation of ocean-acoustic 
parameters [17], [35]. Using the EOF approach to parameterize 
the environment, (7) can now be expressed as 

maximize P{r„, Zo, Oo) (11) 

{oi, fc = l, K ) 

where K < .V and is related to F by 

K 

r = E(F) + ^a,V^,. (12) 

t—i 


B. Simulation Results 

The environment adaptation technique described above is 
first applied to simulation data. To make the simulation as 
realistic as possible. Ave modeled the source-array geometry 
corresponding to the Inly 1989 experiment with a 14-Hz 
source deploved ;ii the locations according to the source ship 
log. The freely drifting sensor array geometries corresponding 
to the navigation lesiilis during the two time intervals, i.e., 
01:47 and 04:38 I’.S f. July 1989 were used in the simulation 










CllLN 




Fig. 14. Matched-rteld simulation of environmental mismatch for the two 
time intervals corrsponding to the experimental data collected during 1989 
experiment. 

study. To simulate the environmental mismatch, similar to that 
of last section, we modified the profiles between 34°N, 140° W 
and 32°N, 150°W by adding a function of the form; 

AC(2) = - Cmean(^) ftVS (13) 

where C 340 N, hoovv is the sound-speed profile taken at 34°N, 
140°W, and Cmean is the mean profile between 34°N, 140°W 
and 32°N, 150°W (refer to the solid line in Fig. 18(b) for the 
shape of AC(a)). Although arbitrary, this perturbation was 
justified by the fact that the sound-speed profiles collected in 
this track were off the signal propagation path. The simulated 
“acoustic data” were generated with an adiabatic normal mode 
model using the sound speed profiles reflecting (13), while the 
replica vectors were generated using the original measured 
sound-speed profiles. The range-azimuth ambiguity surfaces 
for the mismatched case during the two time intervals are 
plotted in Fig. 14. The A’s are the “true” source locations 
according to the source log, and the *’s arc the MFP esti¬ 
mated source locations, i.e., the highest peak in the ambiguity 
surfaces. As expected, the estimated source locations using the 
mismatched environment were off in range by roughly 100 km 
to 150 km (2 to 3 CZ's) for both time intervals. 

I) Sound-Speed Adaptation: We now proceed to the envi¬ 
ronment adaptation technique and assume that the source-array 
geometry is known exactly during the first time interval 
(01:47). Under the assumption that the adiabatic approximation 
is adequate to predict acoustic pressure field in a slowly 
varying range dependent environment for MFP, one can show 
that there will be some equivalent range independent sound- 
speed profile [31). The first simulation case is to invert for 
the range-independent sound-speed profile representing the 
environment along the signal propagation path between 140°W 
and 150°W in a matched-field sense. Fig. 15(a) shows the 
excess (demeaned) sound speed profiles for the upper ocean 
derived from 30 AXBT measurements made between 34°N, 
140°W and .32°N, 150°W in July, 1989. Table IV lists the 
five largest eigenvalues obtained through eigen-decomposition 
of the sound speed covariance matrix. As can be .seen, only 
the first few eigenvalues are significant. Wc thus use the 


eigenvectors or KOl-'s eone-.p.svlnu' lo ihe two largest eigen¬ 
values in spanning the ve.iul. -p.i. ■ - \unn.ili/ed versions of 
the F.OF's corresponding 10 the iwu largest eigenvalues are 
shown as solid and doiieil tuiww lespeeiively. in Fig. 15(b). 
The eigenvalues or v anaiiees .s'l i. spondiiig to these FOF's 
were Ai - np = 54.(lti and \ . respectively 

To ensure all possible parameiei v.ilues are reachable in the 
search spaces, we allow the values of the liOF coefficients 
to vary within ±6rr„. Using the mean sound-speed profile, 
the first two FlOF's. and the initial solution of the EOF 
coefficients of (0, 0). the optimi/ation is performed with 
the fast annealing procedure. Fig 16 shows the convergence 
properties of a typical annealing nin. In this example, the 
temperature was initialized at 2(X) and was reduced to 0.2 | 

over 1000 iterations. The first and second panels are the 
trajectories of the EOF coefficients while the third panel is 
the cost function learning curve as the annealing proceeds. 

As expected, the cost function learning curve declines as the 
iteration goes on, but occasionally the curve increases to a 
higher energy state thus indicating the escaping out of the 
local minima. After 350 iterations, the optimization process 
converges to the minimum energy state, and the solution of 
the EOF coefficients found at the 1000th iteration is (9.00, 
21.91). To validate the optimal solution, the energy (cost 
function) surface as a function of the EOF coefficient values 
is calculated exhaustively on a regular grid in ni and 03 (with 
a grid size of 1) bounded by (-50, 50). which corresponds to 
10201 evaluations of the cost function as displayed in Fig, 17. 
The surface shows a global minimum at f>i = 9, 02 = 22 
with numerous local minima scattering around. The joint 
trajectories of the EOF coefficients as the annealing proceeds 
are overlaid on the energy surface plot. A good agreement 
between the solutions obtained by grid search and optimization 
is observed. It is of interest to know whether the optimal 
solution of the EOF coefficients varies from run to run. The 
environment adaptation procedure is then repeated for nine 
times, each time with 1000 iterations. The solutions are given 
in Table V. The convergency properties and the consistent 
agreement among all runs are again observed, which confirms 
the fitness of the global optimization algorithm. 

The adapted sound-speed profile derived from the mean 
profile and the two EOF coefficients found at the 1000th 
iteration is plotted by dotted line in Fig. 18. For comparison, 
the modified sound-speed profiles (i.e., the “true” profiles) 
used to simulate the “acoustic data” are averaged and plotted 
by solid line, and the measured profiles that were used to 
model the replica vectors are averaged and plotted by dashed 
line. As can be seen, the adapted profile tracks the “true” 
profile closely. We now proceed to the localization phase of 
the technique. The measured sound-speed profiles between 
140°W and 150°W are replaced by the single adapted sound 
speed profile, and normal matched-field processing resumes. 
Fig. 19 shows the optimized range-azimuth ambiguity surfaces 
for both time intervals. The environmental adapted source 
locations match those of an ideal simulation (no mismatch). 

2} VV'rtit’ Number Adaptation: The second implementation 
of the environment adaptation technique is to invert for the 
modal wave numbers at the source frequency (14 Hz) for 


2 


( 



I' 

i> 

1 

2 ' 


a 



1 

I 


Fig. 15 
AXBT 
Normal 


E 


the ac 
The a 
speed 
wave 
To CO 
the sa 
execs; 
numb 
AXB' 
of the 
showi 
the h 
now I 
surf at 
joint 
.'.nnca 










I '‘'i ’» > 


■ ( Ml N AND HOrXiKISS M l SOUKC'I: I.CXTALIZATION 


’IM 


;Ji-n 
IS Ol 
■ .III' 

S(h) 
JPs 
•ely. 

I the 
tents 
)file, 
EOF 
with 
ence 
. the 
> 0.2 
the 
el is 
jeds. 
s the 
to a 
" the 
•cess 
in of 
900. 
(cost 
diues I 
with I 
ds to 



joint j 
eeds j 
ment j 
ition I 
imal I 
The I 
nine 
'jven 
stent 
hrms 

nean 
OOth 
ison, 
hies) 
jtted 
d to 
shed 
true" 

X of 
vecn 
ound I 
mes. 
faces 
•urcc 
;h). 
ation 
r the 
) for 



.Oi 06 0.4 -03 0.0 0.2 0.4 06 06 

Nonnalized Souod Speed EOFs (o/s) 


(b) 

Fig. 15. (a) Excess (demeaned) sound-speed profiles computed from 30 
AXBT measurements made between 140°W and 150°W. July 1989. (b) 
Normalized versions of the first and second EOF's derived from (a). 


TABLE IV 

The Five Largest Eigenvalues Obtained From 

ElGEN-DECOMPOSmON OF THE SOUND-SPEED COVARIANCE MATRIX 


Number 

Eigenvalue 

1 

54.06 

2 

35.96 

3 

11.93 

4 

2.81 

5 

1.81 


the acoustic waveguide of interest in a matched-field sense. 
The assumptions and conditions are identical to the sound 
speed adaptation case with one exception, that is, the modal 
wave number EOF coefficients are now the search parameters. 
To compare these two implementations, we followed exactly 
the same path of investigation. Fig. 20(a) shows the first 16 
excess (demeaned) wave number estimates of the modal wave 
number at the source frequency (14 Hz) obtained from 30 
AXBT measurements made in July 1989. Normalized versions 
of the EOF’s corresponding to the two largest eigenvalues are 
shown as solid and dashed curves in Fig. 20(b). Note that 
the lag in the wave number covariance matrix estimate is 
now the mode instead of the depth. Fig. 21 shows the energy 
surface computed by exhaustive .search and an example of the 
joint trajectories of the wave number EOF coefficients as the 
annealing proceeds. Using as a reference the averaged model 



