Event Detection in Acoustic Undersea Sensor Networks

Event Detection in Acoustic Undersea Sensor Networks
Arsalan Tavakoli
Department of Computer Science
University of Virginia
Summary: In the past five years ad-hoc sensor networks have received a good deal of
research attention, and one of the popular applications that has emerged is event
detection services. This paper looks at acoustic undersea communications, and more
specifically, event detection in undersea acoustic sensor networks. I first present an
overview of acoustic undersea communications and event detection services, and then
compare and contrast this with the terrestrial equivalents. The paper also presents a
confidence level algorithm used to reduce false alarms, which is one of the main
problems that currently exist in detection applications. Afterwards the details and the
results are laid out for the simulation that tests the effectiveness and accuracy of the
confidence level algorithm. The simulator uses both self-generated data as well as realworld acoustic sensor data from a Navy experiment. Finally, the paper concludes by
presenting an analysis of the simulation detailing the strengths and weaknesses of the
algorithm and laying out plans for future work.
1. Introduction
Ad-hoc sensor networks became popular
because they were powerful, yet
presented a multitude of potential
applications, many of them initially
within the military realm as the
government was the source of the
majority of the initial funding. One of
the most popular applications, due to its
wide variety of potential uses, has been
event detection. This involves detecting
the presence of an object within the
sensor network, tracking its location as it
moves through the network, and also in
certain instances classifying the object,
such as whether it is a person, a vehicle,
One particular use for this
technology is in a military environment,
where a large network of sensor nodes is
scattered in enemy territory where it can
perform reconnaissance and relay this
message back to military headquarters.
More consumer-oriented applications
include security and traffic monitoring
In an event detection application, the
sensor nodes use their sensor readings to
detect the presence of an object within
their sensing radius. The difficulty is
that the sensor nodes are not always
100% accurate, and so a major problem
that often presents itself is how to reduce
false alarms. A positive false alarm is
when a sensor node’s reading leads it to
detect an object that does not exist, and
conversely a negative false alarm is
when a sensor node fails to detect an
object that does exist. Both of these are
unwanted results, and so researchers are
consistently trying to reduce the number
of false alarms. One of the best methods
has been to require a certain degree of
aggregation in order to report an object,
which means that multiple nodes have to
detect it. This method presents new
problems and complexities, but it does
serve as the foundation for the
confidence level algorithm presented in
this paper.
To date the majority of event detection
research, and for that matter sensor
network research in general, has focused
on terrestrial applications. Many of the
same principles hold in undersea
environments, yet there are stark
differences as well. To begin with,
fundamental hardware items such as the
sensor nodes themselves differ, and a
completely different communication
medium is used as well. In order to be
able to proceed with undersea event
detection research, the principle
differences between the terrestrial and
undersea environments have to first be
2. Acoustic Undersea Sensor
In order to be able to effectively explore
acoustic under sensor networks and
compare them with their terrestrial
counterparts, they have to be broken
down into multiple parts.
2.1 Acoustic Undersea
The majority of sensor nodes use RF
radio communication to communicate
with one another. On the most recent
MICA2 [1] motes, this allows for an
approximately 100ft communication
radius when the mote’s antenna is
broadcasting at full power.
For undersea environments, RF radio
communication is infeasible because it
can only be done at very low
frequencies, which require large
antennae and high transmission power
[2]. Therefore, acoustic communications
are used as they are a much better fit for
undersea environments. As Table 1
shows, depending on the bandwidth they
can provide a wide variety of ranges. A
typical undersea modem provides a
communication range of approximately
1000 meters with a bandwidth of
This large communication
range, coupled with the larger sensing
radius discussed below, allows for a
much more spread out and sparse
network that is just as effective as dense
terrestrial networks.
