Sensor deployment and target localization in distributed sensor networks

TL;DR: A virtual force algorithm (VFA) is proposed as a sensor deployment strategy to enhance the coverage after an initial random placement of sensors to improve the coverage of cluster-based distributed sensor networks.

Abstract: The effectiveness of cluster-based distributed sensor networks depends to a large extent on the coverage provided by the sensor deployment. We propose a virtual force algorithm (VFA) as a sensor deployment strategy to enhance the coverage after an initial random placement of sensors. For a given number of sensors, the VFA algorithm attempts to maximize the sensor field coverage. A judicious combination of attractive and repulsive forces is used to determine the new sensor locations that improve the coverage. Once the effective sensor positions are identified, a one-time movement with energy consideration incorporated is carried out, that is, the sensors are redeployed, to these positions. We also propose a novel probabilistic target localization algorithm that is executed by the cluster head. The localization results are used by the cluster head to query only a few sensors (out of those that report the presence of a target) for more detailed information. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

Summary

1. INTRODUCTION

• Distributed sensor networks (DSNs) are important for a number of strategic applications such as coordinated target detection, surveillance, and localization.
• The authors present the virtual force algorithm (VFA) as a sensor deployment strategy to enhance the coverage after an initial random placement of sensors.
• The VFA algorithm is based on disk packing theory [Locateli and Raber 2002] and the virtual force field concept from robotics [Howard et al. 2002].
• Based on the information received from the sensor and the knowledge of the sensor deployment within the cluster, the cluster head executes a probabilistic scoring-based localization algorithm to determine likely position of the target.
• The dimensions of the grid provide a measure of the sensor field.

2. RELATED PRIOR WORK

• Sensor deployment problems have been studied in a variety of contexts [Brooks and Iyengar 1997; Iyengar et al.
• Radar and sonar coverage also present several related challenges [Priyantha et al. 2000].
• It is well known, however, that there is inherent uncertainty associated with sensor readings; hence, sensor detections must be modeled probabilistically [Dhillon et al. 2002].
• The AGP problem can be informally stated as that of determining the minimum number of guards required to cover the interior of an art gallery.
• Other related work includes the placement of a given number of sensors to reduce communication cost [Kasetkasem and Varshney 2001] and optimal sensor placement for a given target distribution [Penny 1998].

3.1 Preliminaries

• For a cluster-based sensor network architecture, the authors make the following assumptions: —After the initial random deployment, all sensor nodes are able to communicate with the cluster head.
• —The cluster head is responsible for executing the VFA algorithm and managing the one-time movement of sensors to the desired locations ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• On the other hand, if a pair of sensors is too far apart from each (once again a predetermined threshold is used here), they exert positive forces on each other.
• This ensures that a globally uniform sensor placement is achieved.
• Figure 1 also illustrates the translation of a distance response from a sensor to the confidence level as a probability value about this sensor response.

3.2 Virtual Forces

• The authors now describe the virtual forces and virtual force calculation in the VFA algorithm.
• If more detailed information about the obstacles and preferential coverage areas is available, the parameters governing the magnitude and direction (i.e., attractive or repulsive) of these forces can be chosen ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• The threshold distance dth controls how close sensors get to each other.
• ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• When sensor detection areas overlap, the closer the sensors are to each other, the higher is the coverage probability for grid points in the overlapped areas.

3.3 Energy Constraint on the VFA Algorithm

• In order to prolong the battery life, the distances between the initial and final position of the sensors are limited in the repositioning phase to conserve energy.
• The authors use dmax(si) to denote the maximum distance that sensor si can move in the repositioning phase.
• The cluster head uses the VFA algorithm to find appropriate sensor node locations based on the coverage requirements.
• No movements are performed during the execution of the VFA algorithm.

3.4 Procedural Description of the VFA Algorithm

• Figure 7 shows the data structure of the VFA algorithm, and Figure 8 shows the implementation details in pseudocode form.
• Due to the granularity of the grid and the fact that the actual coverage is evaluated by the number of grid points that have been adequately covered, the convergence of the VFA algorithm is controlled by a threshold value, denoted by c. Let us use c to denote the current grid coverage of the number iteration in the VFA algorithm.
• For the binary sensor detection model without the energy constraint, the upper bound value denoted as c̄ is kπr2; for the probabilistic sensor detection model or binary sensor detection model with the energy constraint, c is checked for saturation by defining c̄ as the average of the coverage ratios of the near 5 (or 10) iterations.
• Since these specific scenarios are extremely unlikely for random deployment, they are not considered in this paper.
• ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.