0 lOD»DKfi400SOOfiOOX>OK»«» 1000 

Iwva* 



0 lOO»)M0400SOO«00 100tDO«nKn) 



0 lOOXlOWDaOOSOOOOOIOOiOOQOO tooo 

Imwom 


Fig. 16. Trajectories of the sound-speed EOF coefficients and cost function 
learning curve for a typical annealing run. 



12 10 I 6 4 2 0 

Relative (dRt 


Fig. 17. Energy surface as a function of sound speed EOF coefficients 
computed by exhaustive search (simulation). 

wave numbers derived from the measured profiles, the “true” 
minus the measured and the adapted minus the measured are 
plotted by solid and dotted lines, respectively, in Fig. 22. TTie 
adapted wave numbers track the "irue ' vsave numbers nicely 
except for the first five modes. A possible explanation of the 


I 

















Ihih IIMKNAI <)( (XI:aNIC KNOlNI'.hRING. VOL IS, NO LILLY 1995 


IABI.I-; V 

O' liMi.'-MKi.N Rim I IS iso.M Nink Runs Using 
i' Si'i I D LOf- Cm H U ii NTS AS Skarch Parameters 


l;()I Cud # 1 


EOFCoef. #2 



M7S ISM I4«S 1490 I49S ISOO ISOS ISIO ISIS IS20 ISIS 
5»auod Spcied (a^) 



Sound Speed Difiereacc (oA) 


Fig. 18. (a) Sound-speed profile derived from Che environmenl adapcation 
technique (dotted line), “true” profile (solid line), and measured sound-speed 
profile (dashed line); (b) the difference version of (a), i.e., using the measured 
profile as reference (dashed line), the “true" minus the measured and the 
adapted minus the measured are in solid and dotted lines, respectively 
(simulation). 


Fig. 19. Self-cohered source locations by envu'onmeni adaptation technique 
using sound-speed EOF coefficients as search parameters. 





■ 0.6 - 0.4 -oa ao 0.2 04 0.6 

Ncnalbed Wtve Nnster BOfh (nd/B) 


deviation from the “true" wave numbers is that these modes are 
weakly excited, thus less weight is given during the adaptation 
process. Again, the environment adapted locations match those 
of the ideal simulation [31]. 

It is of interest to know whether the true source location 
is unique in the neighborhood of the source location. The 
adaptation procedure is then repeated for each assumed source 
location within a spatial window extended 16 km in range 
and 1.5** in azimuth (approximately 60 km in cross range) 
enclosing the true source location. Fig. 23 confirms that the 
range-azimuth maximum energy surface indeed has a peak that 
corresponds to the true source location. This suggests that a 


Fig. 20. (a) Excess (demeaned) borizonlal wave numbers at 14 Hz derived 
from 30 AXBT measurements made between 140“W and I50°W. July 1989. 
(b) Normalized versions of the first and second EOF's derived from (a). 


weakly range-dependent environment can be approximated by 
a range-independent environment in a matched-field sense. 

Although both implementations of the environment adapta¬ 
tion technique produce similar results under the example given 
above, the computation burden for the two approaches differs 
significantly. For the sound speed case, evaluation of the cost 
function requires the invocation of the acoustic propagation 
model to compute the modal eigenfunctions and wave numbers 




















> I ' I, 



I 


f 


I 

I 


derived 
y l9Xy 
.11 

led by 
l^e 

dapia- 
eivcn 
li Iters 
e cost 
e.ition 
tubers 


I Ml N \M I IK ll U ;KIS^ \ 1 I Si H Kl I I I H \1 1 / \ l II IN 


, - j r --,-^ -, 



•jO ^ M 10 10 0 10 K) 10 40 W 

bOFC«tr ti 




IS 10 S 0 

RelJtive Power (OBl 

Pig. 21. Energy surface a.s a function of wave number [X)P coefficients 
computed by exhaustive search (simulaiionf 



•10* -4-ia’ •2Ma' 0 2M0' 4-10' 6*10' 

Wtve Number Differaice (r«dAn) 

Fig. 22. Deviations in adapted wave numbers and ’ime” wave numbers from 
the measured model wave numbers (simulation). 


