LOCATION AND TOPOLOGY DISCOVERY IN WIRELESS SENSOR NETWORKS
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LOCATION AND TOPOLOGY DISCOVERY IN WIRELESS SENSOR NETWORKS By CHRISTOPHER JERRY MALLERY A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY WASHINGTON STATE UNIVERSITY School of Electrical Engineering and Computer Science MAY 2009 c Copyright by CHRISTOPHER JERRY MALLERY, 2009 All rights reserved
LOCATION AND TOPOLOGY DISCOVERY IN WIRELESS SENSOR NETWORKS
Figure 3.2: Least-squares Multilateration (k = 4)
Initially every node will only be aware of its own estimated
position, making it unable to re-
calculate a new estimated position, in which case it will broadcast
its current estimated position
to its 1-hop neighbors. In the next iteration, every node will be
aware of their estimated position,
those of its 1-hop neighbors and the estimated distances of its
1-hop neighbors made through direct
ranging. This information allows a node to begin recalculating its
own position estimate. Since
each node’s initial position is the origin, this first
recalculation will place a node roughly the av-
erage estimated distance it is from all of its 1-hop neighbors away
from the origin in an arbitrary
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direction. Every node then broadcasts its new position estimate, in
addition to the position esti-
mates it has received from its 1-hop neighbors and the distance
estimates it has made for its 1-hop
neighbors. The size of an ANIML packet depends on the node’s 1-hop
neighborhood. ANIML’s
total message complexity is the product of the number of nodes and
iterations. In most randomly
deployed topologies ANIML usually requires only 10 to 15
iterations.
In the third, and subsequent iterations, every node is aware of
their own estimated position,
those of its 1- and 2-hop neighbors, the estimated distance of its
1-hop neighbors made through
direct ranging and the estimated distances of its 2-hop neighbors.
ANIML infers a node’s distance
from a 2-hop neighbor by adding the received distance estimate
between the intermediate 1-hop
neighbor and the 2-hop neighbor to the directly calculated distance
estimate of the intermediate
1-hop neighbor. While there are possibly other ways to obtain a
more accurate distance to a node’s
2-hop neighbors, since the sum of distances provides a gross
overestimate due to triangular in-
equalities, we chose the straightforward sum of distances in ANIML.
In addition, since a node can
receive duplicate information about any 1- or 2-hop neighbor, ANIML
always utilizes the smallest
inferred distance it has estimated to any node. Now every node is
fully able to take advantage of
least-squares multilateration to recalculate a more accurate
position estimate, at least relative to
its immediate neighbors, because its immediate neighbors’ estimated
positions have spread apart
and not all located at in the same spot. Additionally, the
availability of 2-hop neighbor infor-
mation allows the nodes of a neighborhood to begin moving closer
towards their actual distance
away from the reference node and any adjoining 1-hop neighborhoods.
This is possible because
ANIML explicitly provides nodes with a sense of how they should
line up globally with adjacent
neighborhoods, while remaining consistent with their 1-hop
neighbors.
In a network where every distance estimate was perfect and the only
unknowns in the net-
work were positions, ANIML would not require an explicit
termination condition. Each node will
converge to a single location. However, having only estimated
knowledge of distance requires an
explicit termination condition. With only estimated distance
estimates, there is no single solution
21
to the localization, so any one slight position estimate change can
cause an unending cascade of
changes in the position estimate of every node in the network. This
makes determining the correct-
ness of ANIML difficult. The termination condition we have most
used is a node keeps its current
position estimate when it has not moved more than 5% of its
transmission range in 5 successive
iterations. Once a node stops, it simply acts as a forwarder for
the messages it receives from still
actively localizing nodes. Unfortunately, it is possible, although
rare, for some nodes to never settle
near a single position. These nodes flip back and forth between two
relatively far apart positions
estimates. In these cases, we employ a cap on the maximum number of
iterations to insure that a
node does not attempt to localize itself indefinitely.
