Association of Narrow Band Sources In Passive Sonar
D. Pillon, N. Giordana, P. Blanc–Benon, and S. Sitbon
Thales Underwater Systems,
525 route des Dolines, BP.157, F-06903 Sophia-Antipolis Cedex, France
Abstract – The problem of track to track association in
passive sonar with multiple platforms and/or time interruptions is considered. Typical case is a submarine equipped
with a hull array (HA) and a towed array (TA). A few methods are applicable and discussed here, coming from detection and estimation theory. Performance of likelihood ratio
test are studied for the binary case to associate one track
from measurement platform 1 to one another from platform
2. Then it is generalized to two sets of tracks using either a motion representation of the target state (Target Motion Analysis, TMA) or directly the spectrum of frequency
lines. Finally, this is also applied to a single antenna like
TA where the two “origins” comes from two different time
periods e.g. before/after an ownship maneuver. Both applications are supported by a theoretic background and at-sea
results.
Keywords: Tracking, estimation, sonar.
1
Introduction
Here is considered the case of data association in passive
sonar with two separate sensors. Such antennas are facing a
paradoxe: yes an increased array gain and efficient spatiotemporal processing enable to detect more and more silent
targets but this range improvement is also true and applicable to non military and strong sources. Drawback is: more
and more acoustic signatures are mixed sometimes together
due to finite resolving power. So this raw output like a continuum of sources must be tracked in order to re-assign the
original labels to their owner. Two practical situations are
studied on both simulated and real signals. First one is a
multi-platform problem, where separate antennas have at
least a common receiving bandwidth: which tracks from
antennas 1 and 2 are matching together, thus coming from
the same target, and which one have to be considered as unmatched? Second is a similar case but with a unique array
having a time interruption so that one need to associate the
detections before and after the interruption: does this new
ISIF © 2002
track appearing after the re-start correspond to that target
already classified? These questions have to be answered
with a maximum of care regarding the delay to answer correctly, and the rate of wrong decision: misleading conclusions may have serious consequences specially in tactical
situation assessment.
Section 2 will introduce data association between 2 separate arrays within likelihood ratio tests and estimation theory. Interesting aspect of performance will be described as
part of combinatorial theory. Section 3 discusses the similar problem of track to track association but from a single array and 2 separate batches of time, before and after
ownship maneuver. Section 4 will be the extensive description of two practical applications within a naval context.
Experimental results are presented showing the ability of
off-line association methods to solve some tricky acoustic
situations. It is a help for the operator to supply the unsupervised automatic detection and tracking function (ADT).
Finally last section will draw conclusions about the implementation of such a batch track-to-track association method
within modern multisensor sonars.
2
2.1
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Multi-platform association
Association from two separate platforms
with frequency and bearing TMA
Figure 1: Schematic view of HA-TA sonar.
As depicted in figure 1, we consider two bearing tracks
relatively to North axis and coming from antenna 1 and
antenna 2. A track is defined as a time collection of true
bearing (relatively to Y North axis) and frequency measurements, for example output from narrow-band ADT
HA
on
,
index
and TA. The bearing measurements are labelled
standing for measured, and frequencies .
!
" #
"$ " "$ % (1)
for & and ' measurements respectively from sensor 1
and 2, where [.]’ stands for transposition.
problem
The
correis to answer the
question:
does
track
1
? Otherwise they are issued from
spond to track
two different sources. According to the binary hypotheses
test within a general Gaussian formalism [5], one have the
following generalized likelihood ratio test (GLRT) to compute:
( 8 9: 2 (2)
/,1 )#*,+.- prob 0
)#*,+ -3254 -76 prob /,1 1 8<;>=
1
1 @ 1 ,A stand respectively for the unknown
Here , and ?
state vector considering that tracks 1 and 2 are coming from
the same source (hypothesis HB of the GLRT),
or that they
are from 2 different sources (hypothesis H of the GLRT).
