This work is supported by Nature Science Foundation of Henan Province China (2008B120010, 2010A510015)

BP localization algorithm based on virtual nodes

in wireless sensor network

Runjie LIU, Kai SUN, Jinyuan SHEN School of Information Engineering

Zhengzhou University Zhengzhou China

E-mail: ierjliu@zzu.edu.cn

Abstract—Accurate localization of nodes is one of the key issues of wireless sensor network (WSN). Considering the proportion of beacons in the network, localization algorithm based on sub-anchors and BP network is proposed in this paper to virtually increase the number of the anchors, and the method of finding appropriate sub-anchors is brought up by the virtual nodes leading to higher localization accuracy. Such algorithm utilizes not only the parallelism of neural networks but also the hops of the nodes, so that it is simple and easy to achieve in the hardware. The simulation shows the effectiveness of using virtual nodes to find sub-anchors, and indicates that sub-anchors and virtual nodes based on BP neural network could greatly improve the accuracy of the unknown nodes and reduce the costs of WSN. Keywords-Wireless Sensor networks; Sub-Beacon; Neural Networks; Virtual Nodes

I. INTRODUCTION Wireless sensor network is widely used in military and

national defense, environmental monitoring, bio-medical and other areas. The locations of nodes in the networks are the necessary and basic information; therefore the accurate localization of unknown nodes is one of the most important issues in WSN. The localization technology requires energy-saving and effective localization algorithm based on the characteristics of WSN. The localization algorithm could be divided into two categories, named by Range-Based approach and Range-Free approach based on whether or not the network needs to measure the actual distances between nodes. The Range-based approach utilizes the distances or angles between nodes to achieve localization such as TOA[1], TDOA[2], RSSI[3] and AOA[4], so that it needs extra hardware supporting and large computing and communicating with high costs and high time-consuming. While the Range-Free approach only depends the connectivity of nodes such as the hops for localization without any extra hardware supporting. However, in general, the accuracy of the Range-Free approach is lower than the Range-Based approach.

In this case, how to improve the accuracy of Range-Free approach receives extensive attentions.

In the Range-Free approach, two typical algorithms are attached with much attentions: the Centroid Algorithm by Dragos Nicelescu [5] and DV-HOP by Nirupama Bulusu[6]. Current algorithms indicate the fact that the higher proportion of the beacons in WSN will lead to higher accuracy of the localization [7]. However, the increase of the beacons will cause the rising costs of WSN. In this paper, it will firstly utilize the BP neural network for the primary localization. In order to obtain higher accuracy of nodes, it proposes the algorithm utilizing the sub-beacons in WSN based on BP neural network. The introduction of the sub-beacons will virtually improve the proportion of the beacons, reducing the application costs of WSN. In order to search for appropriate sub-beacons, it brings forward the concept of the virtual nodes functioning to search for the appropriate sub-beacons. The simulation shows fewer localization errors of BP neural network. Moreover, it at the same time shows the effectiveness of sub-beacons to improve localization accuracy.

II. LOCALIZATION ALGORITHM BASED ON BP NEURAL NETWORK

A two-layer BP neural network is used to estimate the location of nodes. In view of simplifying the structure and the cost of the localization system, the centralized localization algorithm based on Rang-Free approach is employed. The minimum hop counts between different nodes are used as input information. The minimum hop counts could be obtained by the following way: the beacons broadcast their own information including the locations and the hop counts to their neighboring nodes. These nodes record such information. They ignore the received information in which the hop counts are larger than the former ones from the same beacons. Then, the receiving nodes add the count hops with one, and broadcast such packets to the neighboring nodes. Therefore, all the nodes in WSN could record the minimum hop counts.

For a WSN, there are N randomly employed nodes, which are marked by n=1, 2, ···N. The former M nodes are the beacons, and the remaining are unknown nodes. Bi= (xi, yi) denotes the location of the i-th node. The localization is to estimate the positions of the remaining (N-M) unknown nodes

978-1-4244-3709-2/10/$25.00 ©2010 IEEE

RA

C B

Fig1：Transformation of Hops

according to the positions of M beacons and some their inter-information such as distance or hops. Let sim denote the minimum hop count between the i-th beacon and m-th beacon. Let Si=[si1,si2,…sim…siM], i=1, 2, ···, M, m=1,2, ···, M. When i=m, sim=0. sjm is supposed as the minimum hop count between the j-th unknown node and m-th beacon. Let Sj= [sj1, sj2,…sjm…sjM] j=M+1, M+2, ···, N, m=1, 2, ···, M.

