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14-08-2015 Publication 


Localization of Short Duration Periodic Signals 





Paul M. Baggenstoss 





Naval Undersea Warfare Center 
Division, Newport 

1176 Howell Street, Bldg 102T, Code 00L 
Newport, Rl 02841 




Naval Undersea Warfare Center 
Division, Newport 

1176 Howell Street, Bldg 102T, Code 00L 

Newnort. Rl 02841 


Distribution A 






A method for localizing signals of interest includes initializing characteristics of the signals. Signals are acquired from a sensor 
array having at least three acoustic sensors. After digitization and conditioning, the signals associated with each sensor are 
validated by comparison with initialized characteristics. The signals are correlated across sensor groups to obtain time 
differences of arrival (TDOA). These TDOA are validated and associated with other TDOA from different times. TDOA from 
different sensor pairs are associated when they share a common sensor. A hyperbola of possible locations is created for each 
validated TDOA. Summation of the hyperbolas gives an intensity function. The location is identified as the most intense point 
in the intensity function. The source can be tracked across time as a computer output. 















Annette M. Campbell 

19b. TELEPHONE NUMBER (include area 


Standard Form 298 (Rev. 8-98) 

Prescribed by ANSI Std. Z39.18 



1176 HOWELL STREET NEWPORT Rl 02841-1708 


Attorney Docket No. 102089 
14 August 15 

The below identified patent application is available for 
licensing. Requests for information should be addressed 

1176 HOWELL ST. 

NEWPORT, RI 02841 

Serial Number 14/041,371 

Filing Date 30 September 2013 

Inventor Paul M. Baggenstoss 

Address any questions concerning this matter to the 
Office of Technology Transfer at (401) 832-1511. 

Approved for Public Release 
Distribution is unlimited 

Attorney Docket No. 102089 


[ 0001 ] The invention described herein may be manufactured and 
used by or for the Government of the United States of America 
for governmental purposes without the payment of any royalties 
thereon or therefor. 

[ 0002 ] None. 


(1) Field of the Invention 

[ 0003 ] The present invention relates to locating and tracking 
the source of short duration periodic signals. More 
particularly it relates to locating and tracking these sources 
utilizing time-difference-of-arrival (TDOA) validation and 
association measures. 

(2) Description of the Prior Art 

[ 0004 ] In passive sonar, as shown in FIG. 1, it is well known 
to deploy an array of acoustic sensors 10 from a vessel 12 in a 
body of water 14. Each acoustic sensor or hydrophone 16 on 
array 10 is positioned a known distance from another hydrophone 
16 along the array line or other such structure. Hydrophones 16 
are capable of receiving acoustic signals 18 from sources such 
as 20. Array 10 is typically joined to a signal processor 22 on 

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Attorney Docket No. 102089 

board vessel 12. Once such a signal has been received at 
several hydrophones 16, signal processor 22 utilizes the time 
the signal 18 arrives at each hydrophone 16 to calculate a time- 
difference-of-arrival (TDOA) between several pairs of 
hydrophones. The signal processor 22 has a sound velocity 
profile from either calculation, a database or a determination 
giving the speed of sound in the body of water 14, and 
separation between the hydrophones 16 is also known. Using the 
known distances, the sound velocity profile and the TDOAs from 
the array, the signal processor can utilize hyperbolic 
calculations to determine the location of source 20. 

[ 0005 ] Source 20 can be a variety of sources, such as 
vessels, pingers, marine mammals or the like. Marine mammals 
and other biological sources often make short duration periodic 
signals such as clicks. It is common to locate whales by 
measuring the time difference for the same click arriving at two 
spaced hydrophones. 

[ 0006 ] There are several deficiencies with the current state 
of the art. First, many false TDOA measurements are created 
with TDOA estimates that are found using correlation. When data 
from two hydrophones are correlated, the noise that is 
independently received at each sensor does not correlate well 
and produces very little or no output. However, when a common 
signal is present at the two hydrophones, it will cause a 

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Attorney Docket No. 102089 

correlation peak at the TDOA estimate. When the signal is weak, 
it is difficult to separate the valid TDOA measurements from 
fluctuations caused by noise or false peaks spaced from the true 
peak by the period of the repeating click sequence. 