3.3.2 Improving ANIML
By restricting distance estimates to only 1- and 2-hop neighbors,
instead of globally propagated
information, such as the positions of anchors, we reduce the
effects of cascading ranging errors;
such cascading errors significantly affect the accuracy of many
range-aware localization techniques
[90]. Naturally, to control the message and computation complexity,
we would have preferred to
restrict ANIML to use only 1-hop neighbor information. However, we
found that while this can
provide accurate localization in some cases, in many cases
individual neighborhoods localize too
rapidly based on only their own 1-hop neighborhood’s information,
fold onto themselves, and get
stuck at a local optimum. This problem is also encountered in ILS
[55] and other techniques
[61, 74]. Such folding of neighborhoods cannot be either detected
or rectified with only 1-hop
neighbor information. Fig. 3.3(a) shows the localization of a
network by ANIML using only 1-
hop neighbor information (estimated positions are denoted by
circles with the arrows pointing to
the true positions). The accuracy of the localization is poor with
an average positioning error
of 90 meters; however the average pair wise distance error is only
21 meters. Several different
ways to address local optima are presented in the literature. For
instance, DV-Hop [61] favors
positioning information from physically closer nodes. ILS [55] by
spreading the localization out
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in successive stages, scoring the error estimates, and controlling
the error propagation. On the
other hand, Savvides et al. [74] presented Kalman filtering-based
localization technique that uses
weighting. However, by simply basing nodes’ position calculations
on 1- and 2-hop information
ANIML can prevent the folding of neighborhoods and from getting
stuck at a local optimum. Two-
hop neighbor information acts as a natural dampener to the
localization process, slowing down the
changes of nodes in each iteration which allows neighborhoods that
would otherwise rapidly reach
a local optimum extra time to receive additional information that
could prevent it from getting
stuck. Fig. 3.3(b) shows the same topology as Fig. 3.3(a) localized
by ANIML using 1- and 2-hop
neighbor information. The localization has an average localization
error of only 8 meters with an
average pairwise distance error of 3 meters.
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Figure 3.3: Comparison of ANIML using 1-hop and 2-hop
Information
One issue with ANIML’s iterative localization approach is that it
can be slow to complete. In
the initial ANIML iterations, nodes’ positions are in a state of
flux; ANIML’s iterative behavior
causes the nodes to settle down, but slowly. However by having
nodes include its number of
hops from the network’s reference node in its broadcasts, it is
possible to increase the speed of
convergence. From the hop-distance, h, to the reference node at the
origin, a node can check if its
position is within the distance range of [r × h, r × (h− 1)] to the
origin, where r is the maximum
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transmission range. Otherwise, the node is able to either push or
pull its position to the closer of
the two bounds in the above range, along the same angle from the
reference node as before. This
push-pull refinement, done prior to broadcasting its new position
estimate, allows a node to place
itself closer to its final position much faster, allowing the
localization to converge more rapidly.
The basic ANIML technique requires no explicit error control
mechanisms, since error control
mechanisms are implicitly built into each step of the technique.
Using a node’s 1- and 2-hop
neighborhood allows for some prevention against neighborhoods
getting stuck at local optima,
without needing to resort to scoring or weighting of received
information. Also, restricting to 2-
hop neighborhood information prevents cascading of ranging errors
over multiple hops. Iteratively
refining a node’s position naturally provides error control by
allowing any transient errors to be
smoothed away over several iterations. Using least-squares
multilateration, on a node’s entire 2-
hop neighborhood, to recalculate a node’s position smoothes out the
affects of error prone distance
estimates. This is even more critical considering that using
triangle inequalities for the 2-hop
distance estimates are gross overestimates. Even after introducing
significant ranging error in the
2-hop neighbor distances, due to triangular inequality,
least-square multilateration is still able to
smooth over these affects and provide good position estimates. The
push-pull technique used to
speed convergence also provides further error control, since it
keeps nodes from drifting too far or
remaining too close to the reference node. This is important not
only for the accuracy of a node’s
own position estimate, but also for the nodes located around
it.
