International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),
ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 09-22 © IAEME
9
3-D LOCALIZATION IN WIRELESS SENSOR NETWORK
Mr. Om Mehta1
IITE, Indus University, Ahmadabad
Prof. Gaurang Raval2
Institute of Technology, Nirma University
ABSTRACT
Wireless sensor networks have a great impact on long time monitoring applications
(environment monitoring, security surveillance, habitat monitoring etc.) but its potential is et to be
discovered, where it can be deployed in time critical situations when disaster happens. There is a
significant gap between existing applications of sensor networks and the requirement of applications
supporting rescue operations that involves the catastrophe of human lives. As we are dealing with the
human lives here, we can’t just rely on the localization schemes that depend upon the connectivity
information (range- free) algorithms only. Further, rescue operations are carried out in highly noisy
environments, so distance based (range-based) localization algorithms generate high error in distance
measurements. An efficient algorithm is needed that can measure the location of the sensor nodes
near to the living being or being attached to them in 3-D space with a high accuracy. To achieve
such kind of accuracy a combination of both the strategies is required.
Keywords: Wireless Sensor Networks, Localization, Range Free, Range Based approach
I. INTRODUCTION
When we face an unfortunate situation such as an earth- quake, hurricane, or similar
disasters, wireless sensor nodes prove to be very useful in search and rescue operations. The wireless
sensor network can be formed on the fly without any previous existing infrastructure. Wireless
sensor networks are dynamically formed over the varying topologies. Wireless sensor networks can
assist in conducting the rescue operations and can provide search in timely manner. In general,
disasters leave the situation worse without power and disruption of communication capabilities
destroying the infrastructures [3]. A sensor network mainly consists of anchor nodes as well as the
other nodes sensing the data. The anchor nodes are location aware sensor nodes which obtain its
location information through some external methods (GPS, TOA [1, 5]). The un- localized nodes
hear the beacons which are broadcasted by the anchor nodes. Determining the location of these un-
localized sensor nodes with respect to the anchor nodes is called localization [2]. The localization
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algorithms generally possess wave-spreading like characteristics in which the intermediate sensor
nodes become location aware and act as a new reference anchor node for the un-localized
neighboring nodes.
All the strategies that are employed for the localization in 2-D spaces are violated in 3-D
spaces [9, 4].2-D spaces cannot be directly extended to 3-D just by increasing one parameter. For
example, the 2-D localization completely fails in determining the depth of the river bed and other
similar sensor network scenarios where the height comes into play. There are several well known
problems that can be easily solved modeling the sensor network as 2-D but are very complex
(sometimes NP- Hard) when modeled as 3-D. Moreover, the main triangulation approach that is
employed for the 2-D space doesn’t fit for the 3-D [7].
The information received from the remote sensors that are several hops far is meaningless
until and unless the location from where the data is received is known [3]. For large scale
application scenarios where the geographical data is to be known for coarse parameters such as
the temperature of an area, the data is aggregated for all the sensor nodes that are located
nearby. Further, the location information is important for many location aware sensor network
protocols. The positional information is used to partition the network into several clusters for
hierarchical routing. For efficient routing the protocols require the information of the location of the
sensor nodes. The sensors employed near the disaster affected sites might contain the vital
parameters of the living being trapped beneath several layers of collapsed surfaces. Based on the size
of the area affected by catastrophe the data can be directed to the rescue team in a multi-hop way.
The data so received by the rescue team can be processed and a map can be generated displaying
the optimized path to send the help service in minimum possible time.
II. RELATED RESEARCH WORK
The wireless sensor network is an open research field. All the components of this network
are still in developing phase. My different localization algorithms have been proposed until now. As
the sensor networks are application specific it is quite hard to generalize the algorithm approaches
for localizations that suits to all the different scenarios. All the localization algorithms have been
broadly classified into two major cate- gories: range based and range free. Both the strategies
employ totally different way of approaches. The range-based method relies on the distance
measurements through different received signal strength strategies. Whereas, the range-free method
relies on the connectivity information only i.e. the nodes can listen to the beacon from the sensor
nodes. The wireless sensor network consists of localized anchor nodes and un-localized sensor
nodes. The range free method uses the connectivity information and bound the nodes location to the
common over- lapped (intersected) area. Different algorithms use different methods to calculate the
nodes location information within the bounded region with respect to the anchor nodes.