Table 1: Acoustic Undersea
Communication Range
2.2 Undersea Hardware and
The equipment used in acoustic undersea
networks is understandably much
different than those used by terrestrial
First of all, undersea sensor nodes are
much more expensive than a typical
sensor node. They are generally much
larger and more difficult to build, as they
have to be able to handle a whole slew
of new conditions, such as being in a
liquid environment and also being
susceptible to natural occurrences such
as corrosion and fouling.
The cost of the equipment and the
general underwater conditions make it
difficult to create dense undersea sensor
networks, and as a result the sensor
nodes are spread out much farther then
they would be in a typical terrestrial
environment. The larger sensing and
communication range help to offset this,
but the sparseness must still be taken
into account when developing detection
algorithms because it becomes much
more difficult to use the degree of
experiencing an increase in negative
false alarms. This is because due to the
large distances between the sensors,
there is very little spatial correlation and
so often the degree of aggregation
requirement will not be met since the
target will only be within one node’s
sensing radius.
Although in our assumptions we have
generally ignored this fact, undersea
sensor networks require much higher
power. This is because there is added
complexity at the receivers, and also
because communication is over much
longer distances. Furthermore, solar
energy can not be used as a power
source. Depending on the duration that
the network has to be left unattended,
energy conservation techniques may
need to be implemented. However,
currently, the size of undersea sensor
nodes has not been restricted and
therefore battery life is not a current
3. Real-World Experiment
In 2003, a group of research scientists
set up a research experiment for testing
out an acoustic undersea sensor network.
The test was performed in Port
(Deployable Autonomous Distributed
System) sensor nodes [3]. The purpose
was to attempt to analyze the
effectiveness of the DADS sensor nodes
in detecting surface movement of boats
and ships, as well as detect the presence
of underwater submarines.
Two different sensor node clusters were
deployed, and each cluster contained
three sensor nodes in a straight line.
Each of these sensor nodes was equipped
with a three dimensional magnetometer,
or magnetic sensor, that would be used
to collect data. The two clusters were on
average approximately 1500m apart, far
enough from each other so that they
would never sense an object at the same
The data could not be monitored in realtime. Instead, the data were stored on
the nodes themselves, and when the
nodes were recovered, the data were
downloaded onto a computer in order to
be analyzed. The main goal was to see
whether the developed trend analysis
method could accurately identify objects
based on the raw sensor data. During
the simulation, video surveillance was
used so that the accuracy of the analysis
could be determined.
Overall, 330 hours of data was gathered
for surface area detection, and nine
hours of data was gathered for
submarine detection.
Because of
discontinuities in the data, only the xaxis data from the magnetometer was
analyzed [4]. I could not solely use this
data for testing the confidence level
algorithm since I needed data for more
than two clusters. However, I used the
data as a foundation to analyze the
frequency of false alarms, and also to
determine for how many contiguous
reports the sensor node would report a
false alarm.
4. Confidence Level Algorithm
As mentioned before, one of the main
problems in event detection applications
is the occurrence of false alarms. This is
dealt with by using multiple sensor node
reports in order to increase accuracy. A
confidence level is simply a way to
quantify that anticipated level of
accuracy, based on a wide variety of
The foundation for the confidence level
algorithm used in this paper was
originally designed by Jingbin Zhang at
the University of Virginia [5].
The algorithm calculates a confidence
value based on two factors: temporal
data, or spatial correlation, and historical
data, in terms of the history of
information on this specific target by the
In order to calculate the temporal aspect
of the data, I made the assumption that
although the sensor nodes do not
precisely know the location of the target,
they are aware of their own location.
The algorithm uses a weighted scheme
in which a sensor node predicts the
position of the target based on the
number of its neighbors who also detect
the target, their location, and its own
concentric circles. Each sub-area is
assigned a weight, where the sum of the
weights must be one. The closer the
sub-area is to the target, the higher the
weight. For the summation term, n is the
numbers of sub-areas for the given
target. p(i) represents the percentage of
nodes in a sub-area that detect the target,
and w(i) represents the given weight of
the sub area.
