The Key Metric forEvaluation Localizationin Wireless Sensor Networks via Distance/Angle Estimation Algorithm (D/A-EA)

Computer Science & Engineering: An International Journal (CSEIJ), Vol.1, No.4, October 2011
DOI : 10.5121/cseij.2011.1404 49
The Key Metric forEvaluation Localizationin
Wireless Sensor Networks via Distance/Angle
Estimation Algorithm (D/A-EA)
Reza Godaz1
, Mohammad Reza KaghazGaran2
1
Islamic Azad University, Mashhad Branch,Department of SoftwareComputer
Engineering, Mashhad, Iran.
rgodaz@mshdiau.ac.ir
2
Islamic Azad University, Mashhad Branch,Department of SoftwareComputer
Engineering, Mashhad, Iran.
kaghazgaran@mshdiau.ac.ir
Abstract
Wireless sensor network localization is an importantarea that attracted significant research interest..
Hence, localization schemes for wireless sensorAlthough mobility would appear to make localization more
difficult, in this paper We present a new method bywhich a sensor node can determine its location by
listening to wireless transmissions from three or more fixed beacon nodes and argue that it can exploit
mobility to improve the accuracy and precision of localization. Our approach does not require additional
hardware on the nodes and works even when the movement of seeds and nodes is uncontrollable. The
proposed method is based on aDistance/ Angle- Estimation technique that does not increase the complexity
or cost of construction of the localization sensor nodes. It determines how the available information will be
manipulated to enable all of the nodes of the WSN to estimate their positions. It is a distributed and usually
multi-hop algorithm.
Keywords:
Wireless sensor network- mobility-multi-hop algorithm
1. INTRODUCTION
Location awareness is important for wireless sensor networks since many applications such as
environment monitoring, vehicle tracking and mapping depend on knowing the locations of
sensor nodes. In addition, location-based routing protocols can save significant energy by
eliminating the need for route discovery [17, 16, 15] and improve caching behavior for
applications where requests may be location dependent [14]. Security can also been enhanced by
location awareness (for example, preventing wormhole attacks [13, 12]). However, putting GPS
receivers in every node or manually configuring locations is not cost effective for most sensor
network applications.
Recently some localization techniques have been proposed to allow nodes to estimate their
locations using information transmitted by a set of seed nodes that know their own locations .We

50
are interested in performing localization in a more general network environment where no special
hardware for ranging is available, the prior deployment of seed nodes is unknown, the seed
density is low, the node distribution is irregular, and where nodes and seeds can move
uncontrollably. Although mobility makes other localization techniques increasingly less accurate,
our the node distribution is irregular, and where nodes and seeds can move uncontrollably.
Although mobility makes other localization techniques increasingly less accurate, our technique
takes advantage of mobility to improve accuracy and reduce the number of seeds required
networks typically use a small number of seed nodes that know their location and protocols
whereby other nodes estimate their location from the messages they receive.
2. Related Work
In sensor networks, nodes are deployed into an unplanned infrastructure where there is no a
prioriknowledge of location. The problem of estimating spatial-coordinates of the node is referred
to aslocalization. An immediate solution which comes to mind is GPS [2] or the Global
Positioning System.
However, there are some strong factors against the usage of GPS. For one, GPS can work only
outdoors.Secondly, GPS receivers are expensive and not suitable in the construction of small
cheap sensor nodes. A third factor is that it cannot work in the presence of any obstruction like
dense foliage etc. Thus, sensor nodes would need to have other means of establishing their
positions and organizing themselves into a coordinate system without relying on an existing
infrastructure.
Localization can be classified as fine-grained, which refers to the methods based on timing/signal
strength and coarse-grained, which refers to the techniques based on proximity to a reference
point. One way of considering sensor networks is taking the network to be organized as a
hierarchy with the nodes in the upper level being more complex and already knowing their
location through some technique .These nodes then act as beacons by transmitting their position
periodically. The nodes which have not yet inferred their position listen to broadcasts from these
beacons and use the information from beacons with low message loss to calculate its own
position. A simple technique would be to calculate its position as the centroid of all the locations
it has obtained. This is called as proximity based localization. It is quite possible that all nodes do
not have access to the beacons. In this case, the nodes which have obtained their position through
proximity based localization themselves act as beacons to the other nodes.
3. Localization Protocol
The constraints in sensor nodes and ranging precision make localization for mobile sensor nodes
a more difficult problem than robot localization. On the other hand, scale can be used to our
advantage. The many nodes in a sensor network can cooperate to share location information. We
assume time is divided into discrete time units. Since a node may move away from its previous
location, it needs to re-localize in each time unit. We are interested in obtaining the probabilistic
distribution of a node’s possible locations. Localization systems can be divided into three distinct
components see Fig. 1 .As a node moves in the network, prior location information will become
increasingly inaccurate. On the other hand, there are new observations from seed nodes that are
able to filter impossible locations. The posterior distribution of a node’s possible locations after
movement and observation is not easy to determine. Except for a few special cases including
linear Gaussian state space models [11], it is impossible to evaluate the distribution analytically
[12].
The Sequential Monte Carlo (SMC) method [10] provides simulation-based solutions to estimate
the posterior distribution of nonlinear discrete time dynamic models. The key idea of SMC is to

51
represent the posterior distribution by a set of m weighted samples, and to update them
recursively in time using the importance sampling method [9]. Since the unconditional variance
of the importance weights will increase [18], re-sampling techniques [19] are used to eliminate
trajectories with small normalized importance weights. SMC has been successfully applied in
targetracking [20], robot localization [5] and computer vision [4]. We provide a brief
introduction below. A more detailed introduction can be found in [21], and an overview and
discussion of SMC’s properties can be found in [3].
Sensor nodes must determine their locations with respect to some fixed beacon nodes using
wireless or infrared signals and possibly engaging in cooperative computations. Existing location
discovery techniques typically use distance or angle measurements from a fixed set of reference
points and apply multi-literation or triangulation techniques to solve for the unknown location.
The distance or angle estimates may be obtained from:
● Received signal strength (RSSI) measurements: where knowledge of the transmitter power, the
path loss model, and the power of the received signal are used to determine the distance of the
receiver from the transmitter. A sensor node estimates the distances from three of more beacon
nodes to compute its location. The major drawback of this method is that multi-path
reflections, non-line-of-sight conditions, and other shadowing effects might lead to erroneous
distance estimate.
● Time-of-arrival and time- difference- of- arrival (TOA, TDOA) measurements: which may be
used to estimate the distance from a set of reference points by measuring the propagation
times (or differences thereof) of the signals. Hence, when a dense network is involved, such as
a sensor network, localization techniques using TOA or TDOA measurements need to use a
signal that has a smaller propagation speed than wireless, such as ultra-sound [16].
● Angle of arrival (AOA) measurements: where special antenna configurations are used to
estimate the angle of arrival of the received signal from a beacon node. A prototype navigation
system described in [12] is also based on a similar concept but it uses a set of optical sources
and a rotating optical sensor for obtaining the angular measurements.
3.1 Location Estimation Algorithm
The mobile localization problem can be stated in a state space form as follows. Let t be the
discrete time, ldenote the position distribution of the node at time t, and o denote the
observations from seed nodes received between time t-1 and time t. A transition equation p
( l|l) describes the prediction of node’s current position based on previous position, and an
observation equation p (l| o) describes the likelihood of the node being at the location lgiven
the observations. We are interested in estimating recursively in time the filtering distribution p
( l | o0, o1…o). A set of N samples Lt is used to represent the distribution l and our algorithm
recursively computes the set of samples at each time step. Since Lt-1 reflects all previous
observations, we can compute l using only L t-1ando. Initially, we assume the node has no
knowledge about its position, so the initial samples are selected randomly from all possible
locations. At each time step, the location set is updated based on possible movements and new
observations. We estimate the location of the node by computing the average location of all
possible locations in Lt. For our experiments, we assume locations are (x, y) positions in two
dimensional Cartesian spaces, but the technique could be used equivalently for three dimensions
or other location representations.

Computer Science Engineering: An International Journal (CSEIJ), Vol.1, No.4, October 2011
52
3.2 Filtering
In this step, the node filters the impossible locations based on new observations. For
simplification of presentation and analysis, we assume that time is discrete and all messages are
received instantly. Hence, at time t, every node within radio range of a seed will hear a location
announcement from that seed. In a realistic deployment, it would be necessary to deal with
network collisions and account for missed messages. Fig. 3 shows an example situation. There
are four types of seeds to consider:
Outsider’s seeds that were not heard in either the current or the previous time quanta. Arriver
seeds that were heard in the current time quantum, but not in the previous one. Leavers– seeds
were heard in the previous time quantum, but not in this one. Insiders – seeds that were heard in
both time quanta. Arrivers and leavers provide the most useful information since the node will
know it was within distance r of lat timet, but not within distance r of l1 at timet. If we only
rely on direct information from seeds, however, a node will not know the previous location of an
arriver, or the current location of a leaver. There are two possible ways to gather this
information:
1. A seed node (S) transmits both its current location andits location at the previous time step in
each announcement:
S → Region HELLO | IDS | l | l
20. Neighbor nodes can transmit information about seed locations:
S → Region HELLO | IDS | l
N → Region HELLO | IDN | {(IDS, l
) }
The second approach is more expensive, but its cost may be combined with neighbor discovery in
applications that require neighborhood information for other purposes. The advantage of the
second approach is it also allows nodes to discover information about outsider seeds without
keeping track of arrivers and leavers. The node knows it is not within distance r of any outsider
seed, but must be within distance 2r of any seed heard by one of its neighbors, time 0 To position
l1 on time 1. The seed is an insider for nodes in region III, an arriver for nodes in region II, a
leaver for nodes in region I, and an outsider for all other nodes.
Combined with neighbor discovery in applications that require neighborhood information for
other purposes. The advantage of the second approach is it also allows nodes to discover
information about outsider seeds without keeping track of arrivers and leavers. The node knows
it is not within distance r of any outsider seed, but must be within distance 2r of any seed heard
by one of its neighbors.
4. Evaluation
The key metric for evaluating a localization technique is the accuracy of the location estimates
versus the communication and deployment costs. Increasing the density of seeds or the frequency
of location announcements should improve accuracy, but the tradeoffs need to be understood to
determine appropriate deployment parameters. In this section, we evaluate the D/A-EA technique
by measuring how its estimated location errors vary with various network and algorithm
parameters described in Section 4.1. In addition, we compare our results to those for other range-
free localization techniques, namely the [1].

53
Localization
System
4.1 Simulation Parameters
In our experiments, we vary parameters of both the sensor network and sensor nodes, and of the
D/A-E Algorithm. For all of our experiments, sensor nodes are randomly distributed in a 500m x
500m rectangular region. We assume a fixed transmission range, r of 50m for both nodes and
seeds. The network and node parameters we vary are:
• Speed of the nodes and seeds (v ,v , s ,s ,). We represent the speed as the moving
distance per time unit. A node’s speed is randomly chosen from [v ,v ]; a seed’s speed is
randomly chosen from [s , v ]. We consider the impact of speeds on both accuracy and
convergence time.
• Node density (n), the average number of nodes in one hop transmission ranges. We study the
effects of varying n use a fixed n = 10 for other experiments.
• Seed density (s), the average number of seeds in one hop transmission range.
Fig. 1: The division of localization systems into three distinct components.
We adopt the random waypoint mobility model [8] for both nodes and seeds. It is one of the most
commonly used mobility models for mobile ad hoc networks. . In the random waypoint model, a
node randomly chooses its destination, its speed of movement, and its pause time after arriving at
the destination. We assume nodes are unaware of their velocity and direction, but have a known
maximum velocityv . As pointed out in [22], the random waypoint model suffers from the
decay of average speed, and this will provide an unsound basis for simulation. We used a
modified random waypoint model to maintain the average speed. Instead of choosing a certain
speed for each destination, nodes randomly vary their speed during each movement. The pause
time is set to 0, so the average speed is exactly

when speed is chosen randomly between 0
andv . we consider how different mobility models affect the localization accuracy.
Distance
Estimation
Position
Computation
Localization Algorithm

54
Fig. 2. Location Estimation Algorithm
We assume a node can judge if it is within radio range r of another node or not, but it cannot get
more precise distance information (for example, measuring distance through received radio signal
strength). For most of the experiments we model radio range as a perfect circle. This model is
not realistic; however, we consider the impact of irregularity on location estimates.
Fig. 3. Seed Movement. The seed moves from l0 at time 0 to position l1 on time 1
4.2 Accuracy
The accuracy of D/A-Depends on the speeds of the seeds and nodes. As time passes, nodes will
receive more seed location announcements and improve their location estimates. Figure 3 shows
the error in the location estimate, measured as a multiple of the node transmission distance r, for
three different scenarios: stationary seeds (s = 0) with nodes moving with v = .2r and r,
and both nodes and seeds moving with v = s = r.
The localization process can be divided into the initialization phase and the stable phase. In the
initialization phase, the estimate error decreases dramatically as new observations are
incorporated. The localization is improved by both the current observation and previous
observations. In the stable phase, the impact of observations (filter) and the node’s mobility
(uncertainty) reach some balance, and the estimate error fluctuates around a minimum value. The
faster the speed of the seeds and nodes, the quicker the stable phase is reached. The post-
Initialization: Initially the node has no knowledge of its location. N is a
constant that denotes the number of samples to maintain:
L0 = {set of N random locations in the deployment area}
Step: Compute a new possible location set Lt based on , the possible
location set from the previous time step, and the new observations, o.
Lt = { }
While (size (L) N) do
R = {

|

is selected from p( |

),

for all i ϵ N}
R filtering = {

|

where

ϵ R and p(o |

)0),
Lt=choose ( Ltᴜ R filtering N)
p ( | )=

I if distance ( , )vmax
1
π v 2
max

55
convergence accuracy is also better for faster moving nodes, since by moving quickly they
encounter more seeds and more rapidly filter our inaccurate samples.
Unlike the D/A-EA technique, the Centroid and Amorphous localization techniques do not
exploit past information, so they do not improve over time. Figure 4 compares the localization
error of different localization techniques over time. The accuracy of D/A-EA improves quickly.
Fig. 4: Accuracy Comparison. n = 10, s = 1, v = s = r.
4.3 Node Speed
Varying node speed is similar to varying the time between location announcements. If
announcements are more frequent, localization is more accurate but communication overhead
increases. We measure maximum node speed as v and distribute actual node speeds between
0 and v using the modified random waypoint mobility model. Figure 5 shows the impact of
node speed on the converged localization error as the distance traveled per announcement time
unit increases from 0.1r to 2r for a few different seed densities and seed velocities. Node speed
impacts the localization process in two ways. The increased speed makes the predicted locations
less accurate since the next possible locations fall into a larger region. On the other hand, faster
movement leads to more new observations in each time step, and hence more impossible
locations can be filtered.
Fig. 5. Impact of node speed.

56
4.4 Seed Density
The estimate errors drop fast as node speeds increase from 0.1r to 0.3r when the seeds are also
moving at the same speed, and then the error gradually increases as the uncertainty resulting from
faster movement increases.
With fixed velocity seeds (s = v = r), the error is least when nodes are slowest, and
increases gradually as nodespeed increases. Figure 5 illustrates that the length ofincreasing the
density of seeds makes localization easier, but increases network and deployment costs. Figure 8
shows the average estimate error of different localization algorithms when seed density varies.
The accuracy of both D/A -EA and Centroid improves as seed density increases since nodes will
receive more location announcements. For the Amorphous technique, since each node receives
the propagated messages from all seeds in the network, the estimate error does not improve much
after there are a sufficient number of seeds (32 in this experiment). D/A -EA performs
adequately even for low seed densities and outperforms the other techniques when seed density is
1 or above. Since the possible location set accounts for previous information about the node’s
location, D/A -EA is much more accurate than Centroid when seed density is low.
4.5 Node Density
Figure 5 shows the impact of node density on estimate error in different localization algorithms.
D/A -EA and Centroid are little affected by node density. D/A -EA requires a threshold node
density in order for nodes to receive two-hop when network density is below 6, but performs best
when information from enough neighbors, but a few neighbors is sufficient. The Amorphous
technique depends on higher network density. It performs poorly network density is larger than
15.
This is because network density has great impact on the accuracy of hop count. [23] And [24]
suggest approaches for improving hop counting based techniques when the node density is low by
increasing the number of seed nodes.
4.6 Motion Model
So far, we have assumed that both nodes and seeds move randomly and independently. In some
applications, the motion of nodes and seeds may be correlated and demonstrate some group
behavior, and this may affect the performance of our algorithm. We use the Reference Point
Group Mobility model (RPGM) [15] to investigate the effect of group behavior on our algorithm.
In RPGM, the motion of a node is the combination of a group motion vector and a random
motion vector. The random motion is based on a reference point that moves according to the
group motion. This provides an approximation for a group of nodes and seeds moving in a current
or being blown by the wind.
We put all nodes and seeds in the same group. The group motion is defined as a random walk
model , in which the direction is chosen randomly between 0 and 360 degrees and the speed is
chosen randomly between 0 and the maximum group motion speed. Each node’s individual
random movement relative to the

57
Fig. 6. Maximum Group motion speed
group motion is selected using the modified random waypoint model as in previous experiments.
To maintain the same group motion for all nodes, we assume there are no boundaries in the
network sonodes can move freely. If a node cannot find enough valid samples after filtering, it
will reinitialize itself by eliminating previous samples and drawing samples from new
observations directly. We also assume a node is awaren of the maximum distance it can move in
one time unit, which is the sum of the maximum individual random movement and the maximum
group motion.
The location accuracy when we keep the maximum random motion speed at r per time unit and
vary the maximum group motion speed. The estimate error increases as the maximum group
motion speed increases. Since all nodes are moving in the same way, the relative positions change
less, so the number of useful new observations received does not increase with increasing group
speed. Because the uncertainty in the prediction phase becomes larger as group motion speed
increases, accuracy is substantially reduced when the group motion dominates the individual node
movement. On the other hand, in some applications it may be possible to control how seeds
move. A strategy that moves seeds in a way to cover the area thoroughly will improve the
accuracy, and especially the convergence time, of D/A -EA.
5. CONCLUSION
Many wireless sensor network applications depend on nodes being able to accurately determine
their locations. This is the first work to study range-free localization in the presence of mobility.
Our main result is surprising and counterintuitive: mobility can improve the accuracy and reduce
the costs of localization. Our simulation experiments .reveal that the D/A -EA technique can
provide accurate localization even when memory limits are severe, the seed density is low, and
network transmissions are highly irregular. Many issues remain to be explored in future work
including how well our assumptions hold in different mobile sensor network applications, how
different types of motion affect localization, and how our technique can be extended to provide
security.
vmax

58
ACKNOWLEDGEMENTS
The authors would like to thank Deputy Research at the Mashhad Branch, Islamic Azad
University support.
The authors are especially grateful to one of the anonymous referees whose comments led to an
improved statistical model.
REFERENCES:
[1] RadhikaNagpal, Howard Shrobe, and Jonathan Bachrach. Organizing a Global Coordinate System
from Local Information on an Ad Hoc Sensor Network. 2nd International Workshop on Information
Processing in Sensor Networks (IPSN). April 2003.
[2] Tracy Camp, Jeff Boleng and Vanessa Davies.A Survey of Mobility Models for Ad Hoc Networks
Research.Wireless Communications and Mobile Computing. Volume 2, Number 5. 2002.
[3] Arnaud Doucet, Simon. Godsill and Christophe Andrieu.On Sequential Monte Carlo Sampling
Methods for Bayesian Filtering.Statistics and Computing. Volume 10, pp. 197-208. 2000.
[4] Michael Isard and Andrew Blake. Contour Tracking by Stochastic Propagation of Conditional
Density. European Conference on Computer Vision, pp. 343-356.
[5] Frank Dellaert, Dieter Fox, Wolfram Burgard and Sebastian Thrun.Monte Carlo Localization for
Mobile Robots.IEEE International Conference on Robotics and Automation (ICRA). May 1999.
[6] Neil J. Gordon, D. J. Salmond, and A. F. M. Smith.Novel Approach to Nonlinear/Non-Gaussian
Bayesian State Estimate. IEE Proceedings. Volume 140, pp. 107-113. 1993.
[7] D. B. Rubin. Using the SIR algorithm to simulate posterior distributions. Bayesian Statistics 3.
Oxford University Press. 1988.
[8] A. Kong, J. S. Liu and W. H. Wong. Sequential Imputations and Bayesian Missing Data
Problems.Journal of the American Statistical Association. Volume 89, pp. 278-288. 1994.
[9] John Geweke. Bayesian Inference in Econometric Models Using Monte Carlo
Integration.Econometrica.Volume 57, Number 6. 1989.
[10] J. E. Handschin. Monte Carlo Techniques for Prediction and Filtering of Non-Linear Stochastic
Processes.Automatica 6. pp. 555-563.1970.
[11] Peter Maybeck. Stochastic Models.Estimation and Control, Volume 1. Academic Press, New York,
1979.
[12] Chris Karlof and David Wagner. Secure Routing in Sensor Networks: Attacks and Countermeasures.
First IEEE International Workshop on Sensor Network Protocols and Applications, May, 2003.
[13] Yih-Chun Hu, Adrian Perrig and David Johnson.Packet Leashes: A Defense against Wormhole
Attacks in Wireless Ad Hoc Networks. IEEE InfoCom 2003. April 2003.
[14] UweKubach and Kurt Rothermel.ExploitingLocation Information for Infostation-Based
Hoarding.MobiCom 2001.
[15] Martin Mauve, JörgWidmer and Hannes Hartenstein.A Survey on Position-Based Routing in Mobile
Ad-Hoc Networks.IEEE Network Magazine. 2001.
[16] Young-BaeKo and Nitin H. Vaidya. Location-Aided Routing (LAR) in Mobile Ad Hoc Networks
.MobiCom 1998.
[17] Brad Karp and H. T. Kung.Greedy Perimeter Stateless Routing.MobiCom 2000.
[18] DragosNiculescu and BadriNath.Ad Hoc Positioning System (APS) Using AoA. IEEE InfoCom2003.

59
[19] D. B. Rubin. Using the SIR algorithm to simulate posterior distributions. Bayesian Statistics 3.
Oxford University Press. 1988.
[20] Neil J. Gordon, D. J. Salmond, and A. F. M. Smith. Novel Approach to Nonlinear/Non-Gaussian
Bayesian State Estimate. IEE Proceedings. Volume 140, pp. 107-113. 1993.
[21] Arnaud Doucet, Nando de Freitas and Neil Gordon.An Introduction to Sequential Monte Carlo
Methods.In Sequential Monte Carlo Methods in Practice, eds. Arnaud Doucet, Nando de Freitas and
Neil Gordon. 2001.
[22] Jungkeun Yoon, Mingyan Liu and Brian Noble.Sound Mobility Models.MobiCom 2003.
[23] RadhikaNagpal, Howard Shrobe, and Jonathan Bachrach.Organizing a Global Coordinate System
from Local Information on an Ad Hoc Sensor Network.2nd International Workshop on Information
Processing in Sensor Networks (IPSN). April 2003.
[24] H. A. Oliveira et al., “Directed Position Estimation: A Recursive Localization Approach for Wireless
SensorNetworks,” 14th IEEE Int’l. Conf. Comp. Communication. AndNetworks, San Diego, CA,
Oct. 2005, pp. 557–62.
[25] T. He et al., “Range-Free Localization Schemes for Large Scale Sensor Networks,” MobiCom ’03:
Proc. 9th Annual Int’l. Conf. Mobile Comp. and Networking, NewYork: ACM Press, 2003, pp. 81–
95.
[26] J. Albowicz, A. Chen, and L. Zhang, “Recursive Position Estimation in Sensor Networks,” 9th Int’l.
Conf. Network Protocols, Nov. 2001, pp. 35–41.
[27] D. Niculescu and B. Nath, “Ad Hoc Positioning System (APS),” IEEE GLOBECOM ’01), San
Antonio, TX, Nov.2001, pp. 2926–31.
[28] L. Lazos and R. Poovendran, “Hirloc: High-Resolution Robust Localization for Wireless Sensor
Networks,” IEEE JSAC, vol. 24, Feb. 2006, pp. 233–46.
[29] L. Lazos and R. Poovendran, “Serloc: Secure Range-Independent Localization for Wireless Sensor
Networks,” Proc. WiSe ’04, 2004, pp. 21–30.
[30] L. Lazos, R. Poovendran, and S. Capkun, “Rope: Robust Position Estimation in Wireless Sensor
Networks,” Proc. IPSN, Apr. 2005, pp. 324–31.
[31] S. Capkun and J.-P.Hubaux, “Secure Positioning ofWireless Devices with Application to Sensor
Networks,”INFOCOM ’05, Miami, FL, Mar. 2005.
[32] D. Liu, P. Ning, and W. Du, “Detecting Malicious Beacon Nodes for Secure Location Discovery in
WirelessSensor Networks,” 25th ICDCS, 2005, pp. 609–19.
Authors
Reza Godaz
He was born in Mashhad, Iran, and received the B.Sc. and M.Sc. degree in software
computer form Islamic Azad University of Najafabad, Iran, in 2002 and 2006. Since
2006 he has been a lecturer with the Islamic Azad University, Mashhad branch,
Mashhad, Iran, which he joined in 2006. His research interests include Networks,
Databases and Semantic Web.
Mohammad Reza Kaghazgaran
He was born in Mashhad-Iran and B.Sc. Software ComputerEngineering of Islamic
Azad University of Mashhad. His researches are Wireless Sensor Network and
Cryptography and Security and recently Vehicular Network Bioinformatics.

The Key Metric forEvaluation Localizationin Wireless Sensor Networks via Distance/Angle Estimation Algorithm (D/A-EA)

Recommended

More Related Content

Similar to The Key Metric forEvaluation Localizationin Wireless Sensor Networks via Distance/Angle Estimation Algorithm (D/A-EA) (20)

More from CSEIJJournal (20)

Recently uploaded (20)

The Key Metric forEvaluation Localizationin Wireless Sensor Networks via Distance/Angle Estimation Algorithm (D/A-EA)