The range-based method uses the sophisticated hardware, radio signals to estimate the
distance between the receiver and the transmitter antennas. Moreover, the range-free approach
reuses the wireless communication radio signals to determine the connectivity between neighboring
sensors and requires no extra hardware support. The range-free methods are used where the precise
location of the sensor nodes is not required and the coarse position estimation up to some level is
tolerable.
III. RANGE-BASED LOCALIZATION SCHEMES:
A. Received Signal Strength (RSS):
RSS is defined as the power measured by a received signal strength indicator (RSSI) by the
receiver. Often, RSS is equivalently reported as measured power [5], i.e., the squared magnitude of
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the radio signal strength [2, 8]. We can consider the RSS of low frequency, RF, or other signals.
Wireless sensors nodes communicate with neighboring sensors, so the signal strength of the radio
can be calculated by each receiver during normal data communication without requiring additional
bandwidth or energy requirements. RSS measurements are relatively can be easily embedded in the
motes, thought of their expensiveness they are most generally used method for distance calculation
[7].The power of the receiving radio signals can be calculated by measuring the voltage[2]:
P = −51.3 × RSSI − 49.2 (1)
Noise is the standard deviation σ of all RSS values that may be observed at a particular
distance in a given environment. Even with adjacent stationary sensor nodes, RSS will vary to
some degree due to noise. The noise affecting the RSS is not constant; it varies with time as well
as environmental conditions. Finally, radio signals can vary significantly in both transmission
strength and receptivity, particularly in cheap, low-power radio devices [4, 5]. The RSS directly
varies with the inverse power of distance. The attenuation rate is the rate σ at which radio signal
strength decreases over distance:
RSS α d−α (2)
Generally, if α =2σ then radio signal strength drops by 3dB every time distance doubles.
Generally 2σ for highly noisy environments. This linear attenuation rate means that the difference
between the radio signal strength varies according to the predefined rate for example; difference
between 1meter and 2meter is similar to the difference between 10meter and 20meter i.e. exactly
3dB. Moreover, a constant level of noise can result in increasing error rates when signal strength is
used to estimate distance.
The received signal strength (RSS) method uses the relation- ship of radio frequency signal
as a function of distance. Now, from the relationship mathematical propagation model also be
derived. studies shows that of the Radio Frequency sig- nal propagation characteristics [7], the
main disadvantages of the methods are that the propagation characteristics of radio signals
could be vary with changes in the surrounding environment temperatures, humidity, pressures, areas
such as: rural, urban. It also suffers multipath effect (weather changes, urban, rural and indoor,
outdoor settings) until one direct line of site the RSS detection is somewhat difficult.
B. Time Based Methods (TOA & TDoA): Time of arrival (TOA) and Time Difference of Arrival (TDoA) calculates distances which
based on the propagation time and that propagation time can directly translated into distance, based
on the known signal propagation speed. These methods can be applied to many different signals,
such as Randio Frequency, acoustic, infrared and ultrasound [5]. They relies on complex hardwares
that is expensive and energy consuming; making it less suitable for sensor network where the
scalability is high of the lifetime of the network is expected to be more.
TDOA is a particular case of TOA approaches are utilized when the source clock time
is known to us. This strategy is analytical in nature and uses the TDOA between pairs of sensor
nodes. The resulting equations are nonlinear but can be reduced to linear in the solution process. The
approach is based on signaling sources sending low frequency at known, locations in and around
the sensor field. Each source broadcasts in a round- robin fashion and the time-of-arrival is
recorded by each sensor node. The differences in the time are calculated and the co-efficient
equations are themselves can then be communicated back to the sensor nodes for calculations.
While radio frequency based localization is promising; there are several reasons for low frequency
signaling techniques to be more desirable. Firstly, the relatively low speed wave results in less
costly hardware as compared to high-bandwidth radio frequency hardware. The low frequency wave
also means that the system will be less sensitive to errors in time-of- flight measurements,
synchronization along with other timing errors. However, low frequency techniques also have
somete disadvantages over radio frequency techniques. Firstly, low frequency waves are highly
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ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 09-22 © IAEME
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deviated by the environmental conditions such as temperature, humidity and pressure resulting in
uneven wave speeds over the area of interest. Secondly, low frequency waves suffer greater
attenuations through edges of buildings and other physical objects rendering it nearly inefficient
[6].
IV. RANGE-FREE LOCALIZATION SCHEMES
A. Centroid Algorithm:
Anchors send their location information to neighbors that keep an account of all received
beacons. Using the averaged out information, simple centroid model is applied for estimation the
listening nodes location. This protocol is referred as the Centroid algorithm.
The following are the steps of the localization:
• Beacon node broadcasts their position.