[ 0007 ] Another issue with the current state of the art arises 
when more than one source is present with each source having a 
similar signal. This can occur when the sources are whales in a 
pod. In this case, a set of hyperbolic solutions will be 
created for each source and many false intersections are created 
when the hyperbolic solutions of one source intersects the 
solutions of another source. It is impossible to know that 
these intersections are false unless additional information is 
made available. One way to resolve these ambiguities is to only 
accept intersections of hyperbolic solutions from hydrophone 
pairs that share one hydrophone (referred to as hydrophone 
triples). This results in a fixed relationship between the TDOA 
measurements that can be checked for consistency. 

[ 0008 ] The problem with the hydrophone triple method is that 
it does not lend itself well to soft decisions, in other words, 
whether the TDOAs are related or not related. Granted, it could 
be adapted to a soft measure simply by measuring how well the 
fixed relationship holds. However, to get a meaningful measure 
of association, it is necessary to compare the full set of click 
arrivals that went into making the TDOA estimate. 

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Attorney Docket No. 102089 

[ 0009 ] As can be seen, there is a need for improved methods 
for detection, TDOA determination and TDOA association for 
localization of sources such as marine mammals and other short 
duration periodic signal sources. 


[ 0010 ] Accordingly, it is an object of the present invention 
to provide a method for locating short duration periodic signal 

[ 0011 ] It is a further object to locate such sources in three 

[ 0012 ] Another object is the ability to distinguish one 
signal source from another in the same environment. 

[ 0013 ] It is yet another object to track signal sources from 
one time to a next. 

[ 0014 ] Accordingly, there is provided a method for localizing 
and tracking a short duration periodic signal source utilizing a 
computer. The method includes initializing signal 
characteristics of signals of interest and acquiring signals 
from a sensor array having at least three acoustic sensors. The 
signals are digitized and conditioned based on initialized 
signal characteristics. The conditioned signals are validated 
for each sensor by comparison with initialized signal 
characteristics. The validated conditioned signal associated 

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Attorney Docket No. 102089 

with one sensor are correlated with the validated conditioned 
signal associated with another sensor for each sensor pair in 
the sensor array to obtain time differences of arrival for each 
sensor pair. These time differences of arrival are validated 
for each sensor pair. Time differences of arrival from 
different times from the same sensor pairs are associated with 
each other, and time differences of arrival from different 
sensor pairs are associated with each other when the time 
differences of arrival share a common sensor. Hyperbolas of 
possible source locations are created for each validated time 
difference of arrival. These hyperbolas are summed to obtain an 
intensity function. The location of the signal of interest can 
be found at a time as the position in the intensity function 
having the greatest intensity. A source can be tracked across 
time by utilizing the identified location and associated 
validated time differences of arrival from different times. The 
identified location and track can be provided as computer 

[ 0015 ] Other objects, features and advantages of the present 
invention will become apparent upon reference to the following 
description of the preferred embodiments and to the drawings, 
wherein corresponding reference characters indicate 

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Attorney Docket No. 102089 

corresponding parts throughout the several views of the drawings 
and wherein: 

[ 0016 ] FIG. 1 is a diagram showing the basic problem and 
signal collection methodology as in the prior art; 

[ 0017 ] FIG. 2 is flowchart giving an overview of the method 
of the current invention; 

[ 0018 ] FIG. 3 is a graph of the raw sensor output of power 
density over time; 

[ 0019 ] FIG. 4 is a graph of the correlated time delay between 
two sensor outputs; 

[ 0020 ] FIG. 5 provides a graph of two first-order smoothed 
click-maps overlaid to show the relationship of one sensor 
output to another; 

[ 0021 ] FIG. 6 is a graph showing the multiplication of the 
two first-order smoothed click maps together to give a second- 
order smoothed click map; 

[ 0022 ] FIG. 7 is a graph show cross sensor correlation 
(correlogram) allowing visual association of sources; 

[ 0023 ] FIG. 8 shows an initial TDOA localization surface; and 

[ 0024 ] FIG. 9 shows a TDOA localization surface using a 

"soft" association measure, using the same data that created the 
initial TDOA localization surface of FIG. 9. 