The iterative nature of ANIML naturally places a node into its
correct position when it neigh-
borhood is well distributed around it, the problem occurs when a
node’s neighbors are biased in one
direction from the node (i.e. corner and edge nodes). Corner and
edge nodes can end up estimating
their position on the “wrong” side of their 1-hop neighborhood.
Since least-squares multilateration
depends on unit vectors from a node’s neighbors to the current
estimate, a node will continue es-
timating its position to be on the “wrong” side of its 1-hop
neighborhood. These corner and edge
nodes that have been placed on the “wrong” side of their 1-hop
neighborhood appear “flipped” into
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their 2-hop neighbors, towards the center of the network.
Additionally our push-pull refinement
cannot help push these flip nodes closer to their proper position
on the boundary of the network
since it is a conservative push. ANIML is naturally capable of
preventing flipped nodes, however
as the network diameter increases the propagation of information
from within the network gets
progressively slower to the edges of the network allowing some
neighborhoods to still move too
rapidly into a local optimum, which is the underlying cause of
flipped nodes.
In order to combat the problem of anomalous flipped nodes we
extended ANIML with a simple
sanity check technique to detect a flip and correct it if
necessary. We could have used known tech-
niques to detect nodes on the periphery of the network and then
treated them differently in ANIML
than internal nodes, however only a small number of boundary nodes
flip and our simple flipped
node sanity check provides effective correction. A node cannot be
sure whether it has flipped or
one, or more, of its 2-hop neighbors being flipped. Without access
to global knowledge of the sen-
sor network it is impossible for a node to be absolutely positive
that it has flipped. However, based
on two observations: corner nodes have much smaller 1-hop
neighborhoods than other nodes and
nodes closer to the reference node are more likely to be well
represented by their neighbors than
nodes farther away from the reference node, this simplistic sanity
check is able to identify most of
the flipped nodes. If a node detecting a flip has a smaller 1-hop
neighborhood than its identified
inconsistent 1-hop neighbors then it is most likely a flipped
corner node and needs to have its own
position corrected. Correction for this case is flipping the node’s
position 180 around the centroid
of its “inconsistent” 1-hop neighbors. Unfortunately, neighborhood
size does not sufficiently iden-
tify flipped edge nodes. Instead, if a majority of a detecting
node’s inconsistent 1-hop neighbors
are closer to the reference node then the node assumes it is the
offending flipped node. Correction
is done by placing the node in the center of its inconsistent 1-hop
neighbors that are closer to the
reference node. In both correction cases, subsequent iterations
would let the previously flipped
node identify better position estimates on the correct side of its
biased neighborhood. This san-
ity check is independently executed at a much lower frequency than
the basic ANIML iterations,
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roughly once for every 10 iterations of ANIML. In most cases, the
sanity check is able to identify
and correct flipped nodes within two such executions.
3.3.3 ANIML-Abs & ANIML-Hop
There are two obvious variants of ANIML: ANIML-Abs and ANIML-Hop.
While ANIML is a
range-aware, anchor-free relative localization technique, the
ability to use anchors to provide ab-
solute localization (ANIML-Abs) and to provide localization in the
absence of ranging equipment
(ANIML-Hop) are both attractive options. Neither variant requires
any changes to the underlying
ANIML technique. For ANIML-Abs there must be at least three anchor
nodes, one of which is
selected to be the network’s reference node. Other anchors act no
differently than the location-
unaware nodes in the network, they just do not need to update or
refine their own coordinates.
Note that ANIML could have taken advantage of the other anchors as
additional reference nodes
to improve ANIML-Abs further. ANIML-Hop, applicable when no ranging
equipment is available,
simply selects the estimated distance for each hop to be 3r/4,
where r is the maximum transmis-
sion range. This value is slightly higher than the expected
inter-node distance in random uniform
distributions of r/ √
(2). ANIML-Hop provides also provides absolute localization, but
does not
require ranging equipment.
