- Email: [email protected]
Density adaptive localization for irregularly deployed wireless sensor networks
Int. J. Electron. Commun. (AEÜ) 66 (2012) 1026–1031
Contents lists available at SciVerse ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.de/aeue
Density adaptive localization for irregularly deployed wireless sensor networks Youngbae Kong a , Younggoo Kwon a,∗ , Jeungwon Choi b , Jonghwan Ko b , Gwitae Park c a
Department of Electronic Engineering Konkuk University, Republic of Korea Agency for Defense Development (ADD), Republic of Korea c Department of Electrical Engineering Korea University, Republic of Korea b
a r t i c l e
i n f o
Article history: Received 15 September 2011 Accepted 20 May 2012 Keywords: Localization Wireless sensor network Irregularly deployed WSNs Fuzzy c-means clustering
a b s t r a c t In wireless sensor networks (WSNs), irregularly deployed nodes can significantly degrade the performance of the localization system. In this paper, we propose a novel localization scheme for the irregularly deployed WSNs. The basic approach is to control the transmission of location messages by using the fuzzy c-means (FCM) clustering algorithm. Next, each node selects its localization method according to the node density. Simulation studies show that the proposed approach can enhance the localization accuracy, while reducing the retransmission messages in the irregularly deployed WSNs. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction Localization technique is indispensable for WSNs, and it is used for various sensor network applications. When any sensor devices are located in the harsh environments, the global positioning system (GPS) can be useless and localization is required for obtaining the location information of each device. Basically, localization system of WSNs is composed of the reference nodes, which know their own locations and the unknown nodes, which do not know their own locations. Based on the information of the reference nodes, sensor nodes can obtain their locations by using the ranging techniques [1]. According to the ranging measurement types, the localization can be divided into the one-hop localization and the multi-hop localization. The one-hop localization estimates the location of the unknown node by using the one-hop reference neighbors, which means that the node can communicate with the reference node directly. If the unknown node does not have sufficient onehop neighbors, the node should utilize the multi-hop localization approach. The multi-hop localization estimates the location of the unknown node by using the connectivity or the hop-distance information [2,3]. To obtain the ranging information, the multi-hop localization utilizes flooding [3]. The flooding is a simple approach to broadcast the location message through the network. The flooding enables the multi-hop localization to estimate the location even when the reference nodes are sparse in the network. In practice, the deployment of WSNs may suffer from limitations due to complicated situations such as the specialized area of
network and the lack of system configuration. The limited deployment of the nodes can make the network density highly irregular, and it can seriously degrade the performance of the localization. The representative problems are the broadcast storm [5] and the localization failure: if the nodes are densely deployed in the network, the multi-hop localization can increase the flooding messages which can cause the communication contention and collision in the localization [5]. The alternative approach is to use the onehop localization, which can reduce the communication overhead due to the redundant messages. However, when the reference nodes are sparse, the one-hop localization may produce the localization failure. In this paper, we propose a density adaptive localization for WSNs. The proposed approach controls the transmission of the location messages by using the fuzzy c-means (FCM) algorithm [6]. Moreover, the proposed approach dynamically selects the localization method according to the node density. The proposed density adaptive localization can overcome the network irregularities and thus improve the localization performance. If any node has sufficient neighbor reference nodes, it estimates its location by using one-hop localization. Otherwise, it estimates its location with the multi-hop localization. Through the proposed approach, the nodes can reduce the communication overhead due to the redundant messages, while maintaining the localization accuracy. Simulation studies show that the proposed approach reduced both the average location error and the communication overhead due to the irregular network density. 2. Problem statement
∗ Corresponding author. E-mail address: [email protected] (Y. Kwon). 1434-8411/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.aeue.2012.05.006
In this paper, we assume that the physical coordinates of the nodes are two-dimensional coordinates. First, each reference node
Y. Kong et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 1026–1031
1027
N(i)
d+1
Fig. 1. (a) Localization in the irregular network density and (b) redundant message problem in multi-hop localization.