(this is computation intensive). In the wave number adaptation 
case, the wave numbers are readily available, and updating the 
wave numbers according to the perturbations involves only 
a few trivial algebraic steps. The difference in computation 
performance for the two implementations is at least 3 to 4 
orders of magnitude. 

C. Experimental Results 

Data collected by the Swallow float array during the July 
1989 experiment in the northeast Pacific were processed in 
the same fashion as the simulated data The acoustic modeling 
was the same as in the simulation. The data considered here 
were recorded at 01:47 and 04:38 PST. 9 July P1S9. Fig. 24 
plots the matched-field rangc-a/.imuth ambiguitv surfaces for 
the two intervals with the highest peak marked with ‘ s and the 
true source locations marked with A s. The shilt m the source 
locations was due to the environmental mismatch as diagnosed 
through simulation in the last section. We empirically selected 



MW nm IM) M91 um MT MS IM) 

Sows tait 



10 •% -6 -4 -2 0 

Power (<JB) 


f'Dj 2^ Range a/imuih energy surface derived from rcp‘-*aling ihe 
tion priKcdure for each rangc^azirnuth cell (simulationi 

the reference source location that corresponded to 01:47 PST. 
9 July 1989, by repeating the adaptation procedure for all 
assumed range-azimuth cells in the neighborhood of the source 
location obtained from the source log. The highest peak in the 
range-azimuth maximum energy surface was found at a range 
of 2489 km and an azimuth 172.1° 131). We then entered into 
the adaptation phase of the technique. The sound-speed EOF 
coefficients were used as search parameters to determine the 
optimal sound speed structure. Fig. 25 shows the optimized 
range-azimuth ambiguity surface for both time intervals using 
the single adapted sound speed structure. As can be seen, the 
environmental adapted source track mimics the track derived 
from the source log. The modal wave number adaptation 
implementation also produced the same results [31], Table VI 
lists the adapted source locations versus the source locations 
according to the VLF source log. The minor discrepancy, 
a 0.2° to 0.6° shift between the true and adapted source 
locations, is thought to be due to the slight uncertainty in 
selecting the coordinate system with respect to true north for 
the float localization (refer to Fig. 2). since the onentation 
of the X axis of the coordinate system was taken to bo the 
ship's position when bottomed floats 9 and 10 were pul into 
the water. A relative motion of approximating 60 ni in the Y 
direction between floats 9 and lO while the floats descended 
to the bottom would cause the O.ti' rotain'ii in the MFP 
results. This order of error between ship position and true 
float position on the bottom has been noted in other Swallow 
float experiments. In addition, uncertainty in niidw aicr sensor 
positions might also contribute to the azimiiili error .i- seen in 
the simulation study. The minor discrepance m r.inec error, a 
4-km shift, is thought to be due to errors in the ,l^^l;nlpllons 
made in modeling the replica vectors. Noneihclcs, 'iie relative 
source movement, a 17-km separation between ih, a vourcc 
locations, is found to be consistent with that ol die mucc log. 














f ig 24 Matchcd held processing of experimental data during the two time 

intervals. 



Fig. 25 Self-cohered source locations by environment adaptation tech¬ 
nique using sound speed EOF coefficients as the search parameters. 


TABLE VI 

Environment Adaptation MFP Results 


Time 

True source 

True source 

Adapted 

source 

range 

Adapted 

source 

azimuth 

range 

azimuth 

00;47 

2493 km 

171.5° 

2489 km 

172.1° 

04:38 

2476 km 

170.7° 

2472 km 

170.9° 


V. Conclusions 

In this paper, we have demonstrated the source localization 
and tracking capability of a freely drifting volumetric array 
with MFP using experimental data. We have also proposed 
and demonstrated an environment adaptation technique to deal 
with the environmental mismatch problem. Data collected 
during the 1989 Swallow float experiment were used to 
perform the study. The geometries of the Swallow float array 
as a function of time during the 1989 experiment have been 
estimated using the 8-kHz range measurement with a least- 
squares based float localization method. The rms position 
errors estimated by the float localization method is less than 
4.5 m, which is within the desired accuracy of one-tenth of a 