The generic measurement equations for bearing and a single frequency, without additive noise, are:
J LK
*DC5EF5*HGI U J B VK
B
BDX
Y[Z M P M P W]\W^ G J VK U P
I I R5T
`
S
I
5
R
T
M U J (3)
RWT
M U P W E_ \ J R5T
a
where ` is the sound speed; <
I RWT U RWT designates the ownJNMO B
NMO
QP
QI P
B U
M
ship position at time . Assuming a constant course and
speed motion for the target, and a stable unknown emitted
frequency B , the target state vector at reference time B is
defined accordingly:
1b
U c P QU P B
IB B I
(4)
Refering to numerous litterature about TMA [1, 2, 3, 4],
the problem of target parameter estimation is somehow the
minimization of a given criterion. Such criterion is generally the quadratic fit between the noisy measurements and
a model for these measurements. Here the use of frequencies and bearings ensures observability of the state vector;
unusual case where ownship and target velocity vectors are
lined up is too specific to occur in long range surveillance
situations.
So, TMA is involved in the maximization of the conditional probalities above. Under Gaussian assumption, the
ML estimation from GLRT resumes to the minimization of
the following quadratic criterion:
Med7f _hg ( ji
k M k qp1 K k M k qp1 nmn nmn
non
kml 4 Lnon
M i
k M k 1 r k M i
M k s1 r k k
nmn kml 4 Nnmn non (5)
kol 4 Lnon
y
stands
for
nmn t7non p1
tvuwex t , where w y is the covariance of
.
is
the
most
consistent TMA estimation
with respect
t
1r
1r to hypothesis HB (resp.
and
for hyp.1 H ). De{
pending on the dimension
of
the
state
vectors
^ ) the
cK
Med7f _Dg ( is z , with | ~} ’s,
1 theoretic
^} ) J1 distribution
M } ^ ) J1 of
. For example in our case, if one assumes a straight line motion with a constant speed and one
single
1 unknown but stable emitted frequency, the dimension
of is 5.
Consequently, the number
of freedom (d.o.f.)
K ofM€degrees
of the chi-square law is &
' SM & M‚ M ' M‚  .
Furthermore, this binary association test between 2 single tone bearing tracks can easily be extended to multi-line
bearing tracks, each of them having many frequency lines
with unknown emitted frequency. The d.o.f. of the test
moves
1 naturally to the difference of unknowns describing
the ’s between H and HB . More generally and in case
where we are interested in associating a set of tracks from
platform 1 to another set from platform 2, one build a suboptimal hierarchical clustering test in order to find which
partition (made of singletons and pairs) is the best among
these 2 sets.
The principleMeisd7the
choose the pair of tracks
f _Dg following:
( and satisfies
the threshold, then
that minimizes
=
proceed to the next “best” pair, and so on until the threshold
condition is violated.
In other words, as long as you associate within possible
identical tracks, the test variable will remain small enough
or noisy like, and as soon as you try to merge two really
different tracks, GLRT will rapidly go over the threshold.
2.2
Association with spectral assignment
The previous binary test can underperform whenever the
available information from the measurements is not sufficient
p1 enough to ensure a “good” covariance matrix for each
; for example the existing tracks are too short in time, or
with a low SNR, the bearings can also be biased (multipath
with TA), ... This is related to the generalized part of the
GLRT.
We propose to forget the bearings and work only with the
frequency lines, neglecting Doppler effect. Originally this
1142
is connected to the assignment problem [6, 7] to optimally
minimize the distance between
{ two populations.
@ , "
non k M … ˆ Œ k Ž on n
4.1
target #
—d K
/,–
It can be reduced to | |
in a subop|
timal version where the pairs are successively made starting with the minimum distance, withdrawing corresponding elements, and so forth for the remaining sets. This is
also viewed as a special case of hierachical data clustering
where the maximum number of elements per classes is 2.
3
Track to track association before/after a detection loss from a
single platform
As a consequence, one can conceive a similar method
where two separate time periods take the same place as the
2 previous platforms. This is of great interest specially for
TA sonar systems. Actually, common situation is a vessel
doing a maneuver for tactical reasons. Often, TA tracks are
lost or erratic until the towed array is stabilized.