It also makes sense that the longer a
target is detected by sensor nodes, the
greater the confidence value should be.
As a result, figure 2 shows the equation
used for determining the historical
aspect of the confidence value.
h(history ) 
 arctg ( f (t ))
Figure 2: Historical Equation
This function can never exceed one. f(t)
is a function of that t that is meant to
increase as the length of time that a
target is detected increases.
Both of these equations are put together
in order to be able to compute the
confidence value at any given point in
Confidence j  h( j  g (temporal))
Figure 3: Confidence Value Initially
Confidence j    Confidence j 1  (1   )  h( j  g (temporal))
i 1
Figure 4: Confidence Value
g (temporal)   p(i ) * w(i )
Figure 1: Temporal Equation
Figure 1 shows the equation used to
calculate, g(temporal), the temporal
aspect of the confidence value. The way
that the algorithm works is that the area
around the target is divided into multiple
Figure 3 shows how to compute the
confidence value the first time that the
target is reported (j = 1), and Figure 4
shows how to computer the confidence
value for the target for all subsequent
reports (j > 1). The number of time slots
since the target has been detected is
signified by j, where j = 1 means the first
report after the target has been detected.
α is also a measure of how much the
confidence value should depend on the
previous confidence value, in order to
minimize drastic fluctuations.
There were some assumptions that were
made when running the simulations,
including those that made the
simulations a little bit easier, as well as
just assigning values to certain
The confidence level algorithm uses
various parameters that need to be set
experimentally, such as the number of
sub-areas, the size of the sub-areas, the
weight of the sub-areas, and also α.
Simulations need to be used where these
parameters are tuned in order to be able
to determine the most appropriate
To begin with, I assumed that there
would only be one target in the sensor
network at the same time. Obviously,
this will not always be a realistic
condition, but having multiple targets
adds a whole new set of complexities
that I was not ready to handle before I
was sure the algorithm worked for a
single target.
The one thing that has to be noted is that
this scheme requires a leader node that
gathers the reports from all the sensor
nodes and computes the confidence
value. The node needs to also store
historical information for each target in
order to be able to calculate the
historical aspect of the confidence value.
consumption was not taken into
consideration, and so no form of energyefficient sensing was performed.
There are many different potential
scenarios for using leader nodes. They
can gather sensor data in addition to
performing their leader duties, or only
handle the task of computation.
Furthermore, they can be elected
dynamically to stay with a target, such as
in EnviroTrack [6], or they can be
elected statically.
4. Simulation Details
For this paper, I used a simulator that
had been custom-made for this particular
confidence algorithm, and tweaked it a
little bit to reflect changes in the
algorithm as well.
4.1 Assumptions
One of the main points that is critical to
the algorithm is that it does not assume
that the nodes can detect the distance to
the target based on sensor readings. This
is a reasonable assumption, as in some
cases, including the 2003 DADS
experiments, the nodes are not able to
estimate the distance to a detected target.
In this algorithm, as mentioned earlier, a
node uses information about the location
of other neighboring nodes that also
detect the target in order to predict that
target’s position. The problem with this
algorithm is that if all the nodes are on
one side of the target, as happens when
only one cluster detects the target, the
predicted position of the target is
incorrect. It is estimated to be closer to
the node than it actually is. As a result,
the confidence value is higher than it
should be, leading to additional false
positive reports.
Future work will
examine the effects on the algorithm
when nodes can accurately determine the
distance to a detected object.
In this simulation, the assumption is that
there are infinite sub-areas, and each is
weighted by (1 / distance to the target).
Figure 5 shows the complete equation
for determining the temporal value
portion of the confidence value equation.
i 1
1  ER * ( )
i 1
1  ER * (
Figure 5: Adjusted Temporal Value
The numerator is meant to calculate the
weights for all the nodes that detect the
object. ‘n’ is indeed the set of all objects
that detect the target, and ‘a’ is the set of
all nodes that are within the sensing
radius of the target. ER is the error miss
rate, or how often the node causes a
negative false alarm. D is the distance
from the specified node to the target, and
SR is the sensing radius. This temporal
value will always result in a value that is
less than one.