4. TARGET LOCALIZATION

• In order to conserve power and bandwidth, the message from the sensor to the cluster head is kept very small; in fact, the presence or absence of a target can be encoded in just one bit.
• Detailed information such as detection strength level, imagery, and time series data are stored in the local memory and provided to the cluster head upon subsequent queries.
• Based on the information received from the sensors within the cluster, the cluster head executes a probabilistic localization algorithm to determine candidate target locations, and it then queries the sensor(s) in the vicinity of the target.

4.1 Detection Probability Table

• After the VFA algorithm is used to determine the final sensor locations, the cluster head generates a detection probability table for each grid point.
• The binary string 110 denotes the possibility that s1 and s2 report a target but s3 does not report a target.
• For each such possibility d1d2d3 (d1, d2, d3 ∈ {0, 1}) for a grid point, the authors calculate the conditional probabilities that the cluster head receives d1d2d3 given that a target is present at that grid point.
• Note that the probability table generation is only a one-time cost.

4.2 Score-Based Ranking

• After the probability table is generated for all the grid points, localization is done by the cluster head if a target is detected by one or more sensors.
• When at time instant t, the cluster head receives positive event message from k(t) sensors, it uses the grid point probability table to determine which of these sensors are most suitable to be queried for more detailed information.
• ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• The authors are using wxy(t) to filter out grid points that are not likely to be close to the actual target location.

4.3 Selection of Sensors to Query

• To select the sensor to query based on the event reports and the localization procedure, the authors first note that for time instant t, if kmax ≥ krep(t), then all reported sensors can be queried.
• When this happens, the authors calculate the score concentration by averaging ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• The grid point with the highest score (or the score concentration) is the most likely current target location.
• The selected sensors provide enough information in the subsequent stage to facilitate target identification.
• The results show that Sq(t) matches S̄q(t) in many cases.

4.4 Evaluation of Energy Savings

• The authors next evaluate the energy saved by the proposed probabilistic localization approach.
• The parameters T1, T2, and T3 denote the lengths of time involved in the transmission and reception, which are directly proportional to the sizes of data for yes/no messages, control messages to query sensors, and the detailed sensor data transmitted to the cluster head.
• Also, E is monotonically nondecreasing with time.
• Figure 12 shows the energy saved for the target trace in Figure 10.

4.5 Procedural Description for Target Localization

• Figure 13 shows the pseudocode of the procedure to generate the probability table for each grid point.
• For an n by m grid with k sensors, the computational complexity involved in generating the probability table is O(nm2k) since the maximum number of sensors that can detect a grid point is k for the worst case.
• Therefore, the computational complexity of the probabilistic localization algorithm is max{O, O(nm2k)} = O(nm2k).
• Even though the worst-case complexity of the localization procedure is exponential ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• In k, in practice, the localization procedure can execute in less time since the number of sensors that can effectively detect a target at a given grid point is quite small.

5. SIMULATION RESULTS

• The authors first present simulation results obtained using the VFA algorithm.
• The simulation results for the probabilistic localization algorithm are then presented using the sensor locations from the VFA algorithm as inputs.
• ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• TargetTrace starts from tstart and ends at tend, with time unit as 1.
• The deployment requirements include the maximum improvement of coverage over random deployment, the coverage for preferential areas, and the avoidance of obstacles.

5.1 Case Study 1: Binary Sensor Detection Model

• Figures 15–18 present simulation results based on the binary sensor detection model.
• Figure 16 shows the final sensor positions determined by the VFA algorithm.
• For the binary sensor detection model, an upper bound on the coverage is given by the ratio of the sum of the circle areas (corresponding to sensors) to the total area of the sensor field.
• For their example, this upper bound evaluates to 0.628 and it is achieved after 28 iterations of the VFA algorithm.
• ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.