• Sensor node listens for beacons from anchors nodes and if they are able to hear the beacons
this means they are under the ranging area covered by these anchor nodes.
• Sensor node computes its position by averaging out all the beacon node locations.
In [6] a range-free, proximity-based, a localization algorithm is proposed containing
location information (xi , yi ) that uses anchor beacons, to estimate sensor node position. After
receiving these beacons from anchor nodes, a sensor node estimates its location using the following
formula for 2-D space [3]:
Estimate its location. The accuracy of the DV-hop method increases as the scalability of the
network increases. The averaged value with more number of anchor nodes produces less error than
the estimated value with less no of anchor nodes with a high deviation from the actual location.
(xest , yest ) = (x1 + x2 + ... + xn , y1 + y2 + ... + yn ) (3)
N N
The advantage of this Centroid localization scheme is its simplicity of calculation and
simplicity in implementing it.
Fig.1. Centroid estimation
B. DV-HOP: DV-HOP assumes that a network consisting of identical sensing nodes and beacon nodes
[5]. Instead of going for the single hop broadcast, anchors flood their locations all over the sensor
network. As the information propagates over each hop an increment counter each time increments
the hop count value. Senor nodes calculate their position based on the received beacon locations,
average distance per hop, the hop count from the corresponding anchor; the working of this strategy
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is quite similar to existing distance vector routing. One anchor node broadcasts a beacon to all
over the network containing the beacon location with a hop count value initially set to one.
The receiving sensor nodes maintain a minimum counter value corresponding to each
anchor. Every time it receives a beacon it increments the hop count value and ignores those
anchors with higher hop-count values. All the way propagating through this mechanism, all sensor
nodes in the network (including other beacons) get the shortest distance, in hops. Beacons perform
this task by obtaining position and hop count information for all other beacons inside the network.
The average one hop distance is then calculated by beacon i using the following formula:
In the above formula (xm, ym) is the location of anchor m, and hm is the calculated distance
in hops, from anchor m to beacon b. Once calculated, beacons spread the estimated size of the hop
information out to the nearby sensor nodes. Once a sensor node calculates the distance estimation to
more than 3 anchors in the plane, it uses triangulation (multilateration) method to estimate its
location. The accuracy of the DV-hop method increases as the scalability of the network increases.
The averaged value with more number of anchor nodes produces less error than the estimated value
with less no of anchor nodes with a high deviation from the actual location.
V. P ROPOSED ALGORITHM
The following steps are performed for calculation of 3-D location:
1) The whole area is divided into grids. The interspacing between the grids is less than the range of
the anchor nodes.
2) A beacon node covers a block of cubes that are within its radio range. The cube size is such
that it covers the largest area in the sphere formed by the radio range.
3) The distance between the un-localized sensor node and the beacon nodes is calculated using
different RSS techniques.
4) A list is maintained by each un-localized node that contains the number of beacon nodes and the
distance from each beacon node.
5) The common intersection area gives the bounded values (max, min).The bounded values
specifies the maximum and minimum values of co-ordinates. The nodes position should be
within this rectangular region.
6) The common intersection area gives the bounded β values (max, min).The bounded values
specifies the maximum and minimum values of co-ordinates. The nodes position should be
within this rectangular region.
7) Check whether the beacon nodes (≥ 3) are forming a plane i.e. they are not on same line.
8) Calculate the location (x, y, z) of un-localized nodes taking the distances into account.
9) Check the whether the calculated values within bounding region. All the values outside the
region are discarded.
10) Change the status of newly localized node to new beacon nodes for further calculation of other
nodes.
A. Range Free Approach Instead of considering a spherical area around a sensor node we consider the sensor
node covers a cubical area. All the nodes within the cubical area can listen to anchor node
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ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 09-22 © IAEME
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other outside it are not considered to be covered by this anchor node. The position of the node
is guaranteed to lie in the intersection of the bounding cubes corresponding to all the beacons
within the radio range. This set itself is a rectangular (sometimes square) cube, whose minimum and
maximum values are computed by iterating the process upon all the beacons heard: at each stage,
the new boundary values are compared to the previous ones, and the smallest set is
In the above formula (xm, ym) is the location of anchor m, and hm is the calculated
distance in hops, from anchor m to beacon b. Once calculated, beacons spread the estimated size of
the hop information out to the nearby sensor nodes. Once a sensor node calculates the distance
estimation to more than 3 anchors in the plane, it uses triangulation (multilateration) method to
kept. Cube is the only regular polyhedron that tessellates a 3-D space. Each cube representing the
bounding area can be represented by the min max values of its coordinates. The radio range
covered by the beacon node P(x, y, z) varies between [xmin , ymin , zmin ] and [xmax ,
ymax , zmax ] represents the bounded range β of a node. r average radio range of the beacon.