periodically broadcasts the location message including its geographic coordinates. After receiving the message, each unknown node calculates the distance between itself and the reference node. When the number of distance information received from the reference nodes is equal to or above three, the node estimates its location by using the localization algorithm such as trilateration or multilateration [1]. If the reference node is within the communication range of the unknown node, the unknown node decides the reference node as the one-hop neighbor reference node. Otherwise, the unknown node calculates the distance to the reference node through the flooding approach. Fig. 1 shows the localization problem in the irregularly deployed WSNs. In Fig. 1(a), the unknown nodes in network area X have the sufficient one-hop neighbor reference nodes. The unknown nodes in region X can obtain their own location by using the one-hop localization. If the reference nodes are sparse as shown in the network area Y, the unknown nodes in region Y have insufficient neighbor reference nodes and thus the one-hop localization may cause the localization failure. An alternative approach, which can obtain the distance to the reference node, is to use the multi-hop localization. If the multihop localization is used in region Y, the nodes should perform the flooding procedure for the propagation of the location information. According to [3], each reference node periodically broadcasts its location message containing the node identifier (ID), the time to live (TTL), and the hop count. On receiving the location message, the node checks the hop count to the reference node, updates the hop count, and retransmits the same message to its neighbor nodes. Before the packet is retransmitted, the TTL field is decremented by 1 to limit the flooding of the location messages in the large area network. A TTL field includes the maximum number of hops that the message is transmitted. Fig. 1(b) shows the problem of the multihop localization in the region Y. As shown in Fig. 1(b), the reference node A broadcasts the location message. On receiving the message, the nodes u, v, and w retransmit the message, and this retransmission may severely produce the contention of the message with each other. Moreover, when the reference nodes A and B try to transmit the location messages simultaneously, the collision can occur due to many redundant messages. Those redundant message may cause the broadcast storm such as contention and collision problems [5]. Therefore, the localization approaches should be adaptive to the irregularly deployed networks .
Fig. 2. Flowchart of the proposed density adaptive localization.
3. Density adaptive localization In this section, we propose a density adaptive localization for irregularly deployed WSNs. Fig. 2 shows the flowchart of the proposed approach. First, the proposed approach controls the transmission of the location message by using the fuzzy c-means (FCM) algorithm. Next, the proposed approach performs the localization by dynamically selecting between the one-hop and the multi-hop localizations. We assume that each reference node j periodically broadcasts the message including the node ID and the d-dimensional location information. Upon receiving the broadcast message, the node i calculates the distance to the reference node j. To reduce the redundant messages due to the flooding, the node i determines the retransmission of the message by using the fuzzy c-means (FCM) algorithm. The FCM is an approach of clustering which allows one group of data to belong two or more clusters [6]. Let X = {x1 , . . ., xn } ⊂ Rd be a finite data set containing the d-dimensional location of the unknown nodes. The clustering problem is to partition the data set X into a set of c clusters (subgroups), and it can be represented as fuzzy sets F1 , F2 , . . ., Fc by minimizing the following object function Jm : Jm =
c n
um xi − vj 2 ij
(1)
i=1 j=1
where m is any real number greater than 1, uij is the membership degree of xi in the cluster j, xi is the d-dimensional location data of the unknown node i, vj is the d-dimensional location data of the reference node j, and xi − vj is d-dimensional norm expressing the similarity between any measured data and the center. xi − vj can ˜ j). Parameter m be obtained through the ranging information d(i, is weighting exponent, which controls the relative weights placed on each of squared errors xi − vj and it is decided between [0,∞]. For most data, when m is between 1.5 and 3, it can produce good performance results [7].
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Y. Kong et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 1026–1031
Reference node (Cluster head)
Unknown node B A
A
~ d (i, A) 1
B ~ d (i, B )
i
i
~ d (i, C )
(a) Flooding procedure
A
2
C
C
uiB
uiA
2
(b) Distance calculation u iA
B
u iB
i
u iC
uiC
1 1/ 2 (1 / 2 ) (1 / 2 ) 1 1/ 5 ( 2 / 1) ( 2 / 1) ( 2 / 2 ) 1 1/ 5 ( 2 / 1) ( 2 / 1) ( 2 / 2 )
(1 / 1)
C
(c) Determination of membership
(d) Resulting fuzzy sets
Fig. 3. Example of the proposed FCM clustering in WSNs.