5.2 Case Study 2: Probabilistic Sensor Detection Model

• Figures 19–21 present simulation results for the probabilistic sensor model.
• Figure 20 shows the final sensor positions determined by the VFA algorithm.
• Shows the improvement of coverage during the execution of the VFA algorithm.
• For the probabilistic sensor detection model, even though there are a large number of grid points that are covered, the overall number of grid points with coverage probability greater than the required level is fewer.
• ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.

5.3 Case Study 3: Sensor Field with a Preferential Area and an Obstacle

• Preferential areas should be covered first, therefore they are modeled as attractive force sources in the VFA algorithm.
• Figure 25 shows the virtual movement traces of all sensors during the execution of the VFA algorithm.
• For case study 2, the VFA algorithm took only 3 min to complete 50 iterations.
• ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• CPU time is important because sensor redeployment should not take excessive time.

5.4 Case Study 4: Probability-Based Target Localization

• The authors evaluate the localization algorithm using the results produced by the VFA algorithm in the sensor deployment stage.
• The authors assume that a maximum of two sensors can be selected for querying by the cluster head.
• There are total of 82 such moves in the simulated target movement trace.
• The parameter E(t) shows the energy saved by ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.
• The localization algorithm for the detection event at time instant t. Figure 29 shows the estimated target location based on the grid point with the highest score.

5.5 Discussion

• From the simulation results, the authors see that the VFA algorithm improves the sensor field coverage considerably compared to random sensor placement.
• The results of the proposed energy-conserving target localization method also show that considerable energy is saved in localizing a target.
• The authors found that the algorithm converged more rapidly for their case studies if wR wA.
• The sensor placement strategy is centralized at the cluster level since every cluster head makes redeployment decisions for the nodes in its cluster.
• The VFA algorithm however is also applicable for alternative location indicators, distance measures, and models of preferential areas and obstacles.

6. CONCLUSION

• The authors have proposed the virtual force algorithm (VFA) as a practical approach for sensor deployment.
• The authors have also shown that the proposed probabilistic localization algorithm can significantly reduce the energy consumption for target detection and location.
• The VFA algorithm can be made more efficient if it is provided with the theoretical bounds on the number of sensors needed to achieve a given coverage threshold.
• Finally, the authors will examine continuous coordination systems instead of discrete coordination systems in this work.

Figures

Fig. 1. Probabilistic sensor detection model.

Fig. 7. Data structures used in the VFA algorithm.

Fig. 23. Initial sensor positions after random placement with obstacles and preferred areas.

Fig. 24. Sensor positions after the execution of the VFA algorithm with obstacles and preferred areas.

Fig. 26. Sensor field coverage achieved using the VFA algorithm with obstacles and preferred areas.

Fig. 25. A trace of virtual moves made by the sensors with obstacles and preferred areas.

Fig. 11. Scoring results for target in the example sensor field at tstart . s1 and s2 have reported.

Fig. 10. Example sensor field with a moving target.

Fig. 16. Sensor positions after the execution of the VFA algorithm (binary sensor detection model).

Fig. 15. Initial sensor positions after random placement (binary sensor detection model).

Fig. 2. An example of virtual forces with four sensors.

Fig. 29. Target localization by the grid point with the highest score.

Fig. 17. A trace of virtual moves made by the sensors (binary sensor detection model).

Fig. 18. Sensor field coverage improvement by the VFA algorithm (binary sensor detection model).

Fig. 5. Coverage versus dth with cth = 0.7 and different λ and β.

Fig. 6. Coverage vs. dth with λ = 0.5 and β = 0.5 and cth = 0.5, 0.7 and 0.9.

Fig. 9. Example of grid point probability table.

Fig. 19. Initial sensor positions after random placement (probabilistic sensor detection model).

Fig. 20. Sensor positions after the execution of the VFA algorithm (probabilistic sensor detection model).