3.4 Performance Evaluation
We implemented ANIML (with and without our flipped node sanity
check), ANIML-Abs and
ANIML-Hop in ns-2. We compared ANIML’s effectiveness to APS
(DV-Hop) [61], a popular
technique for baseline comparisons. Since the authors’ own results
show that DV-Hop outper-
forms DV-Distance, we compare against DV-Hop instead of the
range-aware DV-Distance. The
simulation environment for ANIML uses 802.11 MAC. We obtained all
DV-Hop data by replicat-
ing the experiments using the DV-Hop authors’ CAML implementation
of APS. We used both 5%
and 10% anchor distributions in the DV-Hop, ANIML-Abs and ANIML-Hop
experiments. We
generated topologies in four different sizes (250 by 250, 500 by
500, 750 by 750 and 1000 by 1000
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m2) and two different node densities (400 and 800 nodes/km2) in
order to investigate ANIML’s
scalability. The maximum transmission range of each sensor is 250
meters, although our presented
results scale to smaller transmission ranges. This makes the hop
distance used in ANIML-Hop ex-
periments 187.5m (3/4 of 250m). Distance estimates for ANIML and
ANIML-Abs are obtained
by adding a uniformly distributed error (0-90%) to the true
distance between two neighboring
nodes to mimic experiments reported in [61]. Each data point
presented in our plots is the average
of ten runs with differing random seeds, with no discarding of
outliers.
The metric for localization effectiveness, used in the literature,
is the average distance away
their estimated positions are from the nodes’ actual positions in
the network. We give the measure-
ment of effectiveness as a percentage of the transmission range of
the sensor nodes in the network.
Since ANIML produces relative localization, the determined network
coordinates may have un-
dergone a global flip, rotation and/or shift making direct
comparisons to the actual coordinates
difficult. Therefore, comparisons are done post localization by (i)
shifting the real coordinates by
the difference between the origin and the reference node’s true
position, (ii) globally rotating both
the real and relative coordinates to place node 1 on the y-axis and
(iii) then, if needed, flipping the
relative set of coordinates to place them in the same coordinate
space. Please note that no scaling
of position estimates is involved in this transformation.
3.4.1 Comparison of Basic ANIML using 1-Hop vs. 2-Hop
Information
Providing only 1-hop neighbor information to ANIML for localization
can lead to poor overall
localization due to neighbors getting stuck at local optima. Figure
3.4 shows the localization effec-
tiveness of ANIML using 1-hop information compared to ANIML using
1- and 2-hop information.
Please note that data points are shifted slightly left and right of
the real values (0.0625, .25, .5625,
1) on the x-axis to allow for clear presentation of the error bars.
Figure 3.4 shows that ANIML
using 1- and 2-hop information provides better overall localization
accuracy than ANIML using
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only 1-hop information. However, using only 1-hop information does
not necessarily prevent AN-
IML from accurately localizing a network, as can be seen by the
best case (i.e. lower error bars)
inaccuracy for ANIML (1hop/400) and ANIML (1hop/800). In fact, the
best case using only 1-hop
information is comparable to the best case using 1- and 2-hop
information. The problem with using
only 1-hop information compared to using both 1- and 2-hop
information, since potential accuracy
is not the issue, is the potential inaccuracy of the resulting
localization. In the 1-hop ANIML cases
the difference between the best case results and the worst case
results (i.e. upper error bars) are
at least two times larger than the 2-hop ANIML cases. A large
difference between the best and
worst case localization of 1-hop ANIML alone does not necessarily
imply inaccurate localization
results, since the worst case results could be isolated outliers
(e.g. the end localization contains
one or more neighborhoods that got stuck at a local optima).