The above clustering problem requires the centralized computation, but the membership value should be determined with the distributed method. An alternative approach is to utilize the ranging information for the other reference nodes k. Membership degree represents the degree of membership between the unknown node i and the cluster j (i.e., reference node). The unknown node i has a membership uij (between 0 and 1) in each cluster j, and memberships close to 1 signify a high degree of similarity between node i and node j. Meanwhile memberships close to zero imply little similarity between node i and node j. The node i determines the membership degree uij for the jth cluster center as follows: uij =
1 c
(2) 1/(m−1)
(xi − vj /xi − vk )
k=1
where vk is the location data of the reference node k which are collected by the node i, and xi − vk is a ranging information between nodes i and k. Fig. 3 shows the example of the proposed FCM clustering in WSNs. For simplicity, we assume that the reference nodes are only A, B, and C in the network and hop-to-hop distances are 1. In the network, the number of clusters is the same to the number of the anchor nodes. As shown in Fig. 3(a), first the anchor node broadcasts the message including its location and node identifier (ID). Upon receiving the message from the anchor nodes A, B, and C, the node i calculates the distance to the each anchor node and forwards the message to other neighbor nodes. After collecting the message for each anchor node, the node performs the clustering as shown in Fig. 3(c). In the FCM clustering procedure, all nodes have the membership degree (between 0 and 1) for each anchor node. The node i calculates the membership value of the each reference node by using Eq. (2). As shown in Fig. 3(d), the resulting fuzzy sets are
decided to the membership degree for each cluster, and the values uiA , uiB , and uiA become 1/2, 1/5, and 1/5 respectively. Based on the membership degree uij , the node i decides the retransmission of the broadcast message for the reference node j. The node i checks whether the membership degree uij is above some threshold T or not. The threshold T is adaptive to the node density: if the nodes are dense, T is set to high. If the nodes are sparse, T is set to low. If uij ≥ T, then the node i retransmits the broadcast message. Otherwise, node i drops the message. For adaptive transmission to the node density, we set the threshold T to the average value of the membership degree of neighbor nodes. Through the proposed approach, each node can control the retransmission according to the node density. After the retransmission based on the FCM clustering, the node i checks whether the one-hop localization is possible or not. The proposed approach performs the localization according to the number of one-hop neighbor reference nodes N(i). If N(i) is larger than d + 1, the proposed approach chooses to apply the one-hop localization. Otherwise, the proposed approach applies the multi-hop localization. If N(i) is equal to or above d + 1, the node i estimates its location by using the one-hop localization. Based on the least square estimation (LSE) approach, the estimated location of the unknown node is given by:
|N(i)|
xˆ i = argmin x0 ∈L
˜ j))2 (x0 − vj − d(i,
(3)
j∈N(i)
where xˆ i is the estimated location of node i, |N(i)| is the number of the neighbor reference nodes, vj is the coordinates of the reference ˜ j) is the ranging information between nodes i and j, and node j, d(i, · denotes the Euclidean norm. To solve the LSE problem, we utilize the minimum mean square error (MMSE) method [9–11]. This approach divides the network area into small grids and calculates the sum of the mean square error for each grid by using the ranging information of each reference node. The estimated location is
Y. Kong et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 1026–1031
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Table 2 Performance results in the randomly deployed WSNs.
Sparse deployment
100m
Performance results
1-Hop
Flooding
Proposed
Average location error (m) No. of location failure
1.35 m 29
2.69 m 0
2.1 m 0
ranging estimate between the device i and the device j is modeled as unbiased Gaussian estimates [8] and it can be written as: d˜ ij = dij +
where d˜ ij is the ranging distance, dij is the real distance, is noise of ranging distance and it is defined as Gaussian random variable of zero-mean with standard deviation. Parameter m is weighting exponent and we set m into 2 in the simulation. We conducted 10 independent simulation runs and calculated the average location error. The average location error ( u ) is defined as follows:
Dense deployment 2
5
1
(45 12) (45,12)
3
(70, 8)
7
4
8
6
(4)
9
u =
100m
N (xu − xˆ u )2 + (yu − yˆ u )2
N
(5)
i=1
Fig. 4. Example of irregular node deployment.
determined as the grid which has the minimum mean square error (MMSE). If |N(i)| is less than d + 1, the proposed approach estimates its location by using the multi-hop localization. Moreover, the node i ˜ j) satisestimates its location by using only ranging information d(i, fying condition that uij ≥ T. This approach can enhance the location accuracy by removing the distance measurement error due to large propagation of the message. The proposed approach can dynamically control the redundant messages and improve the location accuracy in the irregular network density. 4. Performance results To analyze the performance of the proposed approach, we performed the simulation by using the MATLAB simulation tool. In the simulation, the reference nodes and the unknown nodes are irregularly deployed in 100 m × 100 m network region. We assume that the maximum transmit range of each node is 25 m and all nodes can communicate with each other directly or indirectly through the flooding. In the initialization procedure of the simulation, the deployment of the nodes is initialized based on the configuration file, which has the number and locations of each node. Fig. 4 shows the example of the irregularly deployed network. First, we deploy the sensor nodes densely in the lower left corner. Meanwhile, we place the nodes sparsely in the upper right corner. By using the above procedure, we can create the irregularly deployed network. Simulation environments are described in Table 1. In Table 1, TTL field is time to live and it can be used for the measurement error due to large propagation of the flooding message when the networks are large. We set TTL to 5 for all scenarios because the network diameter is 100 m × 100 m and the maximum transmit range is 25 m. The
where N is the number of the simulation runs, (xu , yu ) is the true location of node u, and (ˆxu , yˆ u ) is the estimated location of node u. First, we compared the proposed approach (Proposed) with the one-hop localization (1-Hop) and multi-hop localization (Flooding) in the irregular network density. A node may fail in getting its own location when it does not have enough anchor nodes, or ranges are faulty, or the starting point of flooding is too far from the true position. In this paper, we call that failure as localization failure. As shown in Table 2, the one-hop localization can obtain more accurate location information compared with other approaches, but it produces the localization failure because of the irregular network density. Meanwhile, the multi-hop localization and the proposed approach have no localization failure, since all unknown nodes can obtain enough ranging information for localization through the flooding. Moreover, compared with the multi-hop localization, the proposed approach reduces the localization error about 26%. Next, we analyzed the total number of the transmission message and the average location error versus the node density. When the number of reference nodes is varied from 10 to 50, the number of unknown nodes is fixed to 20 in the network. When the number of unknown nodes is varied from 10 to 50, the number of reference nodes is fixed to 20 in the network. The transmission message is the flooding message in the multi-hop localization and the proposed approach. Fig. 5 shows the total transmission messages versus the number of the reference nodes. As shown in Fig. 5, the transmission
Table 1 Simulation environments. Parameter
Description
X R M N TTL m
Network side Maximum transmit range No. of reference nodes No. of unknown nodes Time to live Noise of ranging distance Weighting exponent for FCM clustering
Value 100 m 25 m 10–50 10–50 5 1m 2
Fig. 5. Transmission message versus the reference nodes.