Hence, the number of the input layer neuron is decided by the beacon nodes. The number of the hidden layer neuron is chosen by the experimental experience. The number of the output layer neurons is two, indicating the coordinates of the nodes, (x, y).

The BP neural network is trained firstly by all the beacons. The input is the minimum hop counts, Si=[si1,si2,…sim…siM]; the output is the corresponding locations of the beacons Bi=(xi, yi)， i=1···M, m=1···M. Then the positions can be forecasted by the trained BP network. Input the minimum hop counts Sj, then obtain the position Bj= (xj, yj), j= (M+1, M+2···N), m=1···M.

For a WSN, there are N randomly employed nodes, which are marked by n=1, 2, ···N. The former M nodes present the beacons, and the remaining are unknown nodes. Bi= (xi, yi) presents the location of the ith node. The localization is then to calculate the locations of the remaining (N-M) unknown nodes according to the locations of M beacons and some their inter-information such as distance or hops. Let Si= [si1, si2…sim…siM] be the minimum hop counts among beacons, and sim indicates the minimum hop count between the ith beacon and mth beacon, i=1···M, m=1···M. When i=m, sim=0. Let Sj= [sj1, sj2…sjm…sjM] be the minimum hop counts among unknown nodes, and sjm indicates the minimum hop count between the jth unknown node and mth unknown node, i=1···M, m=1···M. The number of the input layer neuron is decided by the beacon nodes; the number of the hidden layer neuron is adopted by the experimental experience; the number of the output layer neurons is set to be two, indicating the coordinates of the nodes, (x, y).

III. LOCALIZATION ALGORITHM BASED ON SUB-BEACONS Many researches indicate that the increase of the beacons

will effectively improve the localization accuracy of the unknown nodes[7]. However, the larger proportion of the beacons will increase the costs of WSN. In order to effectively improve the accuracy of the localization and simultaneously save costs, the sub-beacons are proposed. It transforms some unknown nodes as the beacons.

How to select the good sub-beacons from all unknown nodes is a difficult problem. Theoretically, it should estimate the positions of all unknown nodes, and then select those nodes with more accurate localization as the sub-beacons. In fact, the real positions of the unknown nodes can not be obtained so that the errors between the real positions and estimated positions can not be known. To handle the problem, virtual nodes are introduced to select appropriate unknown nodes as the sub-beacons.

The virtual nodes do no exist in the reality, neither process the capacity to communicate with other nodes. We can

assume the virtual nodes do exist and randomly distribute in the network with accurate positions. Let the number of the virtual nodes as P with the respective positions Ck=(xk, yk). Let Sk=[sk1,sk2,…skm…skM], where skm indicates the least hop counts from the k-th virtual node to the m-th beacon, k=1,2,···P, m=1···M.

The localization of virtual nodes needs know the minimum hop counts between the virtual nodes and the beacons. The minimum least hop counts can not be directly gotten because the virtual nodes can not communicate information. We transform the distances between the virtual nodes and the beacons into the hop counts in this paper. Firstly computes the distances between the virtual nodes and the beacons, and then compares the distances with the wireless range of beacons. As shown in Fig1, A is a beacon, and B and C are two virtual nodes. R denotes the wireless range of A. It is clear that the distance between A and C is less than R (DAC<R), therefore the hop count is one-hop. The hop count between A and B is multi-hop because the distance between B and A is larger than R (DAB>R). In the situation of multi-hop counts, the hop count between A and B can not be directly fixed on by the distance. It needs to consider comprehensively the hop counts of B and neighboring nodes.

After obtaining the least hop counts between the virtual nodes and the beacons, we can use the trained BP neural network to estimate the positions of the virtual node. The input of the BP neural network is Sk=[sk1,sk2,…skm…skM], and the output is the position of the corresponding virtual node as the C’k = (x’k, y’k), k=1,2,···P, m=1···M.