However, if the worst case results
of 1-hop ANIML were outliers the overall mean inaccuracy would be
located closer to the best
case result in all 1-hop ANIML cases, not near the middle of the
error bars, as is the case with the
mean inaccuracy of the 2-hop ANIML cases. Therefore, while 1-hop
ANIML has the potential to
provide as accurate localization as 2-hop ANIML, there is much
larger potential for 1-hop ANIML
to produce wildly inaccurate localization.
3.4.2 Basic ANIML vs. Improved ANIML
Figure 3.5 shows the localization effectiveness of the basic ANIML
technique compared to the
basic ANIML technique extended with our flipped node sanity check.
Again note that data points
are shifted slightly left and right of the real values on the
x-axis to allow for clear presentation
of the error bars. The data shows that ANIML augmented with our
flipped node sanity check
provides better overall localization than the basic ANIML
technique. The worst case localizations
(i.e. upper error bars) of the non-enhanced ANIML cases are caused
directly by end localizations
in which 2-hop information was not completely sufficient to prevent
one or more neighborhoods
from getting stuck at local optima. These outliers cause a larger
difference between the best case
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Figure 3.4: 1-Hop ANIML vs. 2-Hop ANIML
localizations (i.e. lower error bars) and the worst case
localizations, which demonstrates increased
potential inaccuracy. The introduction of our flipped node sanity
check allows ANIML to identify
and repair neighborhoods stuck at local optima that adding 2-hop
information could not prevent,
therefore decreasing the potential of ANIML producing an inaccurate
localization. This prevention
of anomalous localization due to unresolved local optima can be
seen by the enhanced ANIML
cases having much tighter error bars than the non-enhanced ANIML
cases. Therefore, ANIML
augmented with our flipped node sanity check greatly reduces the
potential inaccuracy of ANIML
by resolving any remaining local optima that using 2-hop
information did not prevent. The data
also demonstrates that ANIML is robust in the presence of less
information on which to base its
localization, since 400 nodes/km2 (the number of nodes ranges from
25-400) provides comparable
localization to 800 nodes/km2 (the number of nodes range from 50 to
800). By comparison, if
ANIML had three perfectly accurate distances from three nodes
knowing their true positions then
it would be able to localize a node perfectly. Since ANIML does not
have the benefit of anchors
or perfect distance estimates, it requires more information than
three nodes, but after a certain
threshold of available information, adding more information
provides only a small increase in
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accuracy.
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ANIML (enhanced/400) ANIML (enhanced/800)
Figure 3.5: Enhanced ANIML vs. the Basic ANIML Technique
Figure 3.6 shows the number of iterations ANIML, with and without
our push-pull mechanism,
performed to localize a network. The results show, as expected,
that ANIML with push-pull con-
verges faster than ANIML without push-pull, particularly as the
diameter of the network increases.
The data also shows that the convergence time of ANIML is not
directly dependent on the number
of nodes in the network and, as expected, increases with the
diameter of the network. The conver-
gence does not depend on the total number of nodes in the network
because ANIML is distributed
and uses only local information. For the localization results to be
globally consistent any node’s
position estimate should be influenced by all other nodes; the
farther apart they are, the longer
ANIML should need before converging. The network diameter, a
measure of this farthest number
of hops, should contribute to convergence linearly.
3.4.3 Uniform Networks
Figure 3.7 shows the localization effectiveness of ANIML, ANIML-Abs
and ANIML-Hop com-
pared to DV-Hop in uniform topologies. The results show that ANIML
provides accurate relative
localization in uniform topologies, since it only incurs very low
single digit inaccuracies in both
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Figure 3.6: ANIML Convergence Time
the 400 and 800 nodes/km2 results. Additionally, the results show
as expected, higher node density
allows ANIML to provide slightly better localization accuracy since
there is more data to provide
more constraints for the underlying least-squares calculation.