The false-positive rate is assumed to be
0.01, and the false negative rate is
assumed to be 0.01 as well. There is no
precise estimate for these values, but
these values are based on reported rates
in various experiments, both aquatic and
terrestrial. These rates will not affect the
relative confidence levels, only the
absolute confidence levels. Therefore,
based on the false report rate, the
confidence threshold for determining if
an object really exists can be adjusted.
Two other variables set are the number
of time periods these false reports
continue for. I based this value on the
data gathered from the DADS
simulation. Although the contiguous
report length varied, and it was difficult
to determine without the ground truth,
the various spurts seemed to last for six
time slots, on average. Therefore, I used
this value for both the false-positiveduration and false-negative-duration
The leader scheme used in the
simulation is one in which a cluster of
nodes is set up (four by default), with
three of the nodes acting as normal
sensor nodes, and sending their reports
to the fourth node, the leader node. The
leader node does not itself gather sensor
data, and is selected statically at run
For the purposes of the simulation, I
needed only four clusters set up in a
square formation. I have included in the
future work section plans to run the
simulation for a longer period of time
and use more than four clusters.
The last assumption regards the sensor
and communication ranges, as well as
the bandwidth.
Based on current
acoustic sensing technology, the sensing
radius is set to be 250m, while the
communication radius is 1000m, and the
bandwidth is 19kbps. My plans to test
variations in these parameters are
included in the future work section.
4.2 Simulation Scenarios
The various simulations that were run
did not involve any modifications to the
actual algorithm itself, but rather
configuration parameters for the
simulation. The parameters break down
into two categories.
The first set
involves parameters that can not be
controlled and which fluctuate, such as
target speed and target route. A wide
variety of values for these two
parameters had to be tested in order to
ensure that the algorithm works well
under various likely scenarios.
Another goal for this simulation was to
determine what the optimal set up was to
maximize the accuracy of the confidence
level algorithm. As a result, during the
simulation I varied two main set-up
parameters: the level of cluster overlap
and the number of nodes in a cluster.
For the speed of the target, I chose the
parameter values of 1 m/s, 3 m/s, 5 m/s,
and 10 m/s. The aim of this simulation
is to replicate the submarine tracking
portion of the DADS experiment.
Therefore, the chosen speeds are
appropriate values for submarine speeds.
The amount that the sensing radius of
each clusters overlaps is referred to as
the cluster overlap variable. I have set
up three different scenarios for this
In the first scenario, the
sensing radius of two clusters can
overlap by 50m, or in other words two
different clusters can detect an object
simultaneously. In the second scenario,
the radii of two clusters are touching, but
not overlapping.
Finally, the last
scenario lays out the clusters in a fashion
such that there is a 100m gap between
the sensing radii. As a result, it is
theoretically possible for the target to
pass between the two clusters
The last parameter that I modified was
the number of nodes in a cluster
(including the leader node). I will set
the values to 4, 6 and 8 to see the
marginal benefit of additional nodes in
the cluster.
5. Simulation Results
For the route of the target, I created three
different options. For the first option,
the target simply moves straight through
the sensor network. For the second
option, the path of the target resembles a
horseshoe on its side in which the target
comes in and then turns around and
leaves. The last option is to proceed in a
straight path until the target reaches the
center of the sensor network and then
turn and proceed due north. These
various scenarios are meant to test the
performance of the confidence level
algorithm as the target passes through
the different clusters’ sensing ranges in
various ways. Screenshots of all three
paths are included at the end of this
There were 81 total simulations, as there
were four values for target speed, three
values for target route, three values for
cluster overlap, and three values for
nodes in a cluster.
For each scenario, I graphed the
confidence value history for each cluster
leader node over time. I have included a
few of the more conclusive graphs at the
end of this paper, and will refer to them
in this analysis.