[xmin , ymin , zmin ] ≤ β ≤ [xmax , ymax , zmax ]
Fig.2. Intersection of bounding boxes
Fig.3.Bounded Value of Sensor Nodes
The intersection of the two cubical areas is done to reduce the area where the un-localized
node is likely to be. As, more number of cubical areas start to merge the common area of
intersection starts to reduce. The new rectangular (sometimes square) area that emerges after
multiple intersections of beacon nodes represents the bounded area.
For example intersection of two bounding cubes;
βnew = β1 I β2 (5)
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Similarly, intersection of multiple boundaries can be done to lower the number of positions
where a sensor node can be present.
βnew = β1 I β2 ........I βn
The method falls under the category of range-free as it only uses the connectivity
information i.e. whether it is able to send receive the beacon nodes from the respective beacon
nodes.
B. Range Based Approach The method uses the distance information between the un- localized node and the beacon
nodes. All the beacon nodes are considered to lie on same plane, w.r.t of these beacon nodes the
nodes localization is determined. A set of three anchor nodes are selected at a time. These three
anchor nodes form a equation of a plane. The standard equation of a plane in 3 dimensional spaces
is:
Qx + Ry + Sz + D = 0 (7)
Here in equation (19), Q, R, S correspond to the anchor nodes D corresponds to the sensor
node with unknown location information.
The normal to the plane is the vector (Q, R, S). Given three points in space Q(x1, y1, z1), S(x2, y2,
z2), S(x3, y3, z3) the equation of the plane through these points is given by the following
determinants.
Expanding the above gives:
Q = y1 (z2 − z3) + y2 (z3 − z1) + y3 (z1 − z2) (8)
R = z1 (x2 − x3) + z2 (x3 − x1) + z3 (x1 − x2) (9)
S = x1 (y2 − y3) + x2 (y3 − y1) + x3 (y1 − y2) (10)
D = −[x1 (y2 z3 − y3 z2) + x2 (y3 z1 − y1 z3) + x3 (y1 z2 − y2 z1)] (11)
The sign of, s = Qx + Ry + Sz + D determines which side the point (x,y,z) lies with
respect to the plane. If s > 0 then the point lies on the same side as the normal (Q, R, S). If s <
0 then it lies on the opposite side, if s = 0 then the point (x,y,z) lies on the plane. pi is the
distance between the point P and the beacon nodes . The distances are measured by using
different received signal strength (RSS) strategies. At least three beacon nodes are required to
calculate the location of unknown sensor node. For a plane Qx+Ry+Sz+D=0 and a point P
(x1 , y1 , z1 ) not necessarily lying on the plane, the shortest distance from P to the plane is:
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Fig.4. Distance of point P from a plane
It follows that if Distance = 0 in equation then P lies in the same plane.
However, in real life environmental conditions where there is interferencing noise the
measuring and calculating errors might change the distance a little bit. As a result P is considered
lying within the same plane if it satisfies the constraint:
−ζ < Distance < ζ (13)
Where ζ is minute deviation caused due to errors. At first it is determined whether there is node
formed: (x − xi )+ (y − yi )+ (z − zi )= p2 (14)
Fig.5. unknown coordinates of P
Solving the above equation we can get multiple values of z because of quadratic equations.By
using proper bounded cubes the proper values of (x,y,z) is being selected so that it satisfies
β = β1 | β2 | β3 (15)
The β cube is calculated using the intersected cubical Rectangle of beacon nodes. Pєβ
If they are not lying on the same plane then multiple beacon values giving rise to multiple equation
are used for finding the values of p(x,y,z) and minimize the error:
(x − xn )+ (y − yn )+ (z − zn )− d2 = 0 (16)
Where (xn , yn , zn ) corresponds to the location of the beacon nodes.
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Solving the above equation approximated distance can be calculated:
p = (αT α)−1 αT k (17)
Further, we bound the multiple values of x,y,z by selecting only those values which are
within the bounding region and rejecting the one which are outside it. The bounding region is where
we have the constrained area of x, y, z. Now substituting the value z in the other equation we can get
the proper value of (x,y,z).MICA2 motes can be also used to check the feasibility of proposed
Algorithm.