˜ the tracks before x x and M™after
K
˜Gathering
, the idea is to scan all the possible pairs /
and to find those which
1 are consistent with a predefined tar-
get motion model (e.g. straight line with constant speed
(eq. 4)). The acceptance test is based upon a chi square law
but with threshold depending
K ˜ M } ^ )on1theW number | of measure|
ments (d.o.f. |
.
x
In case of poor TMA convergence, one can shift from
TMA association to multi-spectral assignment, whenever
the time interruption is moderate (otherwise the direct
search through the assignment matrix (6) could be affected
by mismatched Doppler effect).
Hull Array and Towed Array track association
Let us consider 2 antennas and a scenario with 4 targets
being detected on TA, and only 3 on HA. Two of them
are in common. The table below defines the kinematic
parameters at time zero.
(6)
with nmn tnmn being a quadratic norm weighted by the variance
of the scalar t (usually estimated from SNR norm and CRB
 ’ and the so-called “rectangular
formulas). Note that |‘
assignment” [7] finds out which frequency lines must be
Z are
K•” Z by/,– pairs. This alsingletons, and which ZDone
K Z associated
d
|c“
|
| operations for
gorithm is said to be
a square matrix of distances. Z
Z
K
Realistic simulation and experimental results
† D "
and „ ƒ … …
…@‡ the
Say ƒ two sets of frequency lines respectively from HA an TA. Individual frequencies k and …@ˆ are supposed to be gaussian
noisy measurements and have the same mean if they come
from the same source. So the global test is JtoŠ minimize the
distance over the permutation of the index ‰
and compare
it to a threshold:
‹
„ ) ^G i
ˆ ŒJ Ž
4
1
2
3
4
5
range
(km)
9
8.2
12
15
16
bearing
/North (deg)
-2
0
-3
-1
1
speed
(kt)
13
19
17
14
21
course
(deg)
112
90
95
102
110
True partition is the following:
Z Z šd d m5”h os›œ š A
?
where | designates the true association between tarZ
get #| from HA and target # from TA. So 2 targets
are
d;
Z
and
#
detected on both
arrays
HA
and
TA:
targets
#
”.W›q 
d

Z d 5HA
other targets #
are alone;
”.s› detects targets #
whereas TA detects targets #
. The number of tracks
here is equal to 7 and sampling time is 6 sec for 160 scans.
We compared the two methods previously seen in above
section regarding the track-to-track association via TMA
estimates (  ) or spectral assignment ( ž ). Figure 2 below
compares such relative association error (averaged over 50
Monte-Carlo runs) between the estimated partition of tracks
and the true one. This is done versus the frequency standard
deviation ŸS .
Such error is defined as the minimum number of shifts
necessary to go from the former to the latter [8]. It is equivalent to a distance between the two partitions. This distance
is normalized by the total number of tracks, and thus appears as %. Obviously the information brought by TMA
is essential to keep the % error small even for high input
frequency variance Ÿ .
Spectral assignment is seen as keeping moderate errors
of association (less than 10% for high Ÿ ), even if TMA
association exhibits lower error rates. Reason is that spectral assignment uses only frequency information, and especially an averaged value over the 160 scans, whereas TMA
association takes benefits of both bearings and frequencies.
However spectral assignment is less constrained by Fisher
information, or conversely TMA often needs a batch of time
1
more important in order to achieve a good state vector
estimate. This will be seen with real signals in following
section. They are in fact complementary processings.
Furthermore we studied the influence of the threshold
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choice, since the association test is working with composite hypotheses: one need to determine a strategy to estimate
the number of common targets, otherwise the cheapest solution (within the theory of statistical tests) is always to declare no association. Figure 3 now is equivalent to figure 2
but with the use of an absolute stop criterion instead of differential: performance is degraded for spectral assignment
method but not that much.
More precisely, differential criterion is a test of the GLRT
variable which is applied only on the single minimum distance while performing step by step the data sets reduction.