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Attorney Docket No. 102089 

[ 0025 ] Referring now to FIG. 2, there is shown a flowchart 30 
giving an overview of the current procedure. Details of each 
step in the method will be provided following this overview. In 
step 32, the method is initialized by developing known 
information for use in the method. This includes a generic 
replica of the signal of interest, a range of frequencies for 
the signal of interest, and a threshold time used to distinguish 
reflected signals from source signals. The method also uses a 
computer model trained from experimental and known data to 
identify valid data and invalid data. This computer model is 
developed before using the current method to localize signal 

[ 0026 ] In step 34, signals are acquired from an array of 
hydrophones having at least three hydrophones as described with 
reference to FIG. 1. The signals are digitized and processed 
separately. A typical input signal in the time domain is given 
in FIG. 3. Each signal is correlated in step 36 with the 
replica developed in step 32. This correlation reduces signals 
from sources other than the source of interest and is known in 
the prior art. Each correlated signal is transformed into a 
frequency domain signal utilizing a Fourier transform in step 
38. In step 40, peaks are found in the time domain. Peaks not 
meeting previously developed parameters concerning frequency and 

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Attorney Docket No. 102089 

timing are eliminated in step 42. A first order smoothed click 
map (SCM1) is developed for each signal in step 44. This SCM1 
is time windowed in step 46 to create a windowed first order 
smoothed click map (WSCM1). In step 48, the SCM1 from one 
hydrophone is correlated with the WSCM1 from a second 
hydrophone. An initial time-difference-of-arrival (TDOA) can be 
given by a peak from this correlation. 

[ 0027 ] In step 50, the initial TDOAs are examined to 
determine if these initial TDOAs are valid. This is performed 
by calculating a second order smoothed click map (SCM2) and 
determining if the clicks occur with an expected inter-click 
interval established in step 32. Another validation test is 
performed by analyzing the autocorrelation function of the SCM2. 
The trained computer model from step 32 can be used to establish 
this validity from these measures as described below. On 
completion of this step, invalid TDOAs are removed from 
processing. In step 52, TDOAs from different time segments are 
associated with each other for tracking a source across time 
segments. TDOAs from different sensor pairs incorporating one 
common sensor can be associated with one another in step 54. 

This step produces an association measure that can be used to 
further modify the analysis. The associated TDOAs are used to 
create hyperbolas indicating the source location in step 56. 
Different sensor pairs give different hyperbolas. These created 

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Attorney Docket No. 102089 

hyperbolas are modified by an association measure calculated in 
step 54 and summed in step 58 to get an intensity function. The 
location of the source is identified as the location with the 
highest intensity value in step 60. 

[ 0028 ] This process is further described as follows. Data 
was acquired as in step 34 at a sample rate of 96kHz. After 
replica correlation, the instantaneous power is shown FIG. 3. 

The base level signal is indicated at 64. Higher level signals 
are given at 66. These periodic signals of interest 66 could be 
whale calls and the current example was captured from calls from 
Blainville's beaked whale. The overall signal is processed in 
step 36 by developing a matched filter derived from calls from 
Blainville's beaked whale using distributed bottom-mounted 
hydrophones. A replica waveform was obtained by starting with a 
single, high signal to noise ratio (SNR) whale click, then 
determining the peak time of the correlator output response for 
a training set of several hundred clicks. Each click was time- 
delayed to align to a data window so that the clicks from all 
training samples were time-aligned. These were then averaged to 
obtain the new reference click. After three repetitions, it was 
found that the replica didn't change significantly. 

[ 0029 ] Utilizing the prior art technique of correlation with 
the replica was conducted utilizing the following equation: 

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Attorney Docket No. 102089 

N -1 

y t = 




where Xt is the input time series from the sensor; 
r, is the replica waveform; 

N is the number of terms in the replica; and 
yt is the signal after correlation. 

After correlation with the replica, the peaks in the signal are 
more distinct. The signal to noise ratio is increased by a 
factor of 3 (+4.7dB) using the sample beaked whale clicks. 

[ 0030 ] After replica correlation, the Fourier transform of 
step 38 was calculated. In this step the time series was 
processed by a Hanning-weighted, seventy-five percent overlapped 
short time Fourier transform (spectrogram) with a transform size 
of 24. This produced a 0.0625 millisecond (msec) time 
resolution. Each Fourier transform bin was normalized 
separately by a time domain median-based background power 
estimator. To obtain total power, a frequency-weighted power 
summing across frequency was performed, selecting only the 
frequency bands in which the beaked whale energy lies (14-40 
kHz). These frequency bands were selected for experimental data 
in the initialization step, step 32. This produced a power time 
series with 0.0625 msec resolution that was searched for local 
maxima above a threshold to identify candidate clicks. A fine 

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Attorney Docket No. 102089 

click time location was then found by parabolic interpolation of 
the power time series. This is step 40 of FIG. 2. 