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Fig. 6. Transmission message versus the unknown nodes. Fig. 8. Average location error versus the unknown nodes.
messages are increased as the reference nodes are increased. Moreover, the retransmission messages of the proposed approach is much less than the messages of the conventional flooding based localization approach. Fig. 6 shows the total transmission messages versus the number of the unknown nodes. The retransmission messages are increased as the unknown nodes are increased, and the messages of the proposed approach is less than the messages of the flooding approach. Performance results show that the proposed approach efficiently controls the retransmission of the messages by using the FCM algorithm. Finally, we compared the location accuracy versus the node density. Fig. 7 shows the average location error versus the number of the reference nodes. As shown in Fig. 7, the average location error is decreased as the reference nodes are increased. This result comes from the reason that as the reference nodes are increased, unknown nodes can collect more ranging information from reference nodes. Therefore, ranging accuracy is enhanced as the reference nodes are increased and it can reduce the location error of unknown node. Moreover, the average location error of the proposed approach is less than the location error of the flooding approach. When the one-hop neighbor nodes are sufficient, the proposed approach estimates the location by using the one-hop localization and thus its location accuracy is increased. Fig. 8 shows the average location error versus the number of the unknown nodes. The average location error is decreased as the unknown nodes are increased. The reason is that as the node density is increased, the ranging accuracy is enhanced and the average location error is decreased. As shown in Fig. 8, location accuracy improvement is very small between 20 and 40 nodes, compared with the location
improvement between 10 and 20 nodes. The results come from the reason that when the unknown nodes are 10, the network is sparse and thus unknown nodes have insufficient ranging measurement information for each anchor node. When the number of the unknown nodes is above some threshold value (i.e. ≥20), the network density is sufficiently dense and the unknown nodes have sufficient ranging measurement information for each anchor node. Therefore, when the number of unknown nodes is between 20 and 40, the location accuracy improvement is small compared with other intervals. The location error of the proposed approach is less than that of the conventional flooding approach. Simulation studies show that the proposed approach can reduce the communication overhead, while increasing the location accuracy. 5. Conclusion In this paper, we propose a density adaptive localization for the irregular network density. The irregularly deployed WSNs may produce the critical problems such as the localization failure and the redundant retransmissions. The proposed approach dynamically controls the transmission of the location messages by using the fuzzy c-means (FCM) algorithm. Moreover, the proposed localization dynamically selects between the one-hop localization and the multi-hop localization according to the number of the one-hop reference nodes. The proposed density adaptive localization can obtain more accurate location and reduce the retransmission messages in the irregularly deployed WSNs. Acknowledgment This paper was supported by Konkuk University in 2011. References
Fig. 7. Average location error versus the reference nodes.
[1] Mao G, Fidan B, Anderson BDO. Wireless sensor network localization techniques. Comput Netw 2007;51(10):2529–53. [2] Ji X, Zha H. Sensor positioning in wireless ad-hoc sensor networks using multidimensional scaling. In: Proc. INFOCOM. 2004. p. 2652–61. [3] Niculescu D, Nath B. Ad hoc positioning system (APS). In: Proc. GLOBECOM. 2001. p. 2926–31. [5] Tseng Y, Ni S, Chen Y, Sheu J. The broadcast storm problem in a mobile ad hoc network. In: Proc. MOBICOM. 1999. p. 151–62. [6] Gath I, Geva AB. Unsupervised optimal fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 1989;(July):773–81. [7] Bezdek JC, Ehrlich R, Full W. FCM: the fuzzy c-means clustering algorithm. Comput Geosci 1984;10(8):191–203.
