INTRODUCTION
Advances in telecommunication technology in recent years have lead to the rapid
development of sensor networks where the sensors are low in cost and power consumption
and can perform multiple functions. Being small in size the sensors can still
acquire and process data and communicate to the other sensors, usually, through
radio frequency channel. The sensors are easy to deploy and costeffective which
have revolutionized the applications of remote monitoring (Ilyas
and Mahgoub, 2006; Wu, 2006).
Since the first introduction of Wireless Sensor Networks (WSN), growing research
and commercial interest, that followed it, brought many applications of WSN.
These applications were created for military, health and civilian purposes (Callaway,
2004).
Applications using localization information are on demand by people more and
more each day. These applications are used to determine the location of the
target in the given environment. There are many localization methods developed
in the past, each of them have different use for each particular application
(Li et al., 2010). The localization applications
are developed to be used indoors and/or outdoors.
Most of the localization applications for outdoors use Global Positioning System
(GPS) to locate the target (Subhan et al., 2011).
Cell phones are also often used as an alternative to GPS to track the location
of a person. Using CellID is the easiest way of positioning with cell phones
but the accuracy of such systems might vary from hundreds of meters to few kilometers.
This depends on the size of the cell. However, both of these systems, GPS and
cell phone, are not very useful in indoor environments. This is because the
accuracy of cell phone positioning technology is not sufficient and GPS systems
can’t penetrate the buildings and other obstacles.
One of the applications which require the localization information is Child tracking. Tracking applications have been developed rapidly. People want to track everything important for them. Child kidnapping is one of the widespread types of crime nowadays in Malaysia and other countries. Many kidnapping cases end with rape and/or murder. And many cases go unsolved. In most of the cases the children are abducted in places with specific perimeter, like shopping malls, markets and playgrounds. Sometimes parents are unsure whether the child just got out of sight and is still within the perimeter of the place or the child has been abducted. The problem is that this causes the delay in the search, because when the related authorities are notified, the search is first concentrated on the inside of the area. A good tracking system that is able to detect the child’s presence in the area and notify the authorities when the child goes out will be very useful. The direction where the child was taken could be known and the search could speed up.
This study explains the process of positioning and describes the techniques which could be used for child tracking. Fuzzy logic, as a positioning technique for Child tracking, will be described.
LOCALIZATION TECHNIQUES
The typical scenario for the indoor localization system is that the target
walks among the sensor nodes in the Wireless Sensor Network (WSN). The sensor
node of WSN which detects the presence of the target node, sends the signal
to the target and receives the reply confirming that it is the target node (Vossiek
et al., 2003). When the reply is received, the sensor node can calculate
the time it took the signal to travel to the target and back and/or the signal
strength of the signal received from the target. These measurements are then
used to estimate the distance between the sensor node and the target node. Then
with the estimated distance between the target and few sensor nodes in WSN,
the location of the target can be calculated.
As can be seen in Fig. 1, the basic of the localization techniques is divided into two steps: First step is to measure the signal related parameters, like time and signal strength; Second step is to calculate the actual position of the target.