Success was judged by looking at the
percentage of time that at least one of the
leader nodes reported a confidence value
higher than the threshold, which in this
case was set to be 0.7. This parameter
can be adjusted experimentally.
The algorithm was definitely successful
in the sense that the cluster that could
sense the target almost always had a
confidence value of nearly one, and so
therefore the most important period was
when the target moved between two
different clusters. The goal was to
minimize the time that no leader’s
confidence level was above the
threshold, at least while the target was
still moving through the network.
The reasoning is that the leader nodes
can communicate with each other, and
so even if a node does not detect the
target yet, it could theoretically have a
confidence level greater than 0 as it
anticipates the arrival of the target.
By far the variable that had the least
effect on the confidence values was the
number of nodes in a cluster. The
difference between four nodes in a
cluster and eight nodes in a cluster was
minimal. The main reason seemed to be
that with the false alarm rate only being
0.01, additional nodes were not needed.
With four nodes in a cluster, while the
target was within the sensing radius, the
additional nodes would have no effect.
This simulation did assume that nodes in
a cluster were packed very tight
together, almost to the point that they
had the exact same sensing radius. In
future work this restriction may be
relaxed to see if there is a significant
effect on the confidence value during
However, this would be
almost equivalent to eliminating clusters
and just creating a dense undersea
network, which is not currently a
desirable outcome.
The only effect that the speed of the
target had was that it reduced the length
of the handover period because the target
moved between two clusters faster.
Therefore, in cases like Graph 7, you see
a significant gap between two different
leader nodes reporting a confidence
value above the threshold because the
slow speed of 1m/s makes the transition
period a lot longer. Generally, a faster
target would affect the confidence level
algorithm because a specified cluster
might not be able to get the required
degree of aggregation. However, in this
case the fastest speed of the target is still
relatively slow, and also the sensing
radius of the nodes is quite large.
The cluster overlap variable had a
significant effect on the performance of
the algorithm. This is because the
farther apart the nodes were, the larger
the non-sensible area in the network
Consequently, the handoff
periods were prolonged, and the
algorithm has been shown to perform
weakly during these transitions.
This was especially apparent when the
target’s route was a straight line, since it
ran exactly between all the sensor nodes,
exposing the areas that were outside all
of the clusters’ sensing radii. When the
overlap was set to touching, only twice
did the confidence value go above the
threshold. When the overlap was set to
be a gap in between, the confidence
value never made it above the threshold.
Graph 4 shows the effect of the straight
line path.
Even with overlapping
clusters, the confidence level algorithm
did not perform too well.
The last variable, target route, had
expected results. The route that had the
best results was the horseshoe route,
because for nearly the entire time it
stayed within the sensing radius of a
cluster and minimized the time that was
spent in transition periods. This can be
seen in Graph 6, where there are only
small intervals when no leader reported a
confidence above the threshold, and this
is consistent with the occurrence of the
handover period.
Meanwhile, the
straight line and upwards hook paths
were both equally bad because in both
situations the target spent a good
proportion of time in areas that were
outside of all sensing radii and so the
algorithm obviously suffered. Graph 5
shows that the hook path caused a lot of
gaps in the data where no leader node
reported a confidence value greater than
the threshold.
6. Algorithm Analysis
The confidence level algorithm overall
worked extremely well. When the target
was within a cluster’s sensing radius, the
leader node almost always reported a
confidence value of one. The main
problem came when the target moved
between two clusters.
Unless the
overlap was quite large, due to the
circular nature of the sensing radius,
there were locations that the target
passed through that were not within the
sensing radius of any cluster. As a
result, these periods often had no leaders
reporting a confidence level above the
There are three main suggestions that
present themselves. First of all, there
needs to be more communication
between the leader nodes in terms of
broadcasting the confidence values.