Y. Kong et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 1026–1031 [8] Patwari N, Hero AO, Perkin M, Correal NS, O’Dea RJ. Relative location estimation in wireless sensor networks. IEEE Trans Signal Process 2003;51(8): 2137–48. [9] Hellebrandt M, Mathar R. Location tracking of mobiles in cellular radio networks. IEEE Trans Vehicular Technol 1999;48(5):1558–62.
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[10] Savvides A, Han CC, Strivastava MB. Dynamic fine-grained localization in ad-hoc networks of sensors. In: Proc. 7th int conf. on mobile computing and networking. 2001 May. p. 166–79. [11] Albowicz J, Chen A, Zhang L. Recursive position estimation in sensor networks. In: Proc. 9th int conf. on networking protocols (ICNP). 2001. p. 35–41.
Contents lists available at SciVerse ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.de/aeue
Density adaptive localization for irregularly deployed wireless sensor networks Youngbae Kong a , Younggoo Kwon a,∗ , Jeungwon Choi b , Jonghwan Ko b , Gwitae Park c a
Department of Electronic Engineering Konkuk University, Republic of Korea Agency for Defense Development (ADD), Republic of Korea c Department of Electrical Engineering Korea University, Republic of Korea b
a r t i c l e
i n f o
Article history: Received 15 September 2011 Accepted 20 May 2012 Keywords: Localization Wireless sensor network Irregularly deployed WSNs Fuzzy c-means clustering
a b s t r a c t In wireless sensor networks (WSNs), irregularly deployed nodes can significantly degrade the performance of the localization system. In this paper, we propose a novel localization scheme for the irregularly deployed WSNs. The basic approach is to control the transmission of location messages by using the fuzzy c-means (FCM) clustering algorithm. Next, each node selects its localization method according to the node density. Simulation studies show that the proposed approach can enhance the localization accuracy, while reducing the retransmission messages in the irregularly deployed WSNs. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction Localization technique is indispensable for WSNs, and it is used for various sensor network applications. When any sensor devices are located in the harsh environments, the global positioning system (GPS) can be useless and localization is required for obtaining the location information of each device. Basically, localization system of WSNs is composed of the reference nodes, which know their own locations and the unknown nodes, which do not know their own locations. Based on the information of the reference nodes, sensor nodes can obtain their locations by using the ranging techniques [1]. According to the ranging measurement types, the localization can be divided into the one-hop localization and the multi-hop localization. The one-hop localization estimates the location of the unknown node by using the one-hop reference neighbors, which means that the node can communicate with the reference node directly. If the unknown node does not have sufficient onehop neighbors, the node should utilize the multi-hop localization approach. The multi-hop localization estimates the location of the unknown node by using the connectivity or the hop-distance information [2,3]. To obtain the ranging information, the multi-hop localization utilizes flooding [3]. The flooding is a simple approach to broadcast the location message through the network. The flooding enables the multi-hop localization to estimate the location even when the reference nodes are sparse in the network. In practice, the deployment of WSNs may suffer from limitations due to complicated situations such as the specialized area of
network and the lack of system configuration. The limited deployment of the nodes can make the network density highly irregular, and it can seriously degrade the performance of the localization. The representative problems are the broadcast storm [5] and the localization failure: if the nodes are densely deployed in the network, the multi-hop localization can increase the flooding messages which can cause the communication contention and collision in the localization [5]. The alternative approach is to use the onehop localization, which can reduce the communication overhead due to the redundant messages. However, when the reference nodes are sparse, the one-hop localization may produce the localization failure. In this paper, we propose a density adaptive localization for WSNs. The proposed approach controls the transmission of the location messages by using the fuzzy c-means (FCM) algorithm [6]. Moreover, the proposed approach dynamically selects the localization method according to the node density. The proposed density adaptive localization can overcome the network irregularities and thus improve the localization performance. If any node has sufficient neighbor reference nodes, it estimates its location by using one-hop localization. Otherwise, it estimates its location with the multi-hop localization. Through the proposed approach, the nodes can reduce the communication overhead due to the redundant messages, while maintaining the localization accuracy. Simulation studies show that the proposed approach reduced both the average location error and the communication overhead due to the irregular network density. 2. Problem statement
∗ Corresponding author. E-mail address: [email protected] (Y. Kwon). 1434-8411/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.aeue.2012.05.006
In this paper, we assume that the physical coordinates of the nodes are two-dimensional coordinates. First, each reference node
Y. Kong et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 1026–1031
1027
N(i)
d+1
Fig. 1. (a) Localization in the irregular network density and (b) redundant message problem in multi-hop localization.