[ 0031 ] In order to remove clicks outside known parameters, 
step 42, a click center frequency was obtained by finding the 
power weighted mean frequency of the click energy from the 
spectrograph at the detected time. 

£kl X kl 2 4 

Skix k l 2 

Any clicks that had mean frequencies less than 20 kHz were 
eliminated in view of an initial determination that the signal 
of interest was above this threshold. Also, spurious peaks that 
occurred due to ringing or energy instability that typically 
occur directly after a loud click were eliminated by searching 
for much louder clicks within 2.5 msec of the click. This range 
of times can be determined in the initialization step by 
knowledge of environmental conditions such as depth. 

[ 0032 ] After elimination of spurious clicks, the method 
proceeds to step 44. Traditionally, TDOA is determined by 
producing an amplitude-versus-time description (amplitude time 
series) of each hydrophone, then correlating the amplitude time- 
series from two nearby hydrophones. If the clicks from a given 
whale are present in each amplitude series, then there will be a 
correlation peak at the corresponding time-delay. It is useful 
to correlate in such a way that the value of the correlator peak 

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Attorney Docket No. 102089 

is an indication of the number of clicks that associate or 
correlate and not a function of click amplitude. To do this, 
amplitude information is eliminated by forming a synthetic time- 
series of impulses at the times of the detected clicks. This is 
called a "click-map". This method further processes the click 
map by implementing time-domain smoothing in order to allow time 
uncertainty to be incorporated into the correlation process. The 
resulting click map is referenced as a first-order smoothed 
click-map (SCM1) since it is derived from the detections of a 
single hydrophone. 

[ 0033 ] A first-order smoothed click-map (SCM1) of length T 
was created from click time locations t n and amplitudes a n . The 
time window T was 12 seconds. A synthetic sample rate of f s = 3 
kHz was chosen, producing a synthetic time series of N= 36,000 
samples. The ideal synthetic time series was constructed in the 
frequency domain as 

Z -j2nkt n f s ( 3 ) 

e n W k . 


The first term in the summand is the Fourier transform of an 
ideal impulse with time delay t ,,. The last term, Wk is a time¬ 
smoothing term implemented as frequency domain shading. The 
method used a frequency-domain Hanning function of total width 
N/4 frequency bins which dropped to zero at k = N/8 on the 
positive side and k = -N/8 on the negative side. In the time- 

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Attorney Docket No. 102089 

domain, this has the effect of a smoothing function, producing 
Gaussian-like "pulse" at each click location of width about 16 
samples. The constant c is given by 

where w t are samples of the inverse FFT of the frequency weights 
W k . This scaling has the desired effect that the correlator 
output approximates the number of clicks, i.e. it will be 
exactly 1 for a single click. 

[ 0034 ] Time-windowing is also needed prior to cross¬ 
correlation to limit wrap-around (circular correlation) effects. 
To prevent correlation loss, however, a time-windowed SCM1 from 
one hydrophone is correlated with a non-time-windowed SCM1 from 
the other hydrophone. The time-windowed SCM1 is given in the 
frequency-domain by 

— (t n —T/2) 4 
e ( T /4) 4 e 

-j2nkt n f s 


W k 



The first term is a Gaussian kernel that shapes the data, 
attenuating energy outside of the center of the time window. 
[ 0035 ] The correlation of step 48 in the frequency domain is 

performed by using the time-windowed SCM1 of one hydrophone, 
from equation (5), and the non-windowed SCM1 of the other 
hydrophone, X% from equation (3). For hydrophones a and b. 

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Attorney Docket No. 102089 

j27rkxf s 

e N 


where X is the complex conjugate of X. This produces a 
correlation result without circular effects, and no overlap loss 
for time delays in the range —T/A < t < T/A . This gives the signal 
having the detail shown in FIG. 4. As can be seen, this signal 
has two prominent peaks as indicated at 68 and 70. 