However, the lower density cases
still provide exceptionally high accuracy demonstrating that ANIML,
while being able to use high
node densities to its advantage, does not need highly dense
topologies to provide effective local-
ization. Additionally, the inaccuracies incurred by ANIML increase
nearly linearly as the network
area increases. The reason being that as the network area increases
so does the diameter of the
network, which leads to an increase in small positioning errors due
to the implicit cascading of
position estimates.
Figure 3.7 also shows that ANIML-Abs provides accurate absolute
localization in uniform
topologies, since it also only incurs very low single digit
inaccuracies in both the 400 and 800nodes/km2
and 5% and 10% anchor density results. ANIML-Abs shows similar
properties as ANIML, such
as increases in node density directly increase localization
accuracy, but it does not require high-
density deployments in order to provide accurate localization. As
expected, ANIML-Abs also
shows the same linear increase in localization inaccuracy as the
network area increases as ANIML.
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While adding a small percentage of anchor nodes will result in the
propagation of less position es-
timates, 5 and 10 percent is not a large enough percentage of
anchor nodes to eradicate cascading
positioning errors. The results also show, the addition of anchors
into ANIML serves only to pro-
vide absolute localization and does not significantly improve the
accuracy of ANIML, since the
accuracy of ANIML and both ANIML-Abs cases are nearly the same.
Therefore, it is to be ex-
pected that increasing the anchor density does not increase the
accuracy of ANIML-Abs, since
ANIML-Abs with 5% anchors and ANIML-Abs with 10% anchors provide
the same localization
inaccuracies.
Lastly, Figure 3.7 shows that ANIML-Hop also provides accurate
absolute localization in uni-
form topologies, in all simulations, once the network diameter is
greater than one. While the 15%
to 10% inaccuracy of ANIML-Hop is clearly higher than ANIML and
ANIML-Abs measured
inaccuracies, it shows that even without ranging equipment, on
which ANIML and ANIML-Abs
highly depend upon, the basic ANIML technique is still able to
provide good localization. The rea-
son that ANIML-Hop and DV-Hop incur a large decrease in
localization in accuracy between the
first two network areas is because without a multiple hop network,
neither technique has any avail-
able information upon which to localize the network. In other
words, in a one-hop network both
ANIML-Hop and DV-Hop place every node in a random position.
Overall, Figure 3.7 shows AN-
IML, ANIML-Abs and ANIML-Hop all outperform DV-Hop in all
simulations. However, while
its excepted that ANIML and ANIML-Abs would provide higher accuracy
than DV-Hop, since
they depend on ranging equipment, the data more importantly shows
that ANIML-Hop, despite its
simple static hop distance estimation, is able to provide better
overall accuracy than DV-Hop and
its dynamic hop distance technique.
For qualitative assessment only, since others do not have a readily
available implementation for
direct experimentation, ANIML’s localization effectiveness is
compared against the localization
effectiveness of MDS-MAP(P), ILS and SDP in uniform topologies
using the data provided in
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Figure 3.7: Localization Effectiveness of ANIML in Uniform
Topologies
[77], [55] and [10]. This data is summarized in Table 3.1. ANIML,
ANIML-Abs and ANIML-
Hop incur less inaccuracy than SDP, ILS and hop-based MDS-MAP(P).
ANIML and ANIML-Abs
provide comparable localization to range-aware MDS-MAP(P). However,
while range-aware and
computationally expensive MDS-MAP(P)’s accuracy is comparable to
ANIML and ANIML-Abs,
the distance measurements used were the true distance plus 5% error
whereas our simulations used
true distance plus a uniformly distributed error between 0 and 90%.
Also, although ANIML-Hop
provides slightly less accuracy than range-aware MDS-MAP(P),
ANIML-Hop requires no ranging
equipment.