Since the positions of the virtual nodes are assumed to be known, it is possible to compare the real positions with the estimated position of the virtual nodes Ck and C’k. Select Q virtual nodes with the minimum errors. Their hop counts to each of the beacon are indicated by Sq=[sq1,sq2, ···sqm···sqM], q=1,2,···Q, m=1···M. Assume that the positions with the same hop counts to each of the beacon are close. Based on this assumption, search for the unknown nodes having the same hop counts to each of the beacon with the Q virtual nodes. Finally name the founded unknown nodes as the sub-beacons.

As shown in Fig 2, assume that there are four beacons

(Nodes1-4, ●), 9 unknown nodes (Nodes 5-13, ○) and 8 virtual nodes (Nodes 14-21, △). The positions of the 8 virtual

Fig2: Searching for sub-beacons

21

20

19 18 17

16

14

13 12

10 9

8 7

6 5

4

3

2 1

15

25 30 35 40 45

8

10

12

14

16

18

20

22

Rang(m)

LE(m

)

BPVN-BPCebtroicDV-HOPRN-BP

Figure 3: Proportion of Beacons and LE

Figure 4: Proportion of Beacons and LE

5 10 15 20 2510

15

20

25

30

35

40

45

50

Proportion of Beacons (%)

LE

(%)

BPVN-BPCentroicDV-HOPRN-BP

nodes are estimated by the trained BP neural network. Then compare them with their real positions. Suppose the 16th, 17th, 19th, and 21th virtual nodes have smaller errors. Then search for the unknown nodes having the same hop counts with these 4 virtual nodes. Node 8 and 13 respectively have the same hop counts with 17 and 21 in this WSN. Therefore, Node 8 and 13 are selected as the sub-beacons.

Re-construct a new BP neural network after the sub-beacons are found. The new network still utilizes the two-layer structure. Train the network by the beacons and the sub-beacons. The positions of all the unknown nodes will be estimated after the training.

IV. STIMILATION AND ANALYSIS To find out the performance of the algorithm proposed in

this paper, The simulations under different conditions are completed for Centroid, DV-HOP, RN-BP (which selects the unknown nodes randomly as the sub-beacons), and VN-BP (which selects the unknown nodes as the sub-beacons based on the virtual nodes) . All the nodes in the simulation are randomly distributed in the area 100m×100m. The results of the forecasting of the BP neural network are influenced by the initial weighs; so that each set of the condition is run for 100 times so as to factually reflect the advantages and disadvantages of different algorithms. The average value of the localization error is used for the comparison.

Localization Error (LE) is defined as the ratio of the Euclid Distance between the estimated position and the actual position and wireless range:

RyyxxLE baba /)()(( 22 −+−= (1) Where (xa, ya) is the actual position of a certain unknown

node, and (xb, yb) is the estimated position, and R refers to the wireless range. Three conditions are simulated: (1) different R, same node number N and M/N (proportion of the beacons), (2) different M/N, same R and N (3) different N, same R and M/N.

A. Wireless Range and Localization Error In the first condition, it focuses on the different R. 200

nodes are randomly distributed in the network including 10 beacons and 190 unknown nodes. The curves of each algorithm are shown in Fig 3. In the same wireless range, the LE of the BP algorithm is less than the Centroid algorithm. When the wireless range is less than 40m, DV-HOP algorithm is less than the BP algorithm; while when the wireless range is larger than 40m, DV-HOP algorithm has more localization errors than the BP algorithm. The introduction of the sub-beacons makes VN-BP reduce the LE than the BP algorithm by 7.37% on average. It indicates the effectiveness of the sub-beacons in reducing LE under different wireless ranges. At the same time, the LE of the VN-BP is reduced by 7.42% than the RN-BP on average, indicating the effectiveness of the virtual nodes in reducing the LE.

B. Proportion of Beacons and Localization Error In the condition of different proportion of beacons, there

are 200 nodes in total with R being set as 40m. The result is shown in Fig 4. It is clear that the LE of the five algorithms declines as the proportion of the beacons increase. Under the same condition, the LE of the BP algorithm is reduced respectively by 14.806% and 10.35% than the DV-HOP algorithm and Centroid algorithm. Especially when the proportion of the beacons is larger than 15%, the LE of the BP algorithm declines rapidly. When the sub-beacons are introduced into the network, the localization accuracy of the VN-BP algorithm is better than the BP algorithm, and the LE is reduced by 3.656% on average. The LE of VN-BP is also lower than the RN-BP, reducing the LE by 2.346% on average. This reflects the effectiveness of the virtual nodes in different proportion of the beacons.