[ 0036 ] The data from the correlation result often contains a 
great number of peaks, but only a very small number are valid. 
Validity can be shown with reference to FIG. 5. The upper 
portion shows the SCM1 of a first hydrophone, and the lower 
portion shows the SCM1 of a second hydrophone. A delay has been 
applied to the second hydrophone equal to the largest 
correlation peak from FIG. 4. The first SCM1 has been 
artificially raised to a resting value of 0.4 for clarity. For 
many of the peaks in the lower SCM1, there is a corresponding 
peak in the upper one. FIG. 6 shows a multiplication of the two 
SCMls together, which is an estimate of the whale source time- 
series based on two hydrophones. This is the second-order 
smoothed click map (SCM2). The SCM2 is always time-referenced to 
the first hydrophone (the one with no delay applied). The 
number of clicks roughly corresponds with the correlator output 
magnitude. FIG. 6 shows one measure of validity because it has 
an inter-click interval (ICI) of .33 seconds. The ICI of the 

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Attorney Docket No. 102089 

regular foraging clicks of the Blaineville's beaked whale are 
known in the prior art to be 0.37 seconds on average with 0.1 
sec standard deviation. 

[0037] In order to objectify the validity analysis, the 
method utilizes initial parameters to identify a set of features 
of the SCM2. These features are obtained from the auto¬ 
correlation function (ACF) and power spectrum (PS) of the source 
time-series estimate. Date form the smoothed ACF has a ripple 
at the .33 second inter-click interval rate and the power 
spectrum has a peak near 3 Hz. A change in the ICI can cause the 
power spectrum to have multiple peaks. Thus, experimentally 
derived characteristics of a valid SCM2 are that the smoothed 
auto-correlation function (ACF) r (x) , normalized for r(0) = 1, 
exhibits ripple at time lag equivalent to the ICI, denoted by T 0 . 
The peaks in the ACF slowly drop in amplitude as x increases. 
Also, the power spectrum (i.e. the Fourier transform of the 
autocorrelation function) exhibits a large peak at the frequency 

[0038] These characteristics can be established by 
calculating the moments of the ACF and saving the value of the 
power spectrum at 1/T 0 . The p-th moment of the ACF is given by: 


r T/4 

= I r(x)T p dx. 



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Moments pi, y 2 , and vc are used to calculated features mul, mu2 
and mu3 as follows: 

VSI Vft <8) 

mul = m, mu2 = - ,mu3 = - 

lii iii 

A further feature identified as specmax can be calculated based 
on the maximum power spectrum value, 

/~T/4 (9) 

argmax I cos(2Tifx) r(x)dx. 

f ^r=0 

In a preferred embodiment, these features are combined in a 
feature vector: 

z = [ specmax, mul, mul, mul ] ( 10 ) 

Feature vector z is used to train a Gaussian mixture model 
utilizing experimental data in order to develop a likelihood 

L = logp (z\Hi) — logp (z\H 0 ) (ID 

where Hi and Ho are the valid and invalid assumptions. The 
advantage of this method is that it doesn't assume Gaussian 
distributions. Correlation peaks with L below an experimentally 
determined threshold are discarded. 

[0039] In step 52 of FIG. 2, TDOAs can be associated across 
different time periods. In the prior art this was done by 
correlating the output of two sensors over time to give a graph 
such as that shown in FIG. 7. In FIG. 7, higher intensity 

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Attorney Docket No. 102089 

tracks are generally interpreted to be the same correlated 
signals over time. For measurements at sequential times on a 
given single hydrophone pair, the time-windows used in the 
correlation will be highly overlapped. In a test of beaked whale 
data a 12-second window with 2 second update period was used, 
resulting in 10 seconds of overlap. If the TDOA measurements 
made at consecutive times are from the same whale, the TDOA 
values will be nearly the same, but will differ slightly due to 
the movement of the whale and the fact that new source clicks 
have moved into the processing window. But, if there is a high 
degree of overlap between the processing windows, many of the 
same clicks will be present in both time updates. So, if the 
source time-series is estimated, click times can be directly 
compared after taking into account the shift in the processing 

[0040] To obtain a measure of click matching, peaks shown in 
the SCM2 were used to locate source clicks then the times of the 
source clicks from sequential time windows were compared. Let n p 
and n q be the number of source clicks detected at time windows p 
and q. Let 

n v n q 


k =1 1=1 


~{t p (k ) - tq(0) 


( 12 ) 

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Attorney Docket No. 102089 

where t p (k) is the k-th source click time from window p and o t is 
a time tolerance value (standard deviation). This is effectively 
a measurement of the number of matching click times because if 
the errors of matching click pairs are nearly zero, and are high 
for invalid click pairs, the exponential term will be nearly 1.0 
for valid and zero for invalid click pairs. 