IHl nUKN.M 01 IHT-ANIC INI'ilNlt RlNt'. Vlll IS. NO T )l I I 


A.i'l'Icnjflh at the highcM rrequency of intcresl 25 11/ ((i im la 
.icr III cticcTncly process the VI.I- acoustic data cotieieiul\ 

I urihemiore. analysis of the experiment acoustic data shoued 
!.:eii Munal-to noise raiio and high coherence ai 14 11/ aiiione 
...I nine lreel> driliing floats during some time inlervals I he 
14 (1/ was a coniinuoiis wave tonal projected by a VLI- source 
iiiNolved in a companion experiment. The high coherence 
among the floais provided an opportunity for matched field 
beanilorming of the VLF acoustic data. The replica vectors 
were modeled with an adiabatic normal mode numerical 
technique using the environmental data collected during the 
experiment. Inttial MFP of the experimental data expertenced 
diflicultics in estimating the source depth and range while the 
source azimuth estimate was somewhat successful. Controlled 
simulation using the same conditions as in the real data 
has revealed that 1) depth resolution indeed is a difficult 
problem for a shallow VLF source in a long-range environment 
due to fewer modes being available and due to low source 
depth-to-wavelength ratio, 2) the range estimate is sensitive 
to environmental mismatch, and 3) the azimuth estimate is 
robust. The main cause of the performance degradation has 
thus been identified to be uncertainty in the environment (i.e , 
sound-speed mismatch). An environment adaptation technique 
using a global optimization algorithm was proposed and de¬ 
veloped to counteract the MFP performance degradation due 
to uncertainty in the ocean acoustic environment. We have 
demonstrated through simulation that with limited a priori 
knowledge of the environment and with a reference source 
at a known location, the environment can be adapted in a 
matched-field sense. Using the adapted environment, other 
unknown source(s) of interest in the vicinity of the reference 
source can be correctly localized. Applying the environment 
adaptation technique to experimental data has shown that 
ttje 14-Hz source was successfully localized and tracked in 
azimuth and range within a region of interest using the 
MFP technique at a later time interval. While both types of 
environmental parameters, i.e., sound speed and wave number, 
provided similar results, the modal wave number adaptation 
implementation has proven to be computationally efficient. 


112) R. 
or 
of 
IS 

I'31 


Acknowledgment 

The authors are indebted to G. D’Spain and J-M. Tran of 
the Marine Physical Laboratory for several useful discussions 
concerning the issues of Swallow float system and random 
array matched-field proce.ssing. They also thank H. Bucker of 
the Naval Command Control and Ocean Surveillance Center. 
RDT&E Division, for many useful discussions on the self- 
cohering technique. 

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George C. Chen (M'89) received the M.S. de¬ 
gree in computer science from the University of 
California at Los Angeles in 1981 and the Ph D 
degree in electrical engineering from the University 
of California at San Diego in 1992. 

Prior to 1985, he was a software engineer with the 
Computer Sciences Corporation, El Segundo, CA. 
and worked on computer networking and database 
systems. Since 1985 he has been a research engi¬ 
neer with die Naval Command, Control and Ocean 
Surveillance Center’s RDTicE Division (formally 
Naval Ocean Systems Center). San Diego, CA. His research interests include 
digiul signal processing, communication systems, and neural networks. 


William S. Hodgkiss (S'68-M'75) received the 
B.S.E.E. degree from Bucknell University. Lewis- 
burg, PA, in 1972, and the M S. and Ph D. degrees 
from Duke University, Durham, NC, in 1973 and 
1975, respectively. 

From 1975 to 1977 he worked with the Naval 
Ocean Systems Center, San Diego, CA. From 1977 
to 1978 he was a faculty member in the Electn 
cal Engineering Department. Bucknell University. 
Lewisburg, PA. Since 1978 he has been a member 
of the faculty of the Scripps Institution of Oceanog¬ 
raphy and on the staff of the Marine Physical Laboratory, University of 
California, San Diego. He is the Applied Ocean Science curricular group 
coordinator. Graduate Department of the Scripps Institution of Oceanography 
His present research interests are in the areas of adaptive digital signal 
processing, adaptive array processing, applications of these to underwater 
acoustics, the propagation of acoustic energy in the ocean and its interaction 
with the sediments beneath the cxean and the sea surface, and the staiisiic.)l 
properties of ambient ocean noise. 




nge and 
usl. Soc.