VI. SIMULATION
The algorithm proposed here, as all the geometric approaches of the localization problem,
requires a large number of sensor nodes and location aware beacons. As we only have a few sensor
nodes, this could not be practically implemented on our MICA2 motes. All the simulations related
to thesis is done in MATLAB.
MATLAB [18] simulator is selected as it easily handles the matrix calculations very
effectively all the stress of the work can be given to the actual work rather than going on
programming details.
We have compared the parameters with a standard Center of Gravity (COG) method. The
simulation is performed by taking 1/3rd of the total nodes as beacon nodes. The total time
calculated here is the combined simulation time of both the proposed one and the COG method.
Giving, an estimation of how much time this proposed algorithm will take to execute.
A. Performance Analysis The percentage of success of the algorithm proposed in this thesis is given by:
di deviation between the actual location of nodes and the estimated location. N total number
of sensor nodes in the network (considering the first layer. contains only beacon nodes). n number
of nodes per layer B. Error Analysis The error is calculated using:
derror = √(xa − xc )2 + (ya − yc )2 + (za − zc )2 (19)
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ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 09-22 © IAEME
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where,
xa , ya , za - are actual sensor node location
xc , yc , zc - are calculated sensor node location.
VII. RESULT
A. Effect of Scalability on the Performance: Here, in graph we can clearly see that as the number of nodes is increased the performance of
the algorithm improves by 10 % - 30 %. Whereas, in COG method the performance improves very
less by 5 %-15 %. For 20 anchor nodes the performance of success is around 60 %, as the no of
anchor nodes are increased the success rate rises above 90 %.It supports the fact that as the
number of beacon nodes in the network increases the calculated location values becomes more
close to the original location.
Fig.6. Anchor nodes vs Percentage Beacons
Here, table shows the sensor network nodes that are used to generate the simulated output.
The beacon nodes are distributed throughout the first layer. All the other sensor nodes are randomly
distributed to respective layers with equal node densities. The uneven horizontal mesh corresponds
to the surface beneath.
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Fig7.Simulation done by 50 anchor nodes, total number of 150 nodes
Fig.8. Simulation done by 500 anchor nodes, total number of 1500 nodes
B. Effect of Noise: The noise here is considered to be Gaussian Noise with mean µ = 0 and standard
deviation σ.Here, we can clearly see that the noise has direct impact on estimation accuracy. As
the noise value increases the success rate of the proposed scheme varies between 55% - 95%.
Though the success rate drops but still it gives better results than other methods.
Fig.9.Noise factor vs Percentage success
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Fig.10. Simulated output taking 150 nodes standard deviation of 0.005
Fig.11.Simulated output taking 150 nodes standard deviation of 0.025
In COG the noise has very less impact because of the nature of COG estimation of value. As
COG method considers the mean of all the locations so a localization error tends to deviate the
calculated values very less.
C. Effect of Radio Range
The simulation is carried out taking the inter layer separation 3m. As the proposed
utilizes both the range-free and range-based strategies there is not much performance change in it.
Further, in case of COG method initially when the radio range is very less the performance of
COG is quite high, intermediate radio ranges the success rate varies between 25%-50%, as the
range of the anchor nodes increases one layer of sensor nodes are affected by multiple layers of
beacon nodes above it giving it a increasing success rate.
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Fig.12. Simulation done taking 150 nodes with radio range 5m
The simulation time taken increases irrespective of the number of sensor nodes as for single layer
information of location from multiple layers of beacon nodes are processed.
VIII. CONCLUSION
The literature survey work has shown that an optimal algorithm has not been
defined yet, that employ both the strategies (range-free range-based) , and thus the development
of a new algorithm has to be founded on the specificities of the situations, taking into account the
size of the network, as well as the deployment methods and the expected results. Localization
algorithms should be designed to achieve low variance as well as low bias as far as possible; at
the same time, they need to be scalable to very large network sizes without dramatically increasing
energy consumption or computational requirements. We have proposed and demonstrated an
algorithm that successfully localizes nodes in a sensor network with noisy distance
measurements. The equations for the proposed algorithm were carried out in MATLAB.
Simulations showed the relationship between noise and ability of a network to localize itself, at
highly noisy environments. The performance stays above 50% i.e. half of the available nodes can be
localized with good approximation.
We also have depicted the effect of scalability on the performance of the algorithm. Results
show that as the scalability of the network increases with the number of beacon nodes; the
performance of the algorithm goes high above 90%. The granularity of the areas estimated may be
easily adjusted by changing the system parameters which makes the proposed algorithm flexible.
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