DTIC ADA626739: Localization of Short Duration Periodic Signals

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1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To)

14-08-2015 Publication

4. TITLE AND SUBTITLE

Localization of Short Duration Periodic Signals

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Paul M. Baggenstoss

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Naval Undersea Warfare Center
Division, Newport

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

8. PERFORMING ORGANIZATION REPORT
NUMBER

102089

9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES)

Naval Undersea Warfare Center
Division, Newport

1176 Howell Street, Bldg 102T, Code 00L

Newnort. Rl 02841

12. DISTRIBUTION / AVAILABILITY STATEMENT

Distribution A

10. SPONSOR/MONITOR’S ACRONYM(S)

NUWC

11. SPONSOR/MONITOR’S REPORT
NUMBER(S)

102089

14. ABSTRACT

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.

16. SECURITY CLASSIFICATION OF:

a. REPORT

Unclassified

b. ABSTRACT

Unclassified

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17. LIMITATION

18. NUMBER

OF ABSTRACT

OF PAGES

SAR

32

19a. NAME OF RESPONSIBLE PERSON

Annette M. Campbell

19b. TELEPHONE NUMBER (include area
code)

401-832-4246

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39.18

DEPARTMENT OF THE NAVY

OFFICE OF COUNSEL

NAVAL UNDERSEA WARFARE CENTER DIVISION
1176 HOWELL STREET NEWPORT Rl 02841-1708

IN REPLY REFER TO

Attorney Docket No. 102089
14 August 15

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

TECHNOLOGY PARTNERSHIP ENTERPRISE OFFICE
NAVAL UNDERSEA WARFARE CENTER
1176 HOWELL ST.

CODE OOT2, BLDG. 102T
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.

DISTRIBUTION STATEMENT
Approved for Public Release
Distribution is unlimited

Attorney Docket No. 102089

LOCALIZATION OF SHORT DURATION PERIODIC SIGNALS

STATEMENT OF GOVERNMENT INTEREST
[ 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.

CROSS REFERENCE TO OTHER PATENT APPLICATIONS
[ 0002 ] None.

BACKGROUND OF THE INVENTION

(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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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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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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[ 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.

SUMMARY OF THE INVENTION

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

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

[ 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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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
output.

BRIEF DESCRIPTION OF THE DRAWINGS
[ 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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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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DETAILED DESCRIPTION OF THE INVENTION
[ 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
sources.

[ 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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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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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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N -1

y t =

I

n*t+i

(i)

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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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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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 .

n

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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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

N

W k

n

(5)

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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j27rkxf s

e N

(6)

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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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
1/To.

[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:

[ip

r T/4

= I r(x)T p dx.

Jr=0

:v

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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
ratio

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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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
window.

[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

"=zi

k =1 1=1

exp

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

2ai

( 12 )

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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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[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,

®l,r

n l n m

= 11

i— 1 7=1

exp

— (tz(0 - t m (j))

2 \

2 a\

(13;

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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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:

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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
accentuated.

[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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Attorney Docket No. 102089

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

1

w k,m = —,l<k<K,l<m<M.
K

(19)

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,r

Yk,m = ^(l “ e am ’ l/A )PlPm
l

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

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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.

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Attorney Docket No. 102089

LOCALIZATION OF SHORT DURATION PERIODIC SIGNALS

ABSTRACT OF THE DISCLOSURE

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

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FIG. 6

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600

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FIG. 7

700

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Y position, (meters)

-1500

FIG. 8

Y position, (meters)

-1500

-2000

-2500

-3000

-3500

-4000

0.95 1 1.05 1.1 1.15 1.2

X position, (meters) x ^

FIG. 9