However, this should only be done if the
value is above the detection threshold in
order to minimize the amount of network
traffic. Second, the confidence values of
neighboring clusters have to play a
larger part in calculating the confidence
value for a leader node in order to
leverage the power of clusters. Lastly,
confidence values need to be much more
stable, especially when they are
decreasing. Currently, when the target
leaves a cluster’s sensing radius, the
confidence value takes an immediate and
drastic plunge.
A more reasonable
method would be to have the algorithm
reduce the confidence level at a rate
inversely proportional to the time that
the target had stayed within the sensing
radius. If within a set time period
another leader did not broadcast a
confidence value (which would by
definition have to be above the
threshold), then the confidence value
could drop drastically.
Using this method, the handoff period
would be much smoother, and the false
alarm rate would not be increased at all.
Testing an improved algorithm that
incorporates leader cooperation is left
for future work.
The last aspect that must be looked at is
the assumption that the nodes can
determine the distance to a target based
purely on their own sensor readings.
Although some sensor node hardware
may be able to do this, a good deal of
equipment, such as those used in the
DADS experiment, can not.
neighbor information to predict the
distance to the node and then calculate
the confidence value based on this
distance. The problem is that this
algorithm, with the current cluster setup, creates a biased distance value,
which causes the confidence level
algorithm to be too high. Either there
needs to be a more accurate way for
calculating the distance to the target,
which seems difficult, the algorithm
needs to be changed to depend less on
distance, or the nodes need to be given
the ability to determine distances to
objects precisely.
One of the goals of this paper was to
suggest an ideal set-up for implementing
this algorithm. The number of nodes in
a cluster should be set at 4 (including the
leader node), because any additional
nodes do not provide any real benefit. In
terms of cluster overlap, having a little
overlap worked the best in this
simulation. However, either touching
sensor ranges or small gaps are
acceptable if the algorithm is modified to
deal with the handover period more
7. Future Work
During the course of this paper, I made a
good deal of assumptions, and although
they were educated ones based on real
data, I would still like to gather more
accurate statistics. For example, with
parameters that can affect the confidence
value significantly, such as the rate of
positive and negative false alarms, I
would prefer to gather more empirical
evidence about what their true value
should be.
All of the scenarios tested for this paper
had only four clusters since this was
enough to create a boxed area through
which the target could pass. However, I
want to run longer simulations with
more clusters because this will allow me
to explore more complex target paths.
Furthermore, because of the sensor
node’s long communication radius,
leader nodes can exchange data with
leaders from non-adjacent clusters, and
so having more than four clusters would
allow me to test the effect of this
I also want to explore various acoustic
undersea modems which have various
sensing and communications radii. The
hope is to discover which combination
provides the best coverage and
effectiveness with the least amount of
equipment and cost.
One of the main aspects that needs to be
explored is how to eliminate the
choppiness during handover periods
between clusters. This paper has laid out
a few suggestions, and so I would like to
implement and simulate the changes in
order to analyze their effectiveness.
Either way, the current method should
be redesigned to incorporate more leader
communication and more stable
confidence values.
One of the important aspects of the
simulation that I wish to explore is the
effect of giving nodes the ability to
determine the distance between the
target and themselves. Currently, the
confidence level is biased upwards
because of the target location prediction
scheme, and therefore the rate of
positive false alarms rises. The hope is
that with this modified assumption, the
algorithm will become more accurate
and the level of false alarms will drop
Lastly, I want to gather more real world
undersea sensor network data. For this
simulation I could only use the data from
the DADS simulation as a foundation for
generating my own data since it only had
two sensors. If I could gather data from
simulations with more than two clusters,
I could compare the trends in the data
with the data generated by the simulator
to ensure that they were similar.
8. Conclusion
In recent years there has been a focus on
event detection services in terrestrial
sensor networks. This paper focused
instead on acoustic undersea sensor
networks, specifically proposing a
confidence level algorithm to reduce the
number of false alarms in event
detection applications.
The algorithm uses historical and
temporal information in clusters in order
to determine a confidence level that
warrants a detection report when it is
higher than a certain threshold.