Fig. 1: 
Steps of localization 
In the first step of localization, the sensor node measures the properties
of the signal between itself and the target node. The most common signal properties
measured are the time, signal strength and angle of the signal (Liu
et al., 2007).
In the second step, the signal parameters measured in the first step will be
used to calculate the location of the target. The calculation usually uses the
geometric methods of calculating the location of a point with known coordinates
of the neighboring points and the distances between them. The two widely used
methods are: Triangulation and Trilateration. These methods are often used with
some other techniques, i.e. statistical, to improve the accuracy of the result,
because the measurements in reallife are not ideal (Koyuncu
and Yang, 2010).
Signal measurement: As has been described in the previous section, the
signal measurement is the first step of localization of an object. In this step,
the sensor nodes measure some defined parameters of the signal that it sends
to the target node. The signal measurements can be taken from any type of signal
used in the communication between the sensor nodes. It can be Radio Frequency
(RF), Infrared (IR), Bluetooth and etc. The most commonly used parameters measure
the time and signal propagation strength (Patwari et
al., 2005). When measuring the time parameters, one or more of the following
are measured: Time of Arrival (TOA), Time Difference of Arrival (TDOA) and Roundtrip
Time of Flight (RTOF). Angle of Arrival (AOA) and Received Signal Strength (RSS)
are the parameters of the signal (Subhan and Hasbullah,
2009) which measure the angle at which the signal is received and the strength
of the signal, respectively.
Time of Arrival (TOA): TOA is the measure of a time it takes the signal to arrive from the transmitter to the receiver (Fig. 2). To find the distance between the two nodes, the transmission time delay (TOA) is multiplied by the propagation speed:
where, d_{ij} is the distance between the two nodes, t_{ij} is the transmission time delay and v_{p} is the propagation speed of the signal.
The main issue in TOA is the clock synchronization. If the nodes are not synchronized,
the calculation results will not be accurate. One way to solve the synchronization
problem is to install the synchronized clocks at the receiver and the transmitter
nodes or attach GPS to the nodes. However, this solution is very costly to install
and maintain (Li et al., 2009; Zhang
et al., 2010).

Fig. 2: 
TOA where t_{TA} and t_{TB} are the measured
one way times, from the target, T, to reference points A and B, respectively 

Fig. 3: 
TDOA where, Δt_{AC} and Δt_{BC}
are the differences in time measurements from sensor A and C (reference
sensor) and B and C, respectively 
Time Difference of Arrival (TDOA): TDOA is very similar to TOA, in a way that it also measures the time delay of the transmission between the two nodes (Fig. 3). Instead of measuring it only once, it measures the time delay of the transmission using two different signals.
The difference of time delay of two signals is used to calculate the distance between the nodes. So, the distance between the two nodes is calculated by the following equation:
where, d_{ij} is the calculated distance between the two nodes, v_{p1} and v_{p2} are the propagation speed of the signal one and signal two, respectively, t_{ij1} and t_{ij2} are the recorded time delays of the two transmissions.
Roundtrip Time of Flight (RTOF): The issue of clock synchronization in TOA is addressed with RTOF. RTOF tries to solve the problem of synchronization with TOA to some extent. By measuring the RTOF, the distance between the two nodes is calculated as follows:
where, d_{ij} is the distance between the two nodes, t_{RT} is time delay of the roundtrip transmission, Δt is the time delay between receiving and sending the signal at the receiving node and v_{p} is the transmission speed.
Although RTOF decreases the requirement of the clock synchronization of TOA,
it does not solve the issue completely. The calculation of RTOF needs to know
the exact delay time of the receiving node which requires very good synchronization
or fast processing speed. Liu et al. (2007) calculate
that the processing time as short as 1 msec, with 25 ppm accuracy crystal clock,
can generate positioning deviation up to several meters (Fig.
4).
Angle of Arrival (AOA): In AOA, the location of the unknown node can
be found by measuring the angle of arrival of the signal. The angle is measured
by the directional antennas or sometimes by the array of antennas.

Fig. 4: 
RTOF where, t_{1} and t_{2} are the measured
roundtrip times, from the target, T, to reference points A and B, respectively
and back 

Fig. 5: 
Sensors A and B measure the RSS, R_{1} and R_{2},
respectively, to the target, T 
When the antennas receive the signal, the difference of time between different
antennas is also known, together with the angle. With these measurements, the
geometry of the sensor nodes and the target node can be constructed. The measurements
from two known sensor nodes are enough to determine the location of the target
in 2D and measurements from three known sensor nodes are enough to determine
the location of the target in 3D. Another advantage of AOA over the other measurements
is that it does not require the synchronization of the clocks of the sensor
nodes. However, the main disadvantage of it is the cost of implementation. To
measure the signal parameters for AOA, it requires the installation of the complex,
large and costly hardware. Another disadvantage is the distance between the
nodes. The distance between the sensor node and the target nodes is inversely
proportional to the accuracy of the angle measurements. This means that the
further away the target from the measuring nodes, the less the positioning precision
would be. In addition, the positioning using this method of signal measurement
is not very suitable for moving targets.
Received Signal Strength (RSS): RSS is the measure of voltage by Received
Signal Strength Indicator (RSSI) circuit of the node. To measure RSS, the sensor
nodes usually do not require any additional hardware. So, the implementation
of RSS measurement is in a way simpler than the measurements of the other mentioned
signal parameters (Rozyyev et al., 2010). After
measuring the RSS, the theoretical models are usually used to convert the RSS
into a distance estimate. Figure 5 shows how RSSI values are
used to locate the target.
Position computation: As has been mentioned in the previous section,
the localization of the target is divided into two steps. The first step, signal
measurement was described also in the previous section. After the measurements
are complete, the computation of the target’s location can be continued
with the second step. In the second step the acquired measurements are put into
respective equations to calculate the location of the target node. There are
many equations and methods derived nowadays on how to compute the location of
the node with known coordinates of the neighboring nodes and known signal measurements
but all of them are derived from the basic geometric formulas of triangulation
and trilateration.
Triangulation: Triangulation is often used with AOA signal parameter. Triangulation does not require knowing the distance between the target node and the neighboring nodes to calculate the distance. It measures the angles between the intersection lines of the target and the reference nodes. The distance can be calculated with those angles. Triangulation only requires two reference points to calculate the location of the target, as shown in Fig. 6.
In Fig. 6, A and B are the minimum required reference points with known coordinates, θ_{1} and θ_{2} are the angles measured with AOA method and T is the target node with unknown coordinates.
Trilateration: Trilateration is another one of the widely used methods to obtain the location of the target node. It uses three reference points to calculate the location of the target in 2D., as shown in Fig. 7, the reference nodes must be noncollinear to be able to position the between them.
If the coordinates of the reference points are known, the location of the target
node can be found as shown in Fig. 7. (x_{1}, y_{1}),
(x_{2}, y_{2}) and (x_{3}, y_{3}) are the coordinates
of reference points A, B and C, respectively.

Fig. 6: 
Triangulation of the objects location based on AOA 

Fig. 7: 
Positioning of the target using trilateration 
R_{1}, R_{2} and R_{3} are the distances between the
target node T and reference points A, B and C, respectively. R_{1},
R_{2} and R_{3} are also the radiuses of the three circles with
origins A, B and C, respectively. With these known the coordinates of T, (x_{T},
y_{T}) can be calculated with the following equations:
Fuzzy logic: Fuzzy logic, first introduced by Zadeh (Akpolat,
2005) in 1965, is the multivalued logic that accepts the estimated values
and returns estimation in result. It doesn’t only consider the exact crisp
values for its input. It accepts a range of values (Zadeh,
1965). Teuber et al. (2006) used Fuzzy logic,
to estimate the location of the target. Chen et al.
(2010) proved that it gives more accuracy than commonly used triangulation
method. However, the main advantage of using Fuzzy logic is not only the accuracy.
To minimize the errors and consider the measurements as in real world scenarios,
mathematical methods of positioning use statistical methods and/or filters after
calculating the values. Using Fuzzy logic allows developers of the application
to skip this step. The use of statistical methods and filters will not be needed.
This saves time by skipping long calculations.
Neural networks: Neural networks are also used as a localization method.
Although, it is not as popular as other mentioned methods, it gives good results.
For the training purpose of the neural networks, the RSS measurements and the
position of the corresponding targets are measured in offline stage. The weights
are obtained after the training. These weights are used to calculate the location
of the hidden layers in the neural network. The weights are multiplied by the
inputs. This process repeats for the hidden layer, to get to the output function.
Bouzenada et al. (2007) explained the target
location in the video images is tracked. Similarly, Neural networks can be used
to track target locations using signal properties. Shareef
et al. (2008) compared four families of Neural Networks for localization.
The authors also prove that in some cases the neural networks give better results,
in terms of accuracy than the other methods.
METHODOLOGY
This section defines the methodology used to develop the child tracking system using fuzzy logic in Wireless Sensor Network (WSN).
System model: All Fuzzy Logic based applications have one component in common, the Fuzzy Inference System (FIS). FIS is the heart of the fuzzy logic applications which does the logic part. Referring back to Fig. 1, we can change it to define the steps of positioning using fuzzy logic which is illustrated in Fig. 8.
Measurement of RSSI: RSSI value will be measured in the first step. The measured value is then to be converted to the distance using the Friis equation:
where, RSSI is the received signal strength, d is the distance between the
nodes, n is the damping coefficient of the signal and A is the absolute value
of the signal strength with 1m distance between the transmitter and the receiver.
Putting the values of A and n into Eq. 6 we get:
Fuzzy inference system: Fuzzy logic toolbox of Matlab was used to design the Fuzzy Inference System (FIS). FIS consists of two main parts: Membership functions and Rules.
Membership functions: The membership functions, define the relationship
of the input and output to the system. The membership functions for Child tracking
were adopted from Chen et al. (2010). In their
study the authors use Mamdanitype Inference, in this study Sugenotype Inference
is used. Instead of Mamdani singletons, Sugeno constants are used for the output
function. Figure 9 shows the membership functions of the input.
The output membership function is Sugeno constant. There are five output constants with values: 0, 0.25, 0.5, 0.75 and 1.
Fuzzy rules: There are five rules in FIS. They are as follows:
• 
If (distance is Very Near) Then (weight is VeryLarge) 
• 
If (distance is Near) Then (weight is Large) 
• 
If (distance is Medium) Then (weight is Medium) 
• 
If (distance is Far) Then (weight is Small) 
• 
If (distance is Very Far) Then (weight is VerySmall) 

Fig. 10: 
The relationship between distance (input) and weight (output) 
Respectively to the rules, the relationship between the input, distance and output, weight, is shown in Fig. 10. The further away the target is from the node, the smaller the weight will be.
Calculating the coordinates: The RSSI values used for the calculations are dummy values which were calculated using the Eq. 5. With input distance, the weight will be obtained from the FIS. For example, when the input distance is 2.5, the weight is 0.625. This weight will then be used to calculate the coordinates of the target by using the following equations:
RESULTS AND DISCUSSION
To theoretically check the positioning using fuzzy logic, four sensor nodes were assumed to be placed in the corners of the square with the area of 6 m^{2}. Five target nodes are assumed to be placed in the square. The coordinates of the reference nodes are known.
The assumed RSSI values by each node are presented in Table 1. Table 2 shows the calculated distance between the reference nodes and the target node. Table 3 displays the calculated coordinates of the target nodes.
The distribution of the assumed positions of target nodes and the calculated positions is shown in Fig. 10. As can be seen from the Fig. 11, the coordinates calculated using fuzzy logic are quite accurate. The further simulations will help to calculate the error rate and the deviation of the nodes from the actual positions.

Fig. 11: 
The location of target nodes 
Table 1: 
RSSI values measured by the reference nodes 

Table 2: 
Distances between the reference nodes and target nodes 

Table 3: 
Calculated coordinates of the target nodes 

CONCLUSION AND FUTURE WORKS
Since the introduction of the Sensor Networks, their development has been rapid. The applications that use these networks developed daybyday. Moreover, these applications, such as health monitoring, have really benefitted people. Localization is one type of applications of sensor networks.
This study has described two steps of localization which are the signal measurement and the position computation. The signal measurement is the process when the sensors, sometimes equipped with special hardware, measure some parameters of the signal which help to estimate the distance to the target. After estimating the distance to the target, the estimated distance from some reference sensors can be used in position calculation, the second step of the localization. Triangulation and Trilateration are the two famous methods used to calculate the position of the target. Nevertheless, the other methods such as Fuzzy Logic and Neural Networks are proven to work just as good, if not better, for some applications.
This study proposed to use fuzzy logic for the positioning for the child tracking application. Using some approximated input, this study showed that fuzzy logic could detect the location of the target.