[0041] Only sequential measurements with (3 above a threshold 
are assumed to associate. It has been determined empirically 
that good thresholds are that (3 should be greater than 7 and the 
TDOA difference should be less than 3 ms (at 2 second update). 
Only those TDOA measurements with at least one sequential 
association were accepted. This means that to accept a TDOA 
measurement, it must be detected in at least two consecutive 
time updates. 

[0042] According to step 54 of FIG. 2, TDOAs obtained from 
different pairs of hydrophones must be analyzed to determine if 
they are related. This is accomplished by click-matching, in 
essentially the same way that consecutive TDOA measurements were 
associated in step 52. The second order smoothed click map 
(SCM2) is obtained for two TDOA measurements made using two 
different hydrophone pairs, but with a shared hydrophone. If 
times are referenced to the common hydrophone, the click times 
should match. 

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Attorney Docket No. 102089 

[0043] Thus, the system has acquired data from at least three 
hydrophones. All of the hydrophone pairs at approximately the 
same time have been correlated to obtain a collection of TDOA 
measurements. Using this data, ai m is calculated as an 
association measure that relates TDOA measurements 1 and m. If 
TDOA measurements 1 and m do not share exactly one hydrophone, 
then a lm = 0. Otherwise, 


n l n m 

= 11 

i— 1 7=1 


— (tz(0 - t m (j)) 

2 \ 

2 a\ 


where ti(i) is the i-th click time for TDOA 1 and t m (j) is the 
jth click time for TDOA m, referenced to the hydrophone that is 
common between TDOA 1 and m. This measure is effectively a count 
of the number of matching click times if we assume that the 
exponential term is near one for valid associations and near 0 
for invalid ones. 

[0044] Localization of the signals is carried out in steps 
56, 58 and 60 utilizing hyperbolic positioning with an intensity 
function. Hyperbolic positioning is a well known technique for 
localizing a signal emitter having an unknown position. 

If the depth z is assumed known, the locus of points 
representing the possible locations of the source are given by a 
hyperbola in the x-y plane. Let i(m) and j (m) be the two 

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Attorney Docket No. 102089 

hydrophone indexes used to measure TDOA m. Let Ti (m) (x, y, z) be 
the model propagation time from position x, y, z to hydrophone 
i(m). Then the model propagation time difference d m is 

d m (x, y, z) = T i(m) (x, y, z) - T j(m) (x, y, z) (14) 

The TDOA measurement, T m should, ideally, be equal to d m (x,y,z). 
The solution of the equation: 

dm(x,y,z)=T m (15) 

is a surface of points that intersects a constant-depth plane on 
a hyperbola. Thus, for every TDOA measurement that has been 
suitably vetted, the corresponding hyperbola is drawn on the x, 
y plane using an assumed depth z. This is given as step 56 of 
FIG. 2. Rather than drawing hyperbolas as thin lines, these 
hyperbolas can be modified to allow for time-delay error by 
assigning a "likelihood" or "probability" to a position on a 
grid based on the difference between the model time delay 
(assuming that position) and the measured time delay (for the 
given hyperbolas). This is known in the art. For an assumed 
depth z, and a particular TDOA measurement m, an intensity is 
assigned to each point x, y according to a Gaussian function 

~( d m (x,y,z)-T m ) 2 ( 16 ) 

l m (x,y,z) = e 2a t 

where er 2 is a time delay variance. When all of the hyperbolas 
are summed an intensity function is obtained: 

20 of 25 

An example of this is shown in FIG. 8. This is the usual prior 
art means for localizing objects. Notice that the hyperbolas add 
together regardless of whether they are truly associated. At the 
correct locations, it is assumed that there will be more and 
consistent contributions, so correct localizations will be 

[0045] The current invention teaches improving on the 
localization given by FIG. 8 and equation (17) by using the TDOA 
association measure, ai ;in . In order to improve the localization, 
the current method sums all pairs of TDOA measurements, adding 
up the product of the spatially smoothed hyperbolas weighted by 
the soft association measure ai m . This gives 

This can be efficiently computed by pre-computing I m {x,y,z), the 
summand in equation (17) for index m. 

[0046] The result of this procedure is shown in FIG. 9 for 
the same data as FIG. 8. Only one point in the plane can be 
seen. This is the localized point given by equation (18). This 
can be provided to a user or another automated system in order 
to guide the user toward or away from the source. If this 

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process is repeated, stepping forward by 2 seconds at a time, a 
sense of the movement of the source is developed. 