periodically broadcasts the location message including its geographic coordinates. After receiving the message, each unknown node calculates the distance between itself and the reference node. When the number of distance information received from the reference nodes is equal to or above three, the node estimates its location by using the localization algorithm such as trilateration or multilateration [1]. If the reference node is within the communication range of the unknown node, the unknown node decides the reference node as the one-hop neighbor reference node. Otherwise, the unknown node calculates the distance to the reference node through the flooding approach. Fig. 1 shows the localization problem in the irregularly deployed WSNs. In Fig. 1(a), the unknown nodes in network area X have the sufficient one-hop neighbor reference nodes. The unknown nodes in region X can obtain their own location by using the one-hop localization. If the reference nodes are sparse as shown in the network area Y, the unknown nodes in region Y have insufficient neighbor reference nodes and thus the one-hop localization may cause the localization failure. An alternative approach, which can obtain the distance to the reference node, is to use the multi-hop localization. If the multihop localization is used in region Y, the nodes should perform the flooding procedure for the propagation of the location information. According to [3], each reference node periodically broadcasts its location message containing the node identifier (ID), the time to live (TTL), and the hop count. On receiving the location message, the node checks the hop count to the reference node, updates the hop count, and retransmits the same message to its neighbor nodes. Before the packet is retransmitted, the TTL field is decremented by 1 to limit the flooding of the location messages in the large area network. A TTL field includes the maximum number of hops that the message is transmitted. Fig. 1(b) shows the problem of the multihop localization in the region Y. As shown in Fig. 1(b), the reference node A broadcasts the location message. On receiving the message, the nodes u, v, and w retransmit the message, and this retransmission may severely produce the contention of the message with each other. Moreover, when the reference nodes A and B try to transmit the location messages simultaneously, the collision can occur due to many redundant messages. Those redundant message may cause the broadcast storm such as contention and collision problems [5]. Therefore, the localization approaches should be adaptive to the irregularly deployed networks .
Fig. 2. Flowchart of the proposed density adaptive localization.
3. Density adaptive localization In this section, we propose a density adaptive localization for irregularly deployed WSNs. Fig. 2 shows the flowchart of the proposed approach. First, the proposed approach controls the transmission of the location message by using the fuzzy c-means (FCM) algorithm. Next, the proposed approach performs the localization by dynamically selecting between the one-hop and the multi-hop localizations. We assume that each reference node j periodically broadcasts the message including the node ID and the d-dimensional location information. Upon receiving the broadcast message, the node i calculates the distance to the reference node j. To reduce the redundant messages due to the flooding, the node i determines the retransmission of the message by using the fuzzy c-means (FCM) algorithm. The FCM is an approach of clustering which allows one group of data to belong two or more clusters [6]. Let X = {x1 , . . ., xn } ⊂ Rd be a finite data set containing the d-dimensional location of the unknown nodes. The clustering problem is to partition the data set X into a set of c clusters (subgroups), and it can be represented as fuzzy sets F1 , F2 , . . ., Fc by minimizing the following object function Jm : Jm =
c n
um xi − vj 2 ij
(1)
i=1 j=1
where m is any real number greater than 1, uij is the membership degree of xi in the cluster j, xi is the d-dimensional location data of the unknown node i, vj is the d-dimensional location data of the reference node j, and xi − vj is d-dimensional norm expressing the similarity between any measured data and the center. xi − vj can ˜ j). Parameter m be obtained through the ranging information d(i, is weighting exponent, which controls the relative weights placed on each of squared errors xi − vj and it is decided between [0,∞]. For most data, when m is between 1.5 and 3, it can produce good performance results [7].
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Y. Kong et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 1026–1031
Reference node (Cluster head)
Unknown node B A
A
~ d (i, A) 1
B ~ d (i, B )
i
i
~ d (i, C )
(a) Flooding procedure
A
2
C
C
uiB
uiA
2
(b) Distance calculation u iA
B
u iB
i
u iC
uiC
1 1/ 2 (1 / 2 ) (1 / 2 ) 1 1/ 5 ( 2 / 1) ( 2 / 1) ( 2 / 2 ) 1 1/ 5 ( 2 / 1) ( 2 / 1) ( 2 / 2 )
(1 / 1)
C
(c) Determination of membership
(d) Resulting fuzzy sets
Fig. 3. Example of the proposed FCM clustering in WSNs.