Table V. Sensors Selected for Querying by the Cluster Head

Table I. Example Probability Table

Full text

Sensor Deployment and Target Localization
in Distributed Sensor Networks
YI ZOU and KRISHNENDU CHAKRABARTY
Duke University
The effectiveness of cluster-based distributed sensor networks depends to a large extent on the cov-
erage provided by the sensor deployment. We propose a virtual force algorithm (VFA) as a sensor
deployment strategy to enhance the coverage after an initial random placement of sensors. For a
given number of sensors, the VFA algorithm attempts to maximize the sensor field coverage. A ju-
dicious combination of attractive and repulsive forces is used to determinethenewsensorlocations
that improve the coverage. Once the effective sensor positions are identified, a one-time movement
with energy consideration incorporated is carried out, that is, the sensors are redeployed, to these
positions. We also propose a novel probabilistic target localization algorithm that is executed by
the cluster head. The localization results are used by the cluster head to query only a few sensors
(out of those that reportthe presence of a target) for more detailed information. Simulation results
are presented to demonstrate the effectiveness of the proposed approach.
Categories and Subject Descriptors: C.2.1 [Computer-Communication Networks]: Network
Architecture and Design—distributed networks; wireless communication; C.2.4 [Computer-
Communication Networks]: Distributed Systems—distributed applications; C.3 [Special-
Purpose and Application-Based Systems]: Real-time and Embedded Systems
General Terms: Algorithms, Performance, Management
Additional Key Words and Phrases: Cluster-based sensor networks, cluster head, sensor field
coverage, sensor placement, virtual force
1. INTRODUCTION
Distributed sensor networks (DSNs) are important for a number of strategic
applications such as coordinated target detection, surveillance, and localiza-
tion. The effectiveness of DSNs is determined to a large extent by the coverage
provided by the sensor deployment. The positioning of sensors affects cover-
age, communication cost, and resource management. In this paper, we focus on
sensor placement strategies that maximize the coverage for a given number of
sensors within a cluster in cluster-based DSNs.
As an initial deployment step, a random placement of sensors in the target
area(sensorfield)isoftendesirable,especiallyifnoapriori knowledgeoftheter-
rain is available. Random deployment is also practical in military applications,
Authors’ address: Department of Electrical and Computer Engineering, Hudson Hall, PO Box
90291, Duke University, Durham, NC 27708; email: {yz1,krish}@ee.duke.edu.
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ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004, Pages 61–91.

62
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Y. Zou and K. Chakrabarty
where DSNs are initially established by dropping or throwing sensors into the
sensor field. However, random deployment does not always lead to effective
coverage, especially if the sensors are overly clustered and there is a small
concentration of sensors in certain parts of the sensor field. The key idea of
this paper is that the coverage provided by a random deployment can be im-
proved using a force-directed algorithm. We present the virtual force algorithm
(VFA) as a sensor deployment strategy to enhance the coverage after an initial
random placement of sensors. The VFA algorithm is based on disk packing the-
ory [Locateli and Raber 2002] and the virtual force field concept from robotics
[Howard et al. 2002]. For a given number of sensors, VFA attempts to maxi-
mize the sensor field coverage using a combination of attractive and repulsive
forces. During the execution of the force-directed VFA algorithm, sensors do
not physically move but a sequence of virtual motion paths is determined for
the randomly placed sensors. Once the effective sensor positions are identified,
a one-time movement is carried out to redeploy the sensors at these positions.
Energy constraints are also included in the sensor repositioning algorithm.
We also propose a novel target localization approach based on a two-step
communication protocol between the cluster head and the sensors within the
cluster. Since the energy consumption in DSNs increases significantly during
periods of activity, which may be triggered, for example, by a moving target
[Bhardwajand Chandrakasan 2002], we propose an energy-conserving method
for target localization in cluster-based DSNs. In the first step, sensors detect-
ing a target report the event to the cluster head. The amount of information
transmitted to the cluster head is limited; in order to save power and band-
width, the sensor only reports the presence of a target,and it does not transmit
detailed information such as signal strength, confidence level in the detection,
imagery or time series data. Based on the information received from the sen-
sor and the knowledge of the sensor deployment within the cluster, the cluster
head executes aprobabilisticscoring-basedlocalization algorithm to determine
likely position of the target. The cluster head subsequently queries a subset of
sensors that are in the vicinity of these likely target positions.
The sensor field is represented by a two-dimensional grid. The dimensions
of the grid provide a measure of the sensor field. The granularity of the grid,
that is, distance between grid points can be adjusted to trade off computation
time of the VFA algorithm with the effectiveness of the coverage measure. The
detectionbyeach sensor ismodeledas a circleon the two-dimensionalgrid.The
center of the circle denotes the sensor, while the radius denotes the detection
range ofthesensor. We first consider a binarydetectionmodelin which a target
is detected (not detected) with complete certainty by the sensor if a target is
inside (outside) its circle. The binary model facilitates the understandingof the
VFA model. We then investigate a realistic probabilistic model in which the
probability that the sensor detects a target depends on the relative position of
the target within thecircle. The details of the probabilistic modelarepresented
in Section 1.
The organization of the paper is as follows. In Section 2, we review prior re-
searchontopics related to sensordeploymentin DSNs.In Section 3, wepresent
details of the VFA algorithm. In Section 4, we present the target localization
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Sensor Deployment and Target Localization in Distributed Sensor Networks
•
63
algorithm that is executed by the cluster head. In Section 5, we present simu-
lation results using the proposed sensor deployment strategy for various situ-
ations. Section 6 presents conclusions and outlines directions for future work.
2. RELATED PRIOR WORK
Sensor deployment problems havebeenstudiedinavariety of contexts [Brooks
and Iyengar 1997; Iyengar et al. 1995; Qi et al. 2001; Varshney 1996]. In the
area of adaptive beacon placement and spatial localization, a number of tech-
niqueshavebeenproposedforbothfine-grainedandcoarse-grainedlocalization
[Bulusu et al. 2001; Heidemann and Bulusu 2001].
Sensor deployment and sensor planning for military applications are de-
scribed in Musman et al. [1997], where a general sensor model is used to detect
elusive targets in the battlefield. The sensor model is characterized by a win-
dow, which includes physical sensor model parameters, sensor location, terrain
characteristics, and the data collected in a certain period of time. The sensor
coverage analysis is based on a hypothesis of possible target movements and
sensor attributes. This analysis generates all possible routes of targets move-
ments. Bayesian networks are used to calculate the probability that a certain
targetisdetectedinaparticularareaduringparticulartimeintervals.However,
the proposed DSNs framework in Musman et al. [1997] requires a great deal of
a priori knowledge about possible targets. Hence, it is not applicable in scenar-
ios where there is no information about potential targets in the environment.
Thedeploymentofsensorsforcoverageofthesensorfieldhasbeenconsidered
for multi-robot exploration [Howard et al. 2002]. Each robot can be viewed as a
sensor node in such systems. An incremental deployment algorithm is used in
which sensor nodes are deployed one by one in an adaptive fashion. Each new
deployment of a sensor is based on the sensed information from sensors de-
ployed earlier.Thefirstsensorisplacedrandomly.Adrawback of this approach
is that it is computationally expensive. As the number of sensors increases,
each new deployment results in a relatively large amount of computation.
The problem of evaluating the coverage provided by a given placement of
sensors is discussed in Meguerdichian et al. [2001]. The major concern here is
the self-localization of sensor nodes; sensor nodes are considered to be highly
mobile and they move frequently. An optimal polynomial-time algorithm that
uses graph theory and computational geometry constructs is used to determine
the best-case and the worst-case coverage.
Radarandsonar coveragealso presentseveralrelated challenges[Priyantha
et al. 2000]. Radar and sonar netting optimization are of great importance for
detection and tracking in a surveillance area. Based on the measured radar
cross-sections and the coverage diagrams for the different radars, the authors
in Priyantha et al. [2000] propose a method for optimally locating the radars to
achieve satisfactory surveillance with limited radar resources.
Sensor placement on two- and three-dimensional grids has been formu-
lated as a combinatorial optimization problem, and solved using integer lin-
ear programming in Chakrabarty et al. [2001, 2002]. This approach suffers
fromtwomaindrawbacks.First,computationalcomplexitymakestheapproach
ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.

64
•
Y. Zou and K. Chakrabarty
infeasible for large problem instances. Second, the grid coverage approach re-
lies on “perfect” sensor detection, that is, a sensor is expected to yield a binary
yes/no detection outcome in every case. However, because of the inherent un-
certainty associated with sensor readings, sensor detection must be modeled
probabilistically [Dhillon et al. 2002].
It is well known, however, that there is inherent uncertainty associated with
sensor readings; hence, sensor detections must be modeled probabilistically
[Dhillon et al. 2002]. A probabilistic optimization framework for minimizing
the number of sensors for a two-dimensional grid has been proposed recently
[Dhillonetal.2002].Thisalgorithmattemptstomaximizetheaveragecoverage
of the grid points. Finally, there exists a close resemblance between the sensor
placement problem and the art gallery problem (AGP) addressed by the art
gallery theorem [O’Rourke 1987]. The AGP problem can be informally stated
as that of determining the minimum number of guards required to cover the
interior of an art gallery. (The interior of the art gallery is represented by a
polygon.) The AGP has been solved optimally in two dimension and shown to
be NP-hard in the three-dimensional case. Several variants of AGP have been
studied in the literature, including mobile guards, exterior visibility, and poly-
gons with holes. Other related work includes the placement of a given number
of sensors to reduce communication cost [Kasetkasem and Varshney 2001] and
optimal sensor placement for a given target distribution [Penny 1998].
Our proposed algorithm differs from prior methods in several ways. First,
we consider both the binary sensor detection model and probabilistic detection
model to handle sensors with both high and low detection accuracy. Second,
the amount of computation is limited since we perform a one-time computation
and sensor locations are determined at the same time for all the sensor nodes.
Third, our approach improves upon an initial random placement, which offers
a practical sensor deploymentsolution. Finally, we investigate the relationship
betweensensorplacementwithinaclusterandtargetlocalizationbythecluster
head in an effort to conserve energy whenever there are activities in the DSN.
3. VIRTUAL FORCE ALGORITHM
In this section, we describe the underlying assumptions and the virtual force
algorithm (VFA).
3.1 Preliminaries
For a cluster-based sensor network architecture, we make the following as-
sumptions:
—After the initial random deployment, all sensor nodes are able to commu-
nicate with the cluster head. This communication is necessary only for the
transmission of the new locations to the nodes. This is done only once per
node and does not require large amount of data to be transferred; therefore,
the energy consumed for this purpose is ignored.
—The cluster head is responsible for executing the VFA algorithm and manag-
ing the one-time movement of sensors to the desired locations
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Sensor Deployment and Target Localization in Distributed Sensor Networks
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—In order to minimize the network traffic and conserve energy, sensors only
send a yes/no notification message to the cluster head when a target is de-
tected. The cluster head intelligently queries a subset of sensors to gather
more detailed target information.
The VFA algorithm combinestheideasof potential field [Howard etal.2002]
and disk packing [Locateli and Raber 2002]. In the sensor field, each sensor
behaves as a “source of force” for all other sensors. This force can be either
positive (attractive) or negative (repulsive). If two sensors are placed too close
to each other, the “closeness” being measured by a predetermined threshold,
they exert negative forces on each other. This ensures that the sensors are not
overly clustered, leading to poor coverage in other parts of the sensor field. On
the other hand, if a pair of sensors is too far apart from each (once again a
predetermined threshold is used here), they exert positive forces on each other.
This ensures that a globally uniform sensor placement is achieved.
Consider an n by m sensor field grid and assume that there are k sen-
sors deployed in the random deployment stage. Each sensor has a detection
range r. Assume sensor s
i
is deployed at point (x
i
, y
i
). For any point P at
(x, y), we denote the Euclidean distance between s
i
and P as d(s
i
, P), that is,
d(s
i
, P) =

(x
i
− x)
2
+ (y
i
− y)
2
. Equation (1) shows the binary sensor model
[Chakrabarty et al. 2001, 2002] that expresses the coverage c
xy
(s
i
) of a grid
point P by sensor s
i
.
c
xy
(s
i
) =

1, if d(s
i
, P) < r
0, otherwise.
(1)
The binary sensor model assumes that sensor readings have no associated
uncertainty. In reality, sensor detections are imprecise, hence the coverage
c
xy
(s
i
) needs to be expressed in probabilistic terms. In this work, we assume
the sensor model given by Equation (2), which is motivated in part by Elfes
[1990]. Our approach can also be used with alternative sensor models that are
based on radio signal propagation models in which signal strength decays as a
power of the distance [Rappaport 1996]; the sensor placement and localization
algorithms are independent of the sensor models.
c
xy
(s
i
) =





0, if r + r
e
≤ d(s
i
, P)
e
−λa
β
,ifr − r
e
< d(s
i
, P) < r + r
e
1, if r − r
e
≥ d(s
i
, P)
(2)
where r
e
(r
e
< r) is a measure of the uncertainty in sensor detection, a =
d(s
i
, P) − (r − r
e
), and λ and β are parameters that measure detection prob-
ability when a target is at distance greater than r
e
but within a distance from
the sensor. This model reflects the behavior of range sensing devices such as
infrared and ultrasound sensors. The probabilistic sensor detection model is
shown in Figure 1. Note that distances are measured in units of grid points.
Figure 1 also illustrates the translation of a distance response from a sensor to
the confidence level as a probability value about this sensor response. Differ-
ent values of the parameters α and β yield different translations reflected by
ACM Transactions on Embedded Computing Systems, Vol. 3, No. 1, February 2004.

Frequently asked questions

Q1. What are the contributions in "Sensor deployment and target localization in distributed sensor networks" ?

The effectiveness of cluster-based distributed sensor networks depends to a large extent on the coverage provided by the sensor deployment. The authors propose a virtual force algorithm ( VFA ) as a sensor deployment strategy to enhance the coverage after an initial random placement of sensors. The authors also propose a novel probabilistic target localization algorithm that is executed by the cluster head. The localization results are used by the cluster head to query only a few sensors ( out of those that report the presence of a target ) for more detailed information. 

Q2. What have the authors stated for future works in "Sensor deployment and target localization in distributed sensor networks" ?

Their future work will be focused on overcoming the current limitations of the VFA algorithm. Since the current target localization algorithm considers only one target in the sensor field, it is necessary to extend the proposed approach to facilitate scenarios for multiple objects localization. Extensions to nonmobile sensor nodes and situations of sensor node failures will also be considered in future work. The VFA algorithm can be made more efficient if it is provided with the theoretical bounds on the number of sensors needed to achieve a given coverage threshold. 

Q3. How is the message from the sensor to the cluster head kept small?

In order to conserve power and bandwidth, the message from the sensor to the cluster head is kept very small; in fact, the presence or absence of a target can be encoded in just one bit. 

Q4. Why is the sensor detection model modeled probabilistically?

because of the inherent uncertainty associated with sensor readings, sensor detection must be modeled probabilistically [Dhillon et al. 2002]. 

Q5. What is the energy constraint for the binary sensor detection model?

For the binary sensor detection model without the energy constraint, the upper bound value denoted as c̄ is kπr2; for the probabilistic sensor detection model or binary sensor detection model with the energy constraint, c(loops) is checked for saturation by defining c̄ as the average of the coverage ratios of the near 5 (or 10) iterations. 

Q6. What is the underlying assumption for a cluster-based sensor network architecture?

For a cluster-based sensor network architecture, the authors make the following assumptions:—After the initial random deployment, all sensor nodes are able to communicate with the cluster head. 

Q7. What is the effect of cluster-based distributed sensor networks?

The effectiveness of cluster-based distributed sensor networks depends to a large extent on the coverage provided by the sensor deployment. 

Q8. What is the point where the target starts to move?

The target starts to move at t = tstart from the grid point marked as “Start” and finishes at t = tend at the grid point marked as “End.” 

Q9. What is the probability table for the detection of a target?

After the VFA algorithm is used to determine the final sensor locations, the cluster head generates a detection probability table for each grid point. 

Q10. What is the probability that the grid point is covered?

Since the term (1 − cx, y (si))(1 − cx, y (sj )) expresses the probability that neither si nor sj covers grid point at (x, y), the probability that the grid point (x, y) is covered is given by Equation (5). 

Q11. What is the upper bound for the coverage of the binary sensor detection model?

For the binary sensor detection model, an upper bound on the coverage is given by the ratio of the sum of the circle areas (corresponding to sensors) to the total area of the sensor field. 

Q12. What is the probability that the grid points are covered?

Note that in both cases, the coverage is effective only if the total area kπr2 that can be covered with the k sensors exceeds the area of the grid.