[0047] In step 62 of FIG. 2, a depth for the source can be 
established. A three dimensional volume can be obtained by 
repeating the procedure at a set of depths. In order to 
maximize this process, a three dimensional peak peaking 
algorithm can be used; however, this results in many local 
maxima. These can be used as candidate position solutions that 
can be associated utilizing the TDOA association measure, ai m . 
One way of performing this association is by utilizing the 
technique taught in Baggenstoss, P.M., "An algorithm for the 
localization of multiple interfering sperm whales using multi¬ 
sensor time difference of arrival", 130 Journal of the 
Acoustical Society of America 2011 (hereinafter "Baggenstoss 
2011"), which is incorporated by reference herein. In this 
technique, candidate solutions compete for the TDOA 
measurements. Weights, w kria , are established that relate the 
TDOA to the solution by approximating the probability that 
measurement m belongs to solution k. These weights are 
iteratively updated as the position estimates are refined. 

[0048] In order to incorporate the inter-TDOA association 
measure, (Xj m , the following steps are utilized. M is the number 
of TDOA measurements and K is the number of candidate solutions. 
The association weights are initialized to the flat condition: 

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Attorney Docket No. 102089 


w k,m = —,l<k<K,l<m<M. 


All TDOA measurements are used by each candidate position k in 
the position update equation. The effect of each TDOA 
measurement in the solution update, however, is weighted by Wk, m 
and many of the weights go to zero or nearly zero. Thus, a 
particular candidate solution can "own" a set of TDOA estimates, 
effectively preventing other solutions from using it. 

[0049] In the current method the TDOA weights, Wk,mi are 
augmented by another weighting. First, a weighting, /? m , is 
defined that depends only on the time delay error, as follows: 

-(d m (x,y,z)-i m ) 2 (2 0) 

where the factor "4" is empirically determined. The TDOA 
association measure, oci ;in , is incorporated by defining the weight 


Yk,m = ^(l “ e am ’ l/A )PlPm 

where the factor "4" is also empirically determined. The 
combined weight: 

W k ,m = Wk,mYk,m (22) 
is used in place of Wk, m in the positional update equation for 
solution k. When combined with the teachings of Baggenstoss 

23 of 25 

Attorney Docket No. 102089 

2011, this allows determination of the depth by utilizing 
associated TDOA measurements. 

[ 0050 ] It will be understood that many additional changes in 
the details, materials, steps and arrangement of parts, which 
have been herein described and illustrated in order to explain 
the nature of the invention, may be made by those skilled in the 
art within the principle and scope of the invention as expressed 
in the appended claims. 

[ 0051 ] The foregoing description of the preferred embodiments 
of the invention has been presented for purposes of illustration 
and description only. It is not intended to be exhaustive nor 
to limit the invention to the precise form disclosed; and 
obviously many modifications and variations are possible in 
light of the above teaching. Such modifications and variations 
that may be apparent to a person skilled in the art are intended 
to be included within the scope of this invention as defined by 
the accompanying claims. 

24 of 25 

Attorney Docket No. 102089 



A method for localizing signals of interest includes 
initializing characteristics of the signals. Signals are 
acquired from a sensor array having at least three acoustic 
sensors. After digitization and conditioning, the signals 
associated with each sensor are validated by comparison with 
initialized characteristics. The signals are correlated across 
sensor groups to obtain time differences of arrival (TDOA). 

These TDOA are validated and associated with other TDOA from 
different times. TDOA from different sensor pairs are associated 
when they share a common sensor. A hyperbola of possible 
locations is created for each validated TDOA. Summation of the 
hyperbolas gives an intensity function. The location is 
identified as the most intense point in the intensity function. 
The source can be tracked across time as a computer output. 

25 of 25 



I O’ 















0 1 


0 3 0 4 

Time (s) 

0 5 

0 6 

0 7 

FIG. 3 

FIG. 4 

FIG. 5 


4.2 4.4 4 6 4.8 



FIG. 6 

5.2 5.4 5.6 5.8 




Window start time (s) 

FIG. 7 



Y position, (meters) 


FIG. 8 

Y position, (meters) 







0.95 1 1.05 1.1 1.15 1.2 

X position, (meters) x ^ 

FIG. 9