An improved distance vector-hop localization algorithm based on coordinate correction

Transcription

1 Research Article An improved distance vector-hop localization algorithm based on coordinate correction International Journal of Distributed Sensor Networks 2017, Vol. 13(11) Ó The Author(s) 2017 DOI: / journals.sagepub.com/home/ijdsn Xing Wang and Yunfeng Nie Abstract In order to improve the localization accuracy of distance vector-hop algorithm under the random topology network scenarios, a novel algorithm named coordinates correction-distance vector-hop is proposed. Coordinates correctiondistance vector-hop defines the pseudo-range error factor to improve the accuracy of average hop distