A multiple power-level approach for wireless sensor network positioning
q
Jen-Yu Fang
a, Hung-Chi Chu
b,*, Rong-Hong Jan
a, Wuu Yang
aa
Department of Computer Science, National Chiao Tung University, Hsinchu 30050, Taiwan
b
Department of Information and Communication Engineering, Chaoyang University of Technology, Taichung County 41349, Taiwan
a r t i c l e
i n f o
Article history: Received 16 May 2007
Received in revised form 28 July 2008 Accepted 30 July 2008
Available online 14 August 2008 Responsible Editor: J.C. de Oliveira Keywords:
Wireless sensor networks Power-level
Positioning
a b s t r a c t
Wireless sensor networks enhance our ability to monitor the physical world. Many recent researches on wireless sensor networks have focused on aspects such as routing, node cooperation, and energy consumption. In addition to these topics, the positioning service is also an important function in sensor networks. This paper presents a multiple power-level positioning algorithm, discusses its capabilities, and evaluates its performance in various environments. The simulation results show that the proposed algorithm exhibits better accuracy than do traditional single power-level methods. In critical situations such as reference node failure, unstable radio transmission range and beacon collision, the pro-posed algorithm still performs well. Finally, the positioning method is implemented on a sensor network test bed, and the actual measurements show that, the average estimation error is 2.5 m when three power-levels are used and adjacent reference nodes are 12 m apart in an outdoor environment.
Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction
With the rapid progress of the wireless network tech-nology, people can conveniently to communicate with one another any time and any place. Mobile devices with wireless capabilities have gradually been integrated into our daily life. A variant of the wireless networks is the wireless sensor network which integrates both wireless and sensor technology into a small device called a sensor node. Each sensor node has the ability to monitor the phys-ical world and return the sensed information to control nodes via wireless communication.
Wireless sensor networks can be applied in many appli-cations, such as military surveillance, environmental mon-itoring, health, home, and commerce[1]. Take a forest-fire detection system for example. A large number of sensor nodes are densely deployed in the forest. They are linked
together with radio communication. Each sensor node re-lays both its location and the surrounding environmental information, such as: temperature, image, air pressure, wind speed, and so on, to the sink node. The sink node, which is a special sensor node, collects the sensed data and replies to the network manager. Abnormal sensed data will trigger a fire warning procedure. The locations of indi-vidual sensors are a necessary part of the sensed data since we want to know the precise location of a forest-fire when it occurs.
In radio communication, the location of a mobile node can be determined by several methods, such as angle of ar-rival (AOA)[2], time of arrival (TOA)[2], time difference of arrival (TDOA)[2], and received signal strength indicator (RSSI). These methods are based on telecommunications technology and need additional network equipment in or-der to determine a mobile node’s location. In recent years, several positioning systems were proposed and imple-mented in real systems[3]such as global positioning sys-tem (GPS)[4], Active Badges[5], Active Bats[6], Cricket[7], RADAR[8], SpotOn[9]and so on. GPS is one of the most popular positioning systems for outdoor environment thus far. The average error of GPS is less than 3 m. However, 1389-1286/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.comnet.2008.07.013
q
This research was supported in part by the National Science Council, Taiwan, ROC, under grant NSC 96-2752-E-009-005-PAE, NSC 96-2219-E-009-006, and NSC 96-2219-E-009-008.
*Corresponding author. Fax: +886 4 23305539. E-mail address:hcchu@cyut.edu.tw(H.-C. Chu).
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Computer Networks
these positioning methods are not suitable for wireless sensor networks due to size, cost, and power consumption constraints.
This paper aims at the scenario wherein a few reference nodes are deployed in static places, along with a lot more sensor nodes that can move around in the sensing field to collect data. A positioning method is developed using transmission signal overlapping region and multiple trans-mission power-levels. The transtrans-mission signal overlapping region of reference nodes was decided in the deployment stage. With the dense deployment in wireless sensor net-works, the whole sensing field can be divided into inde-pendent regions. It should be noted that the indeinde-pendent region means the signal overlapping region that was formed by the set of different reference nodes. The inde-pendent region is helpful location information for narrow-ing down the possible location of a sensor node with geometric analysis. Furthermore, based on the power-lev-els of the transmission signal the whole sensing field can be divided into more and smaller independent regions. This improves the positioning accuracy. The proposed method is suitable for sensor networks that are con-strained in terms of energy consumption, computation power, and device cost. This method also provides good location accuracy.
The remainder of this paper is organized as follows. The next section summarizes previous efforts in positioning re-search. Section3 presents a distributed cell-based posi-tioning method. The multiple power-level posiposi-tioning approach and simulation results are presented in Sections 4 and 5, respectively. A hardware implementation of the proposed method is given in Section6. Finally, a conclusion is given in Section7.
2. Related works
As the wireless mobile device is in widespread use, it becomes more important in relation to a positioning de-mand for many wireless applications and services. There are many positioning methods in wireless networks, which can be classified into two classes: centralized positioning systems and distributed positioning systems. These posi-tioning methods will be discussed in this section. 2.1. Centralized positioning systems
A centralized positioning system has a central server. The server collects the sensed data, accepts location que-ries, and sends replies back to the querying node. The loca-tion of a sensor node is obtained from the central server. Several mechanisms have been proposed for use in deter-mining a node’s location in a centralized positioning sys-tem. In AOA, TOA, and TDOA [2], additional devices are used in the network to determine the direction and the time (or time delay) of the signal, which are then used to calculate a node’s location. Such solutions do not require modifications being made to mobile devices, but produce less accurate position estimates, and incur more network traffic. In an assisted GPS (AGPS)[10]system, an assistant server with a reference GPS receiver helps a handset with a
partial GPS receiver to measure the range and estimate its position. The assistant server, which is a more powerful computing platform than a GPS receiver, has the ability to obtain information from the wireless channel. The assis-tant server communicates with a GPS receiver via a wire-less channel to help the receiver quickly and efficiently estimate its location. In RADAR[8], a node converts the re-ceived signal strength (RSS) to distance information and uses a triangulation method to estimate a node’s location. A convex positioning[11]system requires a central server to gather the connection information among all sensor nodes. The server uses the information to calculate a node’s location. A cell-based positioning system[12] uti-lizes overlapped radio transmission signals of a transmitter to define several independent regions from the working area and a central location server to gather the information of independent regions and then estimates positions. Although these positioning methods produce acceptable position estimates, three major challenges still remain:
Time synchronization: Because of central servers, nodes’ locations could not be modified quickly when network topology changes.
Limited network bandwidth: There are a limited number of usable channels. At any instant, only a few nodes can successfully transmit messages to the central server. System instability: All nodes’ locations are determined by the central server. A broken communication link between a node and the central server would cause the positioning system to fail.
2.2. Distributed positioning systems
In a distributed positioning system, that is, one without a central server, every sensor node gathers the sensed data and uses a positioning algorithm to estimate its own loca-tion. GPS is a typical distributed positioning system[4]. It relies on 24 satellites that orbit around the earth and broadcast precise velocity, latitude, longitude, and altitude information. GPS produces more accurate location esti-mates but takes a longer time to first fix (TTFF) and incurs the additional cost of setting up a GPS receiver for each sensor node. One mechanism that does not rely on GPS measures the distances among the nodes to build a coordi-nated system by which relative positions of the nodes can be calculated [13]. Two area-based positioning mecha-nisms were also proposed [14,15]. One mechanism im-poses the centroid of selected reference points to estimate its own position[14]. The other mechanism nar-rows down the possible region in which a particular node may reside. The region is formed by choosing three an-chors from among all of the audible anan-chors and tests whether it is inside the triangle formed by these three an-chors. The location of a node will be determined by the center of gravity of the intersection of triangles [15]. Niculescu and Nath introduced an ad hoc positioning sys-tem using GPS-like triangulation for estimating nodes’ locations via distance-vector routing[16]or AOA[17]for range measurement. Based on multidimensional scaling (MDS), Shang et al. used the connectivity information to
derive the locations of the nodes[18]. In order to reduce the number of anchors, a few mobile anchors (equipped with the GPS capability) broadcast their current positions periodically[19]. Other sensor nodes that are deployed in static place use the receiving information to estimate their own locations. Note that our proposed method is based on static RNs and mobile SNs while the method in [19] is based on mobile anchors and static SNs. While all of the above distributed positioning systems produce acceptable location accuracy, there are still a number of defects:
In GPS systems, not all sensor nodes can afford the GPS capability. Due to the limitations of sensor nodes in size, cost and power consumption, GPS receivers should be used sparingly.
Owing to the limited computational power of sensor nodes, simpler positioning mechanisms are preferred to more complex ones.
3. Cell-based positioning method
A cell-based positioning system simply utilizes the characteristics of cell overlapping in geometry. It is noted that a cell is formed by a signal overlapping region. When a sensor node needs to determine its own location, a re-quest is sent to the location server. The location server cal-culates the sensor’s location, and then sends the result to the requesting sensor node.
A classical cell-based positioning system is centralized. Because communications between a sensor and a location server consume energy, the classical centralized, cell-based method is not suitable for sensor networks. In order to maintain the advantages of cell overlapping that divides the working area into several independent regions, a dis-tributed cell-based positioning method is proposed [20]. Each node makes use of the beacon signals which were broadcast periodically from the anchors to estimate its own location. In this paper, we design a distributed multi-ple power-level, cell-based positioning method for wire-less sensor networks.
First, certain beacon frames of the anchor contain the anchor’s position, all power-levels, and the power-level of this beacon. A sensor node estimates its position based on the information in the beacon frames. The proposed method is distributed and simple. Distributed means that the location is determined by individual sensor node. There is no need for a GPS receiver or a central server. Simple means that sensor nodes only use a simple connectivity metric and positioning data in the beacon frames to calcu-late their own locations. Sensor nodes require little compu-tation. This method is described in the next section.
4. Multiple power-levels positioning method
The signal overlapping technique was used to perform node localization[12]. An extension of the signal overlap-ping technique with multiple power-level is used in this method. The basic idea of our multiple power-levels posi-tioning method is that each reference node (RN)
periodi-cally broadcasts beacon frames that contain its coordinates, coverage radii and current coverage radius. Each power-level of RN has its own coverage radius. A ref-erence node is a special-purpose sensor node which knows its own coordinate and has an unlimited supply of electric power. Sensor nodes (SNs) receive the beacon frames to perform localization autonomously.
The proposed localization algorithm can be broken down into four major steps: (1) initial setup, (2) broadcast-ing beacon frames, (3) processbroadcast-ing beacon frames, and (4) computing a node’s location. The first two steps are per-formed at RNs and the last two steps are perper-formed at SNs. The four steps are presented follows:
Step 1: Initial setup. Reference nodes are randomly deployed in the sensing area and their positions can be obtained in advance. It is assumed that the entire sensing area is jointly covered by all RN’s signals. We define that pjiis the power-level j of RN i and rji is the coverage radius of power-level pj
i. InFig. 1, the coordinates of RNs 1 through 4 are (0, 100), (100, 100), (0, 0), and (100, 0), respec-tively. Each RN has four power-levels with the cov-erage radii (20, 40, 60, and 80).
Step 2: Broadcasting beacon frames. Reference nodes peri-odically broadcast beacon frames that contain the coordinates of RN, RN’s coverage radii of the multiple power-levels and the coverage radius of the current power-level. The beacon frame SPu i
from RN i in the uth power-level contains the fol-lowing data:
SPu
i ¼ fðxi;yiÞ; Pi;p
c ig;
where (xi, yi) is the coordinate of RN i, Piis the set fp1
i;p2i; . . . ;p j
ig of power-levels of RN i, and pci is the current power-level. It is noted that Pi¼ fp1i;p2i; . . . ;p
j
ig where j is the maximum num-ber of power-levels and pc
i is an element of Pi. According to the free space propagation model, the transmitted signal power can be translated into the signal coverage radius[21]:
PrðdÞ ¼
PtGtGrk2
ð4
p
Þ2d2L; ð1Þwhere Ptis the transmitted signal power. Gtand Gr are the antenna gains of the transmitter and the re-ceiver respectively. L is the system loss, k is the wavelength, and d is the signal coverage radius. It is common to select Gt= Gr= 1 and L = 1.
Therefore, the content of the beacon frame with power-levels can be transformed into the coverage radii by Eq.(1). This transformed beacon frame SRu i
from RN i in the uth power-level, contains the fol-lowing data:
SRu
i ¼ fðxi;yiÞ; Ri;r
c ig;
where (xi, yi) is the coordinate of RN i, Ri is the coverage radius set fr1
i;r2i; . . . ;r j
ig of the multiple power-levels of RN i, and rc
i is the coverage radius of the current power-level. Note that Ri¼ fr1
r2 i; . . . ;r
j
ig where j is the maximum number of power-levels and rc
i is an element of Ri.
For example, as shown in Fig. 1, RN 1 has four power-levels (i.e. j = 4) and periodically broadcasts different beacon frames for each power-level. The contents of the transformed beacon frames for four power-levels are: In power-level 1: SR1 1¼ fð0; 100Þ; ð20; 40; 60; 80Þ; 20g. In power-level 2: SR2 1¼ fð0; 100Þ; ð20; 40; 60; 80Þ; 40g. In power-level 3: SR3 1¼ fð0; 100Þ; ð20; 40; 60; 80Þ; 60g. In power-level 4: SR4 1¼ fð0; 100Þ; ð20; 40; 60; 80Þ; 80g.
In this paper, it is assumed assume that the cover-age radii of power-levels can be controlled and obtained in the initial stage. Section 4.1 shows how to determine a suitable coverage radius for each power-level.
Step 3: Processing beacon frames. After each SN receives enough beacon frames for a short period, it esti-mates its distance from the RN-based on the min-ima of the coverage radii of the received beacon frames. TakeFig. 1for example, the SN A receives beacon frames from RN 1. The contents of the transformed beacon frames are as follows:
In power-level 2: SR2 1¼ fð0; 100Þ; ð20; 40; 60; 80Þ; 40g. In power-level 3: SR3 1¼ fð0; 100Þ; ð20; 40; 60; 80Þ; 60g. In power-level 4: SR4 1¼ fð0; 100Þ; ð20; 40; 60; 80Þ; 80g.
The SN A can obtain the appropriate coverage radius by minimizing the current coverage radii, i.e. Min{40, 60, 80}=40. According to the coverage radius set and the appropriate coverage radius, the estimated distance from RN 1 to SN A is between 20 and 40 units.
Step 4: Computing a node’s location. After an SN deter-mines its distance ranges from various RNs, the region where this SN may reside can be deter-mined. It is assumed that this SN is located at the centroid of the region. The details of comput-ing a node’s location will be discussed in Section 4.2.
4.1. Setting up the optimal coverage radii
An SN’s location is determined by the coverage radii of the beacon frames. Intuitively, more and finer-grained coverage radii would result in better estimations at the cost of more delicate electronics in the sensors and more RN 1 (0,100) RN 2 (100,100) RN 3 (0, 0) RN 4 (100,0) 80 60 40 20 X Y A
complicated calculations. According to this experiment, there is little marginal advantage when the number of power-levels exceeds 4.
InFig. 1, the differences between adjacent coverage ra-dii are always a constant (20). However, this is not neces-sarily the case, in this experiment, we tried several alternatives.
In this simulation, the working area is a 100 100 square. There is an RN on each of the four corners, and 10,000 sensor nodes are deployed in the square area for each unit distance. These SNs are placed at coordinates (0, 0), (0, 1), . . . , (0, 99), (1, 0), (1, 1), . . . , (1, 99), . . . , (99, 0), (99, 1), . . . , (99, 99). Positions of sensor nodes are estimated with the proposed localization algorithm and are com-pared to the actual positions. The average error is a good indication of the overall performance of our localization algorithm. We assume that the area covered by an RN’s sig-nal is a circle.
In our simulation, all possible cases of coverage radii of RNs are considered (i.e. using brute force method) and the number of power-levels ranges from 1 to 7. The coverage radii range from 1 to 99. The simulation results are shown inTable 1. As seen, as the number of power-levels increase, the average error decreases. When the number of power-levels exceeds 4, the reduction in the average error is only marginal.
We also used two strategies for testing various coverage radii: (1) the difference of the coverage radii between adja-cent power-levels is a constant and (2) the ratio of the cov-erage radii between power-levels m + 1 and m ispffiffiffiffiffiffiffiffiffiffiffiffiffim þ 1. In the latter strategy, it is easy to verify that the rings be-tween adjacent power-levels cover the same area, as
shown inFig. 2. The simulation results of the two strategies are shown inTables 2 and 3, respectively. The average er-rors ofTables 1–3are plotted inFig. 3for comparison. It is obvious that the second strategy (equal-area rings) ap-proaches the optimal coverage radii when the number of power-levels is 4 or larger. In terms of average errors, the second strategy is always better than the first.
4.2. Node localization
An SN determines the ring’s location from the power-levels of the beacon frames that it can receive from an RN. When receiving multiple RN beacon frames, the SN is located in the overlapping area of the rings. We assume that the SN is at the centroid of the of the overlapping area and the coordinate of it is (xe, ye). There are four cases to consider:
Type 1: The sensor node receives beacon frames from only one reference node. In this case, the SN is assumed to be exactly where the RN i is located since the centroid of a ring is the center of the two circles enclosing the ring. (Note that the RN is located at the center of the circles.) The esti-mated position of SN is:
ðxe;yeÞ ¼ ðxi;yiÞ:
TakeFig. 4for example. SN A is located in the ring whose thickness is proportional to rm
i and r mþ1 i , where rm
i and rmþ1i are the smallest coverage ra-dius and the second smallest coverage rara-dius, respectively, that A can receive from RN i. How-ever, according to this centroid method, the esti-mated location of A is the centroid of the ring, which is exactly where RN i is located. The error of this estimation is proportional to rm
i, rather than the difference rm
i rmþ1i . When rmi is large, Table 1
Optimal coverage radii for various numbers of power-levels
Number of power-levels Optimal coverage radii Average error
1 (81) 20.0966 2 (62, 98) 10.2869 3 (54, 79, 99) 7.3186 4 (47, 69, 85, 99) 5.8686 5 (37, 57, 76, 89, 99) 4.9995 6 (37, 54, 69, 81, 91, 99) 4.2993 7 (33, 48, 63, 74, 83, 91, 99) 3.714
RN i
r
ir
ir
ir
i 1 2 3 4Fig. 2. The equal-area rings.
Table 2
Coverage radii for the first strategy
Number of power-levels Coverage radii Average error
1 (99) 31.2008 2 (50, 99) 15.2251 3 (33, 66, 99) 10.5579 4 (25, 50, 75, 99) 8.6427 5 (20, 40, 60, 80, 99) 7.1742 6 (17, 33, 50, 66, 83, 99) 6.0276 7 (14, 28, 42, 57, 71, 85, 99) 5.6187 Table 3
Coverage radii for the second strategy
Number of power-levels Coverage radii Average error
1 (99) 31.2008 2 (70, 99) 12.9954 3 (57, 81, 99) 7.8615 4 (49, 70, 86, 99) 6.0703 5 (44, 63, 77, 89, 99) 5.2614 6 (40, 57, 70, 81, 90, 99) 4.4241 7 (37, 53, 65, 75, 84, 92, 99) 3.9646
the estimation error could be significant. A possi-ble improvement is to use directional antennae for RNs. However, this solution will incur high cost, power consumption and system complica-tion. In this paper, we only considered an omni-directional antenna for simplicity.
Type 2: The sensor node can receive beacon frames from exactly two reference nodes. Let RNs i and j be the two reference nodes. In this case, the esti-mated position of SN should be the centroid of the overlapped region of the two rings deter-mined from the strengths of the signals received from RNs i and j. However, computing the exact coordinate of the centroid is too complex a task for a sensor node. An approximation method is used in the following.As shown inFig. 5, let rm i and rn
i be the least coverage radius that SN can receive beacon frames from RN i and j, respec-tively. We draw a circle whose center is RN i and whose radius is rm
i and a similar one around RN j. The intersection of the overlapped region
of the two circles and the line linking RNs i and j is a line segment, denoted as L inFig. 5. The esti-mated location of the sensor is taken to be the midpoint of the line segment L. Let the coordinates of RNs i and j be (xi, yi) and (xj, yj), respectively. Let (xe, ye) be the coordinate of the midpoint M of L. Thus, we can obtain the follow-ing equation:
xe¼ xiþ ðxj xiÞt;
ye¼ yiþ ðyj yiÞt:
(
ð2Þ The length of the line segment from RN i to mid-point M is rm
i L2. Therefore, we derive the equation: 1 2 3 4 5 6 7 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Number of power level
Average accuracy
Optimal Coverage Radius First strategy
Second strategy
Fig. 3. The average error of optimal coverage radius set, first strategy and second strategy.
RN i
r
ir
i m m+1 A(x
i,y
i)
Fig. 4. Type 1 signal overlapping region.
L
(x
e,y
e)
r
i mRN i
(x
i,y
i)
RN j
(x
j,y
j)
r
jn Ar
jn-1r
im-1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxi xeÞ2þ ðyi yeÞ 2 q ¼ rm i L 2: ð3Þ
Solving Eqs.(2) and (3), we obtain
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxiþ ðxi xjÞt xiÞ2þ ðyiþ ðyi yjÞt yjÞ 2 q ¼ rm i L 2) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ððxi xjÞtÞ2þ ððyi yjÞtÞ 2 q ¼ rm i L 2) t ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxi xjÞ2þ ðyi yjÞ 2 q ¼ rm i L 2 ) t ¼ 2r m i L 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxi xjÞ2þ ðyi yjÞ 2 q :
Let ij be ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxi xjÞ2þ ðyi yjÞ2 q . The coordinate of SN, (xe, ye), is xe¼ xiþ ðxi xjÞðrmi rnj þ ijÞ 2 ij ; ye¼ yiþ ðyi yjÞðrmi rnj þ ijÞ 2 ij :
Type 3: The sensor node can receive beacon frames from exactly three reference nodes. As shown in Fig. 6, the position of SN is taken to be the inter-section of L1and L2for the sake of easy computa-tion. In this case, three line segments (L1, L2, and L3) can be obtained, and any two of them can determine the SN’s position. To reduce the estimation error, two smallest line segments (L1 and L2) are selected. Because a long line segment
indicates a large overlapping region of two RNs, it has the higher estimation error. The detailed explanation of this trick will be shown later. Let i, j, and k be the three reference nodes whose coordinate are (xi, yi), (xj,yj) and (xk, yk), respec-tively. Let rm
i, rnj, and rok be the least coverage radius of the beacon frames received from RNs i, j, k, respectively. We draw three circles whose centers are RN i, j, and k and whose radii are rm
i, rn
j, and rok, respectively. Let I1and I2be the inter-section points of the circles around RNs i and j. Let I3and I4be the intersection points of the cir-cles around RNs i and k. Let L1be the line segment connecting I1 and I2. Let L2 be the line segment connecting I3and I4. The position of SN is taken to be the intersection of L1and L2.
The equations of L1and L2are
L1:ð2xj 2xiÞxeþ ðxiÞ 2 ðxjÞ 2 þ ð2yj 2yiÞye þ ðyiÞ 2 ðyjÞ 2 ¼ ðrm i Þ 2 ðrn jÞ 2 ; L2:ð2xk 2xiÞxeþ ðxiÞ2 ðxkÞ 2 þ ð2yk 2yiÞye þ ðyiÞ 2 ðykÞ 2 ¼ ðrm i Þ 2 ðro kÞ 2 :
The coordinate of their intersection can be ob-tained by solving the above two equations. There-fore, the estimated coordinate of SN, (xe, ye), is
where A1= 2xj 2xi, B1=(xi)2(xj)2, C1= 2yj 2yi, D1= (yi)2 (yj)2, E1 ¼ ðrm iÞ 2 ðrn jÞ 2, A2= 2xk 2xi, B2= (xi)2(xk)2, C2= 2yk 2yi, D2= (yi)2 (yk)2, and E2¼ ðrm i Þ 2 ðro kÞ 2 .
Type 4: The sensor nodes can receive beacon frames from k (k P 4) reference nodes. We first select four ‘‘appropriate” RNs among these k RNs and then estimate the sensor node’s location based on the four RNs.
(1) Selection of four appropriate RNs
Selecting the most ‘‘appropriate” RNs is criti-cal to the precision of the estimation. There are two factors that should be considered: First, notice that a smaller overlapped region of the circles around two RNs will result in a
xe ¼ B2 C1 B1 C2þ C1 D2 C2 D1þ C2 E1 C1 E2 A1 C2 A2 C1 ; ye ¼ A2 B1 A1 B2þ A2 D1 A1 D2þ A1 E2 A2 E1 A1 C2 A2 C1 ;
I
4I
1L
2L
1RN i
(x
i,y
i)
RN j
(x
j,y
j)
RN k
(x
k,y
k)
r
imr
j nr
koI
2I
3 AL
3I
5I
6more precise estimation. Take Fig. 7 for example, there are three overlapped regions that are formed by circles around RN i and its three neighbors (j, k, and l). As the over-lapped region becomes smaller, the average error tends to decrease. So selecting the pair (i, l) is more plausible than selecting either the pair (i, j) or the pair (i, k).
Second, the intersection of the two lines L1 and L2might fall out of the overlapped region (seeFig. 8). We should be careful that this sit-uation will not occur. On the other hand, if the intersection of every pair of lines falls out of the overlapped region, we will instead choose only a line and consider this as a type-2 case. Thus, we select two RNs, say a and b, among the k RNs to form a line Labsuch that dLabis
minimized. Then, we select another two RNs, say c and d, to form line Lcdsuch that
p
/3 < hcd< 2p
/3 (where hcdis defined in the sixth step below). If there is more than one candidate pair (c, d), we will choose the one with the smallest dLcd. The algorithm isdescribed as follows.
1. Compute dij¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxi xjÞ2þ ðyi yjÞ 2 q
, for all i, j = 1, 2, . . . , k.
2. Compute dLij¼ riþ rj dij, for all i, j = 1, 2, . . . , k.
3. Find dLab¼ minfdLijg.
4. Compute mab=(ya yb)/(xa xb).
5. Compute mij=(yi yj)/(xi xj), for all i = 1, . . . , k, j = i + 1, . . . , k, i – a, and j – b. 6. Compute hij¼ cos1 1 þ mabmij ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ðmabÞ2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ðmijÞ2 q 0 B @ 1 C A for all i = 1, . . . , k,j = i + 1, . . . , k, i – a, and j – b.
7. Choose c and d such that dLcd¼ minfdLijj
p
=3 < hij<2p
=3; Lij–Labg. The intersec-tion of Laband Lcd is taken as the esti-mated location of the SN.8. If no Lcdsatisfies the condition in step 7 above, estimate the SN’s location with RNs a and b as is done in the above type-2 case.
(2) Node localization based on four RNs
As shown inFig. 9, after four appropriate RNs are selected, the position of SN is taken to be the intersection of L1and L2.
Let i, j, k, and l be the four reference nodes, whose coordinate are (xi, yi), (xj, yj), (xk, yk), and (xl, yl), respectively. Let rm
i , rnj, rok, and rsl be the least coverage radius of the beacon frames received from RNs i, j, k, l, respectively. We draw four circles whose centers are RN i, j, k, and l and whose radii are rm
i, rnj, rok, and rsl, respectively. Let I1and I2be the intersection points of the circles around RNs i and k. Let I3and I4be the intersection points of the cir-cles around RNs j and l. Let L1be the line seg-ment connecting I1and I2. Let L2be the line segment connecting I3and I4. The position of SN is taken to be the intersection of L1and L2. Note that the line segments of L1and L2 are the two smallest line segments.
The equations of L1and L2are
L1:ð2xl 2xjÞxeþ ðxjÞ2 ðxlÞ2
þ ð2yl 2yjÞyeþ ðyjÞ
2 ðylÞ 2 ¼ ðrn jÞ 2 ðrs lÞ 2 ; L2:ð2xk 2xiÞxeþ ðxiÞ2 ðxkÞ 2
þ ð2yk 2yiÞyeþ ðyiÞ
2 ðykÞ 2 ¼ ðrm iÞ 2 ðro kÞ 2 : The coordinate of their intersection can be obtained by solving the above two equations. Therefore, the estimated coordinate of SN, (xe, ye), is where A3= 2xl 2xj, B3= (xj)2 (xl)2, 2yl 2yji, D3= (yj)2 (yl)2, E3¼ ðrnjÞ 2 ðrs lÞ 2, A 4= 2xk 2xi, B4= (xi)2 (xk)2, C4= 2yk 2yi, D4=(yi)2 (yk)2, and E4¼ ðrm
iÞ 2 ðro kÞ 2 . Based on the proposed node localization men-tioned above, it is possible to estimate the node’s position. It is obvious that the estima-tion error of our method can be improved by using the region of the ring formed by the adjacent coverage radius of an RN or the re-gion formed by some coverage radii. However, the positioning estimation with overlapping ring region will greatly increase the complex-ity and computational cost. Based on the de-sign philosophy of wireless sensor networks, each sensor node has the restriction of
xe ¼ B2 C1 B1 C2þ C1 D2 C2 D1þ C2 E1 C1 E2 A1 C2 A2 C1 ; ye ¼ A2 B1 A1 B2þ A2 D1 A1 D2þ A1 E2 A2 E1 A1 C2 A2 C1 ;
electricity, computational capability and com-munication bandwidth. A complicated or high computational method is not suitable for wireless sensor networks. Therefore, in this paper, a simple positioning method for wire-less sensor networks with acceptable accu-racy is considered.
5. Simulation results
In order to evaluate the proposed localization mecha-nism, we presented several experiments for four situations: failure of RNs, loss of beacon frame, unstable radio propaga-tion model, and random placement of RNs. In addipropaga-tion, we compared our localization mechanism with the range-free positioning method[15] and ad hoc positioning method [16] in terms of computational complexity, communica-tion overhead and average accuracy. Note that for each L 2 L1
RN i
(x
i,y
i)
RN l
(x
l,y
l)
RN j
(x
j,y
j)
RN k
(x
k,y
k)
r
imr
j nr
kor
lsI
4I
1I
2I
3 AFig. 9. Type 4 signal overlapping region.
A A A RN i RN j RN k RN i RN i RN l dij d L ik dL il d L ij
Fig. 7. The effect of average error for different overlapping regions.
(x
e,y
e)
L
ijL
klA
RN i
RN j
RN k
RN l
experiment, the average error was obtained by 20 runs. The parameters for the experiments are listed inTable 4. 5.1. Reference nodes failure
Reference nodes broadcast beacon frames periodically to provide location information for SNs. In this experiment, we considered the failure rate of RNs in a mesh structure to
demonstrate the robustness of the proposed method. Hun-dred RNs were placed in a mesh structure (i.e. the vertical and horizontal distance between a pair of adjacent RNs were 100) in the 1000 1000 working area. Additionally, 10,000 SNs were also placed in a similar mesh structure in the working area. Should any RNs fail, the estimation er-ror of the locations of nearby SNs could worsen. The max-imum error was up to 99 with high RN failure rate. Certain SNs could not even be located (i.e. maximum error = 99) at all because all nearby RNs had failed. Increasing the num-ber of RNs could reduce the numnum-ber of SNs that cannot be located. The number of SNs that cannot be located and the average error for various RN failure rates are shown in Table 5.
When the RN failure rate was 10%, the number of SNs that could not be located was 280 and the average error was 12 units distance. The defect in the proposed method is in the high failure rate of RNs. Nevertheless, this problem Table 4
Simulation parameters
RN failure Beacon frame loss Unstable radio propagation Random placement of RNs
Power-levels 4 4 4 4
Coverage radii (47, 69, 85, 99) (47, 69, 85, 99) (47, 69, 85, 99) (47, 69, 85, 99)
Number of RNs 100 4 (at corner) 4 (at corner) (100, 200, 300, 400, 500)
Sensor nodes 10,000 10,000 10,000 10,000
Working area 1000 1000 100 100 100 100 1000 1000
Failure rate (0%, 1%, 5%, 10%, 20%) 0% 0% 0%
Loss rate 0% (0%, 1%, 5%, 10%, 20%) 0% 0%
Propagation model Ideal Ideal Unstable Ideal
Network structure Mesh Mesh Mesh Random
Table 5
The average error for RNs failure
RNs failure (%) Unlocate SNs Average error Maximum error
0 0 5.8686 22.0227 1 2 6.425 77.026 5 66 8.7686 99 10 280 11.917 99 20 1310 18.4823 99 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Cumulative probability (%) Error distance
Reference Node Failure (CDF)
0% RNs failure 1% RNs failure 5% RNs failure 10% RNs failure 20% RNs failure
can be overcome by current hardware manufacturing tech-nology. The cumulative distribution function (CDF) of the error distance is shown in Fig. 10. When the rate was 10%, our method resulted in an 80% error distance to with-in 15 units distance. Accordwith-ing to this experiment, we con-clude that the proposed method has high positioning accuracy (low error distance) in low RNs failure rate. In high RN failure rate, there are lots of unlocated SNs since the beacon frames cannot be received by the SNs. 5.2. Beacon frame loss
In a wireless network, a channel can only be used for a single pair of SNs (transmitter and receiver) at any time. Given the limited number of channels, beacon signals are frequently lost due to signal collisions. In this experiment, we studied the effect of beacon frame loss. We tested four beacon frame loss rate: 1%, 5%, 10%, and 20%. There were four RNs, which were deployed in the four corners of the 100 100 mesh area.Table 6shows the average errors
un-der various beacon frame loss rates. When the beacon frame loss rate was no greater than 5%, the average error increased slightly. When the rate exceeded 5%, the average error became intolerable. As the beacon loss rate became larger than 20%, the maximum error exceeded 90.
There are two approaches to reducing the beacon frame loss. One utilizes random backoff or the frequency-division mechanism to reduce beacon collision. The other is for the sensor node to listen for a period of time to collect enough beacon frames.Fig. 11is the CDF of the error distance rel-ative to the beacon frame loss rate. When the rate was 10%, our method resulted in an 80% error distance to within 15 units distance. Even when the rate was 20%, our method achieved an almost 100% accuracy to within 41 units dis-tance. According to this experiment, it is concluded that the beacon loss rate (less than 20%) slightly affects the average error. It is possibly because the lost beacon frame can be retrieved during another beacon broadcast period. 5.3. Unstable radio propagation model
In reality, the coverage of RNs is irregular due to the multipath propagation effect. In order to evaluate the per-formance of this method under unstable radio propagation, the shadowing model[21]was considered. The shadowing model can be represented by
PrðdÞ Prðd0Þ dB ¼ 10b log d d0 þ XdB;
where Pr(d) is the power of the received signal at distance d, b is the path loss exponent, and XdBis a Gaussian random Table 6
The average error for beacon loss
Beacon frame loss rate (%) Average error Maximum error
0 5.8686 22.0227 1 6.0916 28.6306 5 6.9899 62.8507 10 8.161 54.9281 20 10.6502 94.4299 0 10 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 30 35 40 45 Cumulative Probability (%) Error distance Beacon Loss (CDF) 0% beacon loss 1% beacon loss 5% beacon loss 10% beacon loss 20% beacon loss
variable (with
l
= 0 and standard deviationr
dB). XdB ac-counts for the random effect on radio propagation caused by the environment. Note that the shadowing model ex-tends the ideal circle model to a statistic model.In this experiment, there were four RNs deployed at the four corners of the 100 100 working area. Ten thousand SNs were organized into a mesh, similar to the first exper-iment. Table 7 shows the average error relative to
r
dB. Whenr
dBwas less than 2, the average error was less than 11 and the maximum error was less than 51. This means that this method is applicable in modestly unstable radio propagation environments.Instability in radio propagation causes a more serious effect in our localization algorithm than do the RN failures and beacon frame losses. The reason for the result is that the shadowing model causes the coverage radius to change as time goes by. The proposed method cannot precisely recognize the localization region of SNs. This means that an SN located in type 1 region might determine its location using the procedure of type 2, 3, or 4 and vice versa. When
the mismatch occurred, the error distance of the proposed method became large.Fig. 12shows the CDF of the error distance in the shadowing model. When
r
dB was 3, this method yielded 80% accuracy to within 20 units distance. 5.4. Random placement of reference nodesThe above three simulations only considered the mesh deployment of RNs and SNs. In this simulation, RNs were randomly deployed in a 1000 1000 square area.Table 8 shows the average error relative to the number of deployed RNs. The average error is roughly in inverse proportion to the number of RNs. When the number of RNs was too few, say 100, a significant part of the sensing area was not covered by any RN. Hence, many SNs could not be lo-cated (with maximum error = 99). When the number of RNs (say 500) was enough to cover the whole sensing area, all nodes could be located and the average error was only 6.957. The problem of unlocated SNs can be solved by
0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Cumulative probability (%) Error distance Shadowing model (CDF) σdB=1 σdB=2 σdB=3 dB=4 dB=5 σ σ
Fig. 12. Error distance CDF for various standard deviation with b = 2 in shadowing model. Table 7
The average error for variousrdBwith b = 2 in shadowing model
rdB Average error Max error
1 6.397 24.5153 2 10.058 50.4385 3 16.7451 78.4235 4 24.0704 86.5351 5 29.9701 93.6641 Table 8
The average error with random placement of RN
Number of RNs Unlocated SNs Average error Maximum error
100 722 30.9267 99
200 80 15.5353 99
300 11 10.0668 99
400 2 8.2485 99
0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Error distance Random Placement (CDF) 100 RNs 200 RNs 300 RNs 400 RNs 500 RNs Cumulative probability (%)
Fig. 13. Error distance CDF for various numbers of RNs with random deployment strategy.
100 150 200 250 300 350 400 450 500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Number of RNs Average accuracy
Range free positioning[15] Ad hoc positioning[16] Proposed method
some possible solutions. One way is to use a density con-trol algorithm to evenly distribute RNs so that the average error can be reduced. Assume that there are n RNs in the sensing field. First, we randomly deploy k RNs in the sens-ing field where k is a constant and k < n (e.g., k = n/2). Find the uncovered region by some existing algorithm. Then, (n k) RNs are planned for deployment in the place that can totally cover the entire uncovered region.Fig. 13shows the CDFs of the average error for various numbers of RNs. When the number of RNs was 300, our method gave 80% accuracy to within a 10 unit distance. The reduction in the average error (by increasing RNs) became less obvious
when the number of RNs exceeded 300. According to this experiment, it is concluded that as the density of RNs in-creases, the number of unlocated SNs and the average error both decrease. This is because that lots of beacon frames can be received with high density of RNs.
5.5. Comparison with existing methods
We considered a simulation environment in which RNs were randomly deployed in a 1000 1000 sensing field for various numbers of RNs. In this simulation environment, the average accuracies of range-free positioning method [15], ad hoc positioning (APS) method[16], and our meth-od are compared inFig. 14. The y-axis is the average accu-racy, which is defined as the ratio of the average error distance Eavg to the maximum transmission range Rmax (i.e. Eavg/Rmax, where Rmax= 99).
As shown inFig. 14, the average accuracy of this pro-posed method is almost the same as that of the APS meth-od [16] and is much better than that of the range-free positioning method [15]. However, when the number of RNs is more than 300, the average accuracies for the three positioning methods are almost the same.
InTable 9, it shows three important properties. First, all possible signal overlapping regions are classified by the number of heard RNs that is less than four (type 1–4) in our method (i.e. the number of RNs in our method only re-quired at least one RN). In APS and range-free method, at least three RNs are needed to perform the localization algorithm. This property indicates that this method can be employed with fewer RNs. Second, the computational complexity of our method is O(1) when the deployment of RNs is regular. This is because that this method can di-rectly apply the four types of node localization. When the deployment of RNs is irregular, our method should select four appropriate RNs that we mentioned in type 4 (Section 4.2). The first two appropriate RNs are decided by the smallest overlapped region of these two RNs (O(n2)). Then Table 9
A summary of the system performance and requirement Proposed
method
APS
Range-free
Total RNs N N N
Beacon transmission Broadcast Broadcast Broadcast
Number of heard RNs n n n
Required RNs P1 P3 P3
Computational complexity O(1) (regular) O(1) (need message exchanging) O(n3 ) O(n2 ) (irregular)
Communication overhead No Yes No
Table 10
The parameters and hardware information about Mote
Component Description
Processor Atmel ATMega 128L
Program flash memory 128K bytes
Configuration EEPROM (Data) 4K bytes
Frequency 868-870 MHz
Radio transceiver Chipcon CC1000
Battery 2 AA batteries RN 1 RN 3 RN 2 RN 0
RN 2
(12,12)
RN 3
(0,12)
Reference node
Test point
X
Y
RN 0
(0,0)
RN 1
(12,0)
a
b
the last two appropriate RNs can be determined among the remaining of RNs (O(n2)). However, the range-free method makes use of the approximate point-in-triangulation (APIT) test algorithm to find a positioning region. The com-putational complexity is bounded by O(N3) since the num-ber of the APIT test is ðn3Þ. In the APS method, the localization algorithm can be performed immediately by receiving the coordinates and the hop counts of at least three different RNs. Third, the APS method must maintain a table that contains the coordinates and hop counts of RNs
and exchange updates with its neighbors. However, with the range-free method and our method these are un-needed. Therefore, the cost of communication overhead and table maintenance in APS method is higher than range-free method and our method. Finally, by considering the computational complexity, communication overhead, and positioning accuracy, our method is more appropriate than either the APS or the range-free method.
6. Hardware implementation
The proposed positioning method was implemented over a collection of MICA2 sensor nodes[22]to verify its feasibility and estimate its accuracy in a real-world envi-ronment. The resource constraints of MICA2 are listed in Table 10. We placed MICA2 sensor nodes as RNs on an out-door skating rink in our campus. The topology is shown in Fig. 15(b) in which four black dots represent four RNs. The distance between two adjacent RNs is about 12 m. The transmission power of each RN was tuned so that its trans-mission range was about 3, 6, and 10 m. Each RN broad-casts a beacon frame every 200 ms. The contents of the beacon frames are listed in Table 11. A white dot with coordinate (x, y), where x and y are integers, inFig. 15(b) represents a test point. Each time we placed an MICA2 sensor node on a test point (white dot), the sensor node
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 2 4 6 8 10 12 Cumulative probability(%) Error distance Perfect model Shadowing model (σ =4, β=2) db Shadowing model (σ =4, β=3) db Implementation
Fig. 16. The average accuracy for hexagonal structure in the experiment. Table 11
The beacon content of RNs for three power-levels
RN Power-level Beacon content
RN 0 1 {(0, 0), (3, 6, 10), 3} RN 0 2 {(0, 0), (3, 6, 10), 6} RN 0 3 {(0, 0), (3, 6, 10), 10} RN 1 1 {(12, 0), (3, 6, 10), 3} RN 1 2 {(12, 0), (3, 6, 10), 6} RN 1 3 {(12, 0), (3, 6, 10), 10} RN 2 1 {(12, 12), (3, 6, 10), 3} RN 2 2 {(12, 12), (3, 6, 10), 6} RN 2 3 {(12, 12), (3, 6, 10), 10} RN 3 1 {(0, 12), (3, 6, 10), 3} RN 3 2 {(0, 12), (3, 6, 10), 6} RN 3 3 {(0, 12), (3, 6, 10), 10}
5 4 3 4 6 6 3 5 2 3 4 4 3 6 3 5 2 4 2 5 4 4 3 2 1 0 5 4 3 4 6 6 3 5 2 3 4 4 3 6 3 5 2 4 2 5 4 4 3 2 1 0 5 4 3 4 6 6 3 5 2 3 4 4 3 6 3 5 2 4 2 5 4 4 3 2 1 0 5 4 3 4 6 6 3 5 2 3 4 4 3 6 3 5 2 4 2 5 4 4 3 2 1 0 5 4 3 4 6 6 3 5 2 3 4 4 3 6 3 5 2 4 2 5 4 4 3 2 1 0 5 4 3 4 6 6 3 5 2 3 4 4 3 6 3 5 2 4 2 5 4 4 3 2 1 0 0 1 2 3 4 4 5 2 4 2 5 3 6 3 4 4 3 2 5 3 6 6 4 3 4 5 x y 0 2 3 6 9 10 12 0 2 3 6 9 10 12 0 2 3 6 9 10 12 0 2 2.5 3 4 6 9 10 12 x y Type 4 Type 1 Type 2 Type 3 Type 3 Type 2 Type 2 (6, 6) (10/3, 10/3) 1 2 3 4 5
collected beacon frames for 9600 ms. Let NA be the total number of beacon frames collected at test point A and NA(i) be the number of beacon frames collected at test point A that were issued from RN i. The sensor node at test point A dis-cards the beacon frames from RN i ifNAðiÞ
NA is less than 0.1.
Based on the beacon frames it collected, the sensor node localized itself by the proposed positioning method. This experiment measured 165 test points as shown inFig. 15.
Fig. 16shows the average accuracy for the experimental and simulation results. We use 12 m as a unit distance in our experiment. As shown inFig. 16, the SN can localize it-self to within 5 m for 94.54% of measurements in the out-door experiments. The experimental results also agree with the simulation results using the shadowing model (
r
dB= 4, b = 3, and b = 4). The positioning error obtained from the experiments is plotted inFig. 17(a) and the local-ization region with its centroid for type 1–4 is shown in Fig. 17(b). The positioning error is lower for the test points at the centroid of the type 1 regions (at corner). The aver-age positioning error was 2.5 m and the standard deviation was 1.2 m. The minimum error was 0 m and the maximum error was 6.73 m across 165 test points. The implementa-tion result is listed inTable 12.7. Conclusion
This study presented a multiple power-levels approach to localization for sensor networks. The proposed method
is simple, fast, energy-efficient, and requires no additional devices. With four power-levels in an ideal propagation model, the average error is less than 6 units. The robust-ness of this method was examined under four conditions: reference node failure, beacon frame loss, unstable radio propagation, and random deployment of RNs. Finally, the positioning method was implemented on a sensor network test bed to verify its feasibility. The actual measurements show that it can achieve average accuracy within 0.21 (i.e. Eavg/Rmax= 2.5/12) unit in an outdoor environment.
The crux of this method is to utilize multiple power-lev-els. Many existing algorithms in wireless networks can be enhanced with the technique of multiple power-levels. For example, routing algorithms can make use of multiple power-levels to measure distances between sensor nodes. A sensor could conserve energy by choosing the lowest power-level when communicating with other nodes. References
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Table 12
The hardware implementation results
x y Err x y Err x y Err x y Err x y Err
0 1 1 0 2 2 0 3 3 0 4 2 0 5 2.5 0 6 6.5 0 7 2.5 0 8 1.5 0 9 0.5 0 10 2 0 11 1 1 0 1 1 1 1.41 1 2 2.24 1 3 1.41 1 4 2.24 1 5 1.41 1 6 1 1 7 1.41 1 8 2.24 1 9 3.16 1 10 2.24 1 11 1.41 1 12 1 2 0 0.5 2 1 2.24 2 2 2.83 2 3 2.24 2 4 2 2 5 2.24 2 6 2 2 7 2.24 2 8 2 2 9 3.04 2 10 2.06 2 11 2.5 2 12 3.2 3 0 1 3 1 3.16 3 2 3.61 3 3 3.16 3 4 3.61 3 5 3.16 3 6 3.61 3 7 3.16 3 8 3 3 9 3.04 3 10 3.61 3 11 3.16 3 12 3 4 0 2 4 1 2.43 4 2 2 4 3 3 4 4 4.47 4 5 4.12 4 6 4.47 4 7 4.12 4 8 2.83 4 9 3 4 10 2.83 4 11 2.43 4 12 3.4 5 0 3 5 1 2.87 5 2 2.24 5 3 3.16 5 4 4.12 5 5 6.73 5 6 6.5 5 7 1.41 5 8 2.24 5 9 3.16 5 10 2.24 5 11 2.69 5 12 4.96 6 0 0 6 1 1 6 2 2 6 3 3 6 4 2.75 6 5 3.14 6 6 3.77 6 7 1 6 8 2.75 6 9 3 6 10 2 6 11 2.24 6 12 2 7 0 2.5 7 1 2.87 7 2 3.61 7 3 3.91 7 4 2.24 7 5 2.36 7 6 3.14 7 7 2.36 7 8 2.24 7 9 3.16 7 10 2.24 7 11 2.69 7 12 2.5 8 0 1.5 8 1 1.8 8 2 4.47 8 3 6.4 8 4 2.83 8 5 2.24 8 6 2.75 8 7 2.24 8 8 2.83 8 9 3 8 10 2.5 8 11 4.12 8 12 1.5 9 0 0.5 9 1 3.16 9 2 3.61 9 3 4.24 9 4 3 9 5 3.16 9 6 3 9 7 1.7 9 8 3 9 9 3.16 9 10 5 9 11 1.41 9 12 0.5 10 0 0.5 10 1 2.24 10 2 2.83 10 3 2.24 10 4 2 10 5 2.13 10 6 2.83 10 7 3.2 10 8 2 10 9 3.61 10 10 4.47 10 11 1.12 10 12 0.5 11 0 1 11 1 1.41 11 2 2.24 11 3 1.41 11 4 2.24 11 5 1.41 11 6 2.24 11 7 1.41 11 8 2.43 11 9 3.16 11 10 2.69 11 11 1.41 11 12 1 12 1 1 12 2 0.5 12 3 1 12 4 4 12 5 1 12 6 0 12 7 2.5 12 8 4 12 9 1 12 10 2 12 11 1
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[22] T.M. Mote,<http://www.xbow.com/Products/productsdetails.aspx? sid=72>.
Jen-Yu Fang received the B.S. and M.S. degrees in Computer and Information Science from National Chiao Tung University, Taiwan, in 2002 and 2004, respectively. His research interests include wireless networks, mobile computing and wireless internet.
Hung-Chi Chu received the B.S. and M.S. degrees in Computer Science and Engineering from Tatung University, in 1995 and 1997, respectively and Ph.D. degree in Computer Science from National Chiao-Tung University in 2006. He is currently an Assistant Professor in Department of Information and Communi-cation Engineering, Chaoyang University of Technology. His research interests include wireless networks, wireless sensor networks and artificial intelligence.
Rong-Hong Jan received the B.S. and M.S. degrees in Industrial Engineering, and the Ph.D. degree in Computer Science from National Tsing-Hua University, Taiwan, in 1979, 1983, and 1987, respectively. He joined the Department of Computer and Information Science, National Chiao-Tung University, in 1987, where he is currently a Professor. Dur-ing 1991–1992, he was a VisitDur-ing Associate Professor in the Department of Computer Science, University of Maryland, College Park, MD. His research interests include wireless networks, mobile computing, distributed systems, network reliability, and operations research.
Wuu Yang received the B.S. degree in Infor-mation Engineering from National Taiwan University in 1982 and the M.S. and Ph.D. degrees in Computer Science from the Uni-versity of Wisconsin at Madison in 1987 and 1990, respectively. He joined the Computer Science Department in the National Chiao-Tung University since August 1992, where he is a Professor currently. His current research interests include Java and network security, programming languages and compilers, and attribute grammars.
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