Simulations showed that the algorithm
was quite effective when the target was
within the sensing radius for a variety of
different scenarios.
The main difficulty lies in the handover
period, or the period of time when the
target moves from one cluster sensing
radius to another one. Often, during this
transition, no cluster has a confidence
value above the threshold, even though
the target has not left the network. The
best way to deal with this is to foster
more communication between leader
nodes and allow confidence values from
other neighboring clusters to be used in
calculating the confidence value.
In the end, the paper achieved its goal of
proving that the algorithm was largely
successful in a variety of different
scenarios. The paper will also hopefully
serve as the foundation for more
research on event detection services in
acoustic undersea sensor networks.
9. References
[1] Crossbow Technology Inc., “MICA2
[2] I. Akyildiz, D. Pompili, T. Melodia,
Acoustic Sensor Networks”, ACM
Sigbed Review, July 2004
[3] K. Rogers, V. Bana, J. Bekkedahl, R.
Brannan, B. Creber, C. Fletcher, D.
Ladd, R. Ricks, D. Sample, T.
Sledzinski, R. Yumori, “Quick Look
July 2003
[4] Migma Systems, “Progress Report:
A New Automated Undersea Sensor
Detection and Fusion System”,
November 2004
[5] J. Zhang, “How to Effectively
Reduce False Alarms in Wireless
Sensor Networks”, November 2004
[6] T. Abdelzaher, B. Blum, Q. Cao, Y.
Chen, D. Evans, J. George, S.
George, L. Gu, T. He, S.
Krishnamurthy, L. Luo, S. Son, J.
Stankovic, R. Stoleru, A. Wood,
“EnviroTrack: Towards an
Environmental Computing Paradigm
for Distributed Sensor Networks”,
International Conference on
Distributed Computing Systems,
March 2004
Graph 1-3 Notes:
Graphs 1-3 are meant to indicate the three different paths that the target could take. The
dotted blue line indicates the path of the target. The large blue circle has a radius of
250m, equal to the sensing radius of one of the sensor nodes. It indicates that any node
that falls within this circle should detect the target. The numbers that can not be read are
the ids of each of the individual nodes, but they are not important in this case as the
subsequent graphs refer to clusters by their location. Lastly, the purple line between two
black dots (the leader nodes) indicates that both leader nodes detected the target and have
communicated this fact to each other.
Graph 1: Target with a Straight Path
Graph 2: Target with Hook Path
Graph 3: Target with Horseshoe Path
10 m/s - Straight - Overlap - 4 Nodes
Confidence Value
Top Left
Top Right
Bottom Left
Bottom Right
97 103 109 115 121 127 133 139 145
Graph 4: 10 m/s Target Speed, Straight Path, Sensing Radius Overlap, 4 Nodes per Cluster
10 m/s - Hook - Touching - 4 Nodes
Confidence Value
Top Left
Top Right
Bottom Left
Bottom Right
97 103 109 115 121 127 133 139 145
Graph 5: Target with 10m/s Speed, Hook Route, Touching Sensing Radii, and 4 Nodes per Cluster
5 m/s - Horseshoe - Touching - 4 Nodes
Confidence Value
Top Left
Top Right
Bottom Left
Bottom Right
23 45 67 89 111 133 155 177 199 221 243 265 287 309 331 353 375 397 419 441 463 485 507 529 551 573 595
Graph 6: Target with 5m/s Speed, Horseshoe Path, Touching Sensor Radii, and 4 Nodes per Cluster
1 m/s - Horseshoe - Gap - 4 Nodes
Confidence Value
Top Left
Top Right
Bottom Left
Bottom Right
143 285 427 569 711 853 995 1137 1279 1421 1563 1705 1847 1989 2131 2273 2415 2557 2699 2841 2983
Graph 7: Target with 1m/s Speed, Horseshoe Path, Sensing Radii Gap, and 4 Nodes per Cluster
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