Table 3.1: Reported Results of ILS, MDS-MAP(P) and SDP
Reported
Method Range Error Inaccuracy ILS 20m 4m 20% MDS-MAP(P) Range-aware
N/A N/A 5% Hop-based N/A N/A 15− 20% SDP 0.2− 0.3m <= .08m <=
40%
33
Figure 3.8 shows the localization effectiveness of ANIML,
ANIML-Abs, ANIML-Hop and DV-
Hop in C-shaped networks. We created our C-shaped topologies by
first creating a random uni-
form deployment over the desired network size of n × n and then
removing all nodes located in
the square (n/2, n/4), (n, 3n/4). ANIML-Abs and ANIML-Hop having
the benefit of anchors do
as well in C-shape topologies as they did in uniform topologies,
while DV-Hop’s accuracy incurs a
small decrease in accuracy compared to uniform networks.
Additionally, most of the relationships
between ANIML, ANIML-Abs, ANIML-Hop and DV-Hop identified from the
results shown in
Figure 3.7 remain true, such as increased anchor density not
significantly increasing the accuracy
of ANIML-Abs and increased node density slightly increasing
localization accuracy. However,
ANIML’s accuracy decreases significantly as the network area
increases. This happens because
in relative localization schemes C-shaped topologies are isomorphic
to S-shaped topologies. Any
application that needs only relative localization, such as
geographic routing, will find the resulting
S-shaped topology to be identical to a C-shaped topology and will
benefit equally in either topol-
ogy. However, the inaccuracy metric used does not accurately
capture this isomorphism and only
sees that the coordinates in one arm of the C, in a global sense,
are in the wrong place. The reason
that this S-shaped localization result could occur in ANIML, and
not in DV-Hop, ANIML-Abs
and ANIML-Hop, is that there are no anchors to keep the two arms of
the C “in place.” However,
the results of ANIML-Abs and ANIML-Hop in C-shape topologies show
that adding anchors to
ANIML completely avoids this C-to-S transformation.
3.4.5 Non-Uniform Networks
Figure 3.9 shows the localization effectiveness of ANIML and DV-Hop
in networks with irregu-
lar node densities. We generated our topologies with non-uniform
node densities by first creating
a random uniform deployment over the desired network area and then
moving half of the nodes
from a random quadrant to another random quadrant of the network.
ANIML and ANIML-Abs
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Figure 3.8: Localization in C-shaped Networks
in networks with irregular node densities provides comparable
accuracy to that of ANIML and
ANIML-Abs in uniform topologies, while DV-Hop and ANIML-Hop as
expected incur a slight
reduction in accuracy. ANIML-Hop’s decrease in accuracy is due to
the simplistic selection of a
static hop distance. A hop distance estimate of 187.5m was selected
based on a node’s neighbors
likely being about 3/4 the maximum transmission range away from the
node in uniformly dis-
tributed networks, but with irregular node densities this
likelihood is no longer the same. However,
despite not dynamically adjusting its hop distance estimate (as
done in DV-Hop), ANIML-Hop
still performs at least as well as DV-Hop in networks with
irregular node densities.
3.4.6 In the Presence of Obstacles
Overall, our experimentation shows ANIML provides effective
localization in the presence of
error-prone range estimates, irregular shapes and densities.
However, in realistic environments,
any localization method must be effective even in the presence of
obstacles. In our simulation ex-
periments, obstacles are incorporated by randomly placing RF opaque
“walls” of length between
25 and 50 meters within uniform network topologies at a density of
16 obstacles per square kilo-
meter (translates to 4 obstacles in the smallest test scenario).
Nodes obstructed by such obstacles
cannot receive each other’s communications.
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Figure 3.9: Localization in Irregular Densities
Figure 3.10 shows the results of localization inaccuracy of ANIML
in networks containing
“RF”-opaque obstacles. There is no comparisons to DV-Hop since the
DV-Hop simulator did not
allow for the simulation of obstacles. The results show that
obstacles do not affect the accuracy of
ANIML and ANIML-Abs. While ANIML-Hop does incur the effects of
obstacles in the network
the results are only slightly worse than ANIML-Hop’s performance in
uniform topologies. The
increase in inaccuracy in ANIML-Hop not seen in ANIML or ANIML-A