The above clustering problem requires the centralized computation, but the membership value should be determined with the distributed method. An alternative approach is to utilize the ranging information for the other reference nodes k. Membership degree represents the degree of membership between the unknown node i and the cluster j (i.e., reference node). The unknown node i has a membership uij (between 0 and 1) in each cluster j, and memberships close to 1 signify a high degree of similarity between node i and node j. Meanwhile memberships close to zero imply little similarity between node i and node j. The node i determines the membership degree uij for the jth cluster center as follows: uij =
1 c
(2) 1/(m−1)
(xi − vj /xi − vk )
k=1
where vk is the location data of the reference node k which are collected by the node i, and xi − vk is a ranging information between nodes i and k. Fig. 3 shows the example of the proposed FCM clustering in WSNs. For simplicity, we assume that the reference nodes are only A, B, and C in the network and hop-to-hop distances are 1. In the network, the number of clusters is the same to the number of the anchor nodes. As shown in Fig. 3(a), first the anchor node broadcasts the message including its location and node identifier (ID). Upon receiving the message from the anchor nodes A, B, and C, the node i calculates the distance to the each anchor node and forwards the message to other neighbor nodes. After collecting the message for each anchor node, the node performs the clustering as shown in Fig. 3(c). In the FCM clustering procedure, all nodes have the membership degree (between 0 and 1) for each anchor node. The node i calculates the membership value of the each reference node by using Eq. (2). As shown in Fig. 3(d), the resulting fuzzy sets are
decided to the membership degree for each cluster, and the values uiA , uiB , and uiA become 1/2, 1/5, and 1/5 respectively. Based on the membership degree uij , the node i decides the retransmission of the broadcast message for the reference node j. The node i checks whether the membership degree uij is above some threshold T or not. The threshold T is adaptive to the node density: if the nodes are dense, T is set to high. If the nodes are sparse, T is set to low. If uij ≥ T, then the node i retransmits the broadcast message. Otherwise, node i drops the message. For adaptive transmission to the node density, we set the threshold T to the average value of the membership degree of neighbor nodes. Through the proposed approach, each node can control the retransmission according to the node density. After the retransmission based on the FCM clustering, the node i checks whether the one-hop localization is possible or not. The proposed approach performs the localization according to the number of one-hop neighbor reference nodes N(i). If N(i) is larger than d + 1, the proposed approach chooses to apply the one-hop localization. Otherwise, the proposed approach applies the multi-hop localization. If N(i) is equal to or above d + 1, the node i estimates its location by using the one-hop localization. Based on the least square estimation (LSE) approach, the estimated location of the unknown node is given by:
|N(i)|
xˆ i = argmin x0 ∈L
˜ j))2 (x0 − vj − d(i,
(3)
j∈N(i)
where xˆ i is the estimated location of node i, |N(i)| is the number of the neighbor reference nodes, vj is the coordinates of the reference ˜ j) is the ranging information between nodes i and j, and node j, d(i, · denotes the Euclidean norm. To solve the LSE problem, we utilize the minimum mean square error (MMSE) method [9–11]. This approach divides the network area into small grids and calculates the sum of the mean square error for each grid by using the ranging information of each reference node. The estimated location is
Y. Kong et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 1026–1031
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Table 2 Performance results in the randomly deployed WSNs.
Sparse deployment
100m
Performance results
1-Hop
Flooding
Proposed
Average location error (m) No. of location failure
1.35 m 29
2.69 m 0
2.1 m 0
ranging estimate between the device i and the device j is modeled as unbiased Gaussian estimates [8] and it can be written as: d˜ ij = dij +
where d˜ ij is the ranging distance, dij is the real distance, is noise of ranging distance and it is defined as Gaussian random variable of zero-mean with standard deviation. Parameter m is weighting exponent and we set m into 2 in the simulation. We conducted 10 independent simulation runs and calculated the average location error. The average location error ( u ) is defined as follows:
Dense deployment 2
5
1
(45 12) (45,12)
3
(70, 8)
7
4
8
6
(4)
9
u =
100m
N (xu − xˆ u )2 + (yu − yˆ u )2
N
(5)
i=1
Fig. 4. Example of irregular node deployment.