C. Number of Nodes and Localization Error In the simulation of different total number of nodes, the

proportion of the beacons is set by 10% and the wireless range is set by 40m. Fig 5 shows the result of the simulation. With the increase of the total number of nodes, in general, the LE of the five algorithms decreases. In the same condition, the BP algorithm is clearly better than the Centroid algorithm with 13.5% decrease on average. When the total number of nodes is 100, the BP algorithm has more localization errors than the

DV-HOP algorithm; however, when the total number of nodes is 200 or more, the LE of the BP algorithm rapidly goes down and becomes lower than the DV-HOP algorithm. After introducing the sub-beacons, the LE of the VN-BP algorithm is reduced by 5.866% on average, indicating the effectiveness of the sub-beacons in different total number of nodes in reducing LE; the LE of the VN-BP algorithm is reduced by 4.036% on average than the RN-BP, showing the effectiveness of the virtual nodes in reducing LE.

V. DISCUSSION AND ANALYSIS The simulations, on the one hand, prove the effectiveness

of the sub-beacons in the localization accuracy. Due to the LE declining as the proportion of beacons increases, the sub-beacons could effectively reduce LE for the reason that the sub-beacons virtually increase the proportion of the beacons. On the other hand, the simulations also prove the effectiveness of the virtual nodes. Comparing with RN-BP algorithm, the VN-BP algorithm could select those sub-beacons with better localization accuracy, and then reduce the errors of the training samples of the BP neural network, and finally reduce the LE.

VI. CONCLUSION The localization of nodes is a hot issue in WSN at

present. Considering the proportion of the beacons in the network, the proposed sub-beacons virtually increase the proportion of the beacons and reduce the localization error. In the comparison of the LE, whether in different wireless range, proportion of beacons and total number of nodes, the algorithm with sub-beacons is better than others without sub-beacons. Moreover, the algorithm VN-BP proposed in this paper has less localization errors in general than other algorithms. Therefore, VN-BP is suitable in WSN. However, there are still many problems that have not considered in this paper such as the influences of the distribution of the virtual nodes, the selected number of sub-beacons and so on. These problems are worthy of being studied in the future.

[1] A.Harter, A.Hopper and P.Steggle, “The Anatomy of a Context-Aware

Application”, Proceedings of the Annual International Conference on Mobile Computing and Networking, pp. 58-68, 1999.

[2] L.Griod and D.Estrin, “Robust Range Estimation Using Acoustic and Multimodal Sensing”, IEEE International Conference on Intelligent Robots and Systems, vol.3, pp. 1312-1320, 2001.

[3] D.Niculescu and B.Nath, “Ad Hoc Positioning System (APS) Using AOA”, Proceedings of the IEEE INFOCOM, vol.3, pp. 1734-1743, 2003.

[4] L.Girod, V.Bychovskiy and J.Elson, “Locating Tiny Sensors in Time and Space: A case study”, Proceeding of the 2002 IEEE International Conference on Computer Design, pp. 214-219, 2002.

[5] N.Bulusu, J. Heidemann and D.Estrin, “GPS-less Low Cost Outdoor Localization for Very Small Devices”, IEEE Personal Communications Magazine, vol.7, pp. 28-34, 2000.

[6] D.Nicolescu and B.Nath, “DV Based Positioning in Ad Hoc Networks”, Telecommunication Systems, vol.22, pp. 267-280, 2003.

[7] M.Yin, J.Shu. L.Liu and H.F.Zhang, “The Influence of Beacon on DV-HOP in Wireless Sensor Networks”, GCCW’06 Fifth International Conference on Grid and Cooperative Computing Workshops, pp. 459-462, 2006.

Figure 5: Number of Nodes and LE

100 200 300 400 5005

10

15

20

25

30

35

40

45

50

Number of Nodes

LE(%

)

BPVN-BPDV-HOPRN-BPCentroid