It is sensitive to any attempt to merge two tracks that do not
belong to the same target.
On the contrary, absolute criterion (Akaı̈ke like) is in fact
a test of the cumulated GLRT variable over the entire hierarchical data clustering process. It appears to be less sensitive
to the correct number of targets whenever the model is not
very accurate.
4.2 Multitrack association before/after TA
maneuver
Here is now a 1-hour real experiment at sea. The
panoramic TA bearing detections is represented in figure
4 as a result of the TMA association. Dotted lines connecting tracks figure what are the decisions for the association
before/after the ownship maneuver: 7 targets are matched
correctly before and after TA maneuver.
Figure 5 does the same for the spectral assignment. Here
a time period of 10 mn batch is used to estimate the assignment after the ownship maneuver. Unless such amount of
time, the performance is naturally degraded: up to 10 targets are now associated correctly.
Whenever the target has dopplerized lines with strong
SNR, the TMA association based on the full bearing and
frequencies sequences is the most powerful (figure 6 for the
raw data of the associated lofargram of target 5). However,
for far target with dim lines the spectral assignment gives
another chance to make the association successfull (see raw
data on figure 7 for the lofargram of target 7)
5
Conclusion
The problem of track-to-track association in passive
sonar has been solved using combined detection and estimation theories.
Combinatorial aspects are solved using hierachical data
clustering or linear sum assignment solvers.
Critical issue is to decide correctly which detected events
from platform one have to be linked to other counterpart on
second platform.
The generalized likelihood ratio test proved to give satisfactory results, assuming that the way the input data are
modelized is suited to the available information. Rich TMA
content can only be used when the target exhibits enough
SNR or during a sufficient time. Otherwise the spectral
assignment approach, simply based on the frequency line
spectrum, is enough to solve the remaining cases of intermittent or weak targets.
References
[1] Nardone, S.C., Lindgren, A.G., and Gong, K.F.
Fundamental Properties and Performance of Conventional Bearings-Only Tracking.
IEEE trans. on Autom. Control, vol. 29, 775-787 (Sept.
1984).
[2] Lindgren, A.G., Gong, K.F., Graham, M.L.
Data Fusion in a Multisensor-Multicontact Environment.
In Proc. of the 20th Asilomar Conf. on SSC. (Pacific
Grove, CA, Nov.1986).
[3] Passerieux, J.M., Pillon, D., Blanc-Benon, P., and Jauffret, C.
Target Motion Analysis with bearing and frequency
measurements.
In Proc. of the 22nd Asilomar Conf. on SSC. (Pacific
Grove, CA, Nov.1988).
[4] Passerieux, J.M., and Pillon, D.
A suboptimal hierarchical approach to bearing tracking
and track to track association.
In Proc. of 5th EUSIPCO-90, Barcelona, Spain, 18-21,
1990.
[5] Van Trees, H.L.
Detection, Estimation and Modulation Theory, Part I
John Wiley & Sons, New York, 1968.
[6] Munkres, J.
Algorithms for the assignment and transportation problems. In Journal of Siam 5, 32-38, Mar. 1957
[7] Bourgeois, F. and Lassalle, J.-C.
An Extension of the Munkres Algorithm for the assignment Problem to Rectangular Matrices.
In Comm. of the ACM, 14 (12), 802-804, Dec. 1971
[8] Blanc-Benon, P. and Pillon D.
Multi-tracks association for underwater passive listening. In Y.T Chan Editor, NATO-ASI series, Kluwer Academic, 473-477, 1989
1144
Figure 2: %assoc. error .vs.
tial
Figure 3: %assoc. error .vs.
Ÿ - stop criterion is differen-
Figure 4: 1-hour panoramic TA bearing detections: TMA
association
Ÿ - stop criterion is absolute
Figure 5: 1-hour panoramic TA bearing detections: spectral
assignment
1145
Figure 6: Associated lofargram of target 5 with TMA association
Figure 7: Associated lofargram of target 7 with spectral assignment
1146