determined as the grid which has the minimum mean square error (MMSE). If |N(i)| is less than d + 1, the proposed approach estimates its location by using the multi-hop localization. Moreover, the node i ˜ j) satisestimates its location by using only ranging information d(i, fying condition that uij ≥ T. This approach can enhance the location accuracy by removing the distance measurement error due to large propagation of the message. The proposed approach can dynamically control the redundant messages and improve the location accuracy in the irregular network density. 4. Performance results To analyze the performance of the proposed approach, we performed the simulation by using the MATLAB simulation tool. In the simulation, the reference nodes and the unknown nodes are irregularly deployed in 100 m × 100 m network region. We assume that the maximum transmit range of each node is 25 m and all nodes can communicate with each other directly or indirectly through the flooding. In the initialization procedure of the simulation, the deployment of the nodes is initialized based on the configuration file, which has the number and locations of each node. Fig. 4 shows the example of the irregularly deployed network. First, we deploy the sensor nodes densely in the lower left corner. Meanwhile, we place the nodes sparsely in the upper right corner. By using the above procedure, we can create the irregularly deployed network. Simulation environments are described in Table 1. In Table 1, TTL field is time to live and it can be used for the measurement error due to large propagation of the flooding message when the networks are large. We set TTL to 5 for all scenarios because the network diameter is 100 m × 100 m and the maximum transmit range is 25 m. The
where N is the number of the simulation runs, (xu , yu ) is the true location of node u, and (ˆxu , yˆ u ) is the estimated location of node u. First, we compared the proposed approach (Proposed) with the one-hop localization (1-Hop) and multi-hop localization (Flooding) in the irregular network density. A node may fail in getting its own location when it does not have enough anchor nodes, or ranges are faulty, or the starting point of flooding is too far from the true position. In this paper, we call that failure as localization failure. As shown in Table 2, the one-hop localization can obtain more accurate location information compared with other approaches, but it produces the localization failure because of the irregular network density. Meanwhile, the multi-hop localization and the proposed approach have no localization failure, since all unknown nodes can obtain enough ranging information for localization through the flooding. Moreover, compared with the multi-hop localization, the proposed approach reduces the localization error about 26%. Next, we analyzed the total number of the transmission message and the average location error versus the node density. When the number of reference nodes is varied from 10 to 50, the number of unknown nodes is fixed to 20 in the network. When the number of unknown nodes is varied from 10 to 50, the number of reference nodes is fixed to 20 in the network. The transmission message is the flooding message in the multi-hop localization and the proposed approach. Fig. 5 shows the total transmission messages versus the number of the reference nodes. As shown in Fig. 5, the transmission
Table 1 Simulation environments. Parameter
Description
X R M N TTL m
Network side Maximum transmit range No. of reference nodes No. of unknown nodes Time to live Noise of ranging distance Weighting exponent for FCM clustering
Value 100 m 25 m 10–50 10–50 5 1m 2
Fig. 5. Transmission message versus the reference nodes.
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Fig. 6. Transmission message versus the unknown nodes. Fig. 8. Average location error versus the unknown nodes.
messages are increased as the reference nodes are increased. Moreover, the retransmission messages of the proposed approach is much less than the messages of the conventional flooding based localization approach. Fig. 6 shows the total transmission messages versus the number of the unknown nodes. The retransmission messages are increased as the unknown nodes are increased, and the messages of the proposed approach is less than the messages of the flooding approach. Performance results show that the proposed approach efficiently controls the retransmission of the messages by using the FCM algorithm. Finally, we compared the location accuracy versus the node density. Fig. 7 shows the average location error versus the number of the reference nodes. As shown in Fig. 7, the average location error is decreased as the reference nodes are increased. This result comes from the reason that as the reference nodes are increased, unknown nodes can collect more ranging information from reference nodes. Therefore, ranging accuracy is enhanced as the reference nodes are increased and it can reduce the location error of unknown node. Moreover, the average location error of the proposed approach is less than the location error of the flooding approach. When the one-hop neighbor nodes are sufficient, the proposed approach estimates the location by using the one-hop localization and thus its location accuracy is increased. Fig. 8 shows the average location error versus the number of the unknown nodes. The average location error is decreased as the unknown nodes are increased. The reason is that as the node density is increased, the ranging accuracy is enhanced and the average location error is decreased. As shown in Fig. 8, location accuracy improvement is very small between 20 and 40 nodes, compared with the location
improvement between 10 and 20 nodes. The results come from the reason that when the unknown nodes are 10, the network is sparse and thus unknown nodes have insufficient ranging measurement information for each anchor node. When the number of the unknown nodes is above some threshold value (i.e. ≥20), the network density is sufficiently dense and the unknown nodes have sufficient ranging measurement information for each anchor node. Therefore, when the number of unknown nodes is between 20 and 40, the location accuracy improvement is small compared with other intervals. The location error of the proposed approach is less than that of the conventional flooding approach. Simulation studies show that the proposed approach can reduce the communication overhead, while increasing the location accuracy. 5. Conclusion In this paper, we propose a density adaptive localization for the irregular network density. The irregularly deployed WSNs may produce the critical problems such as the localization failure and the redundant retransmissions. The proposed approach dynamically controls the transmission of the location messages by using the fuzzy c-means (FCM) algorithm. Moreover, the proposed localization dynamically selects between the one-hop localization and the multi-hop localization according to the number of the one-hop reference nodes. The proposed density adaptive localization can obtain more accurate location and reduce the retransmission messages in the irregularly deployed WSNs. Acknowledgment This paper was supported by Konkuk University in 2011. References
Fig. 7. Average location error versus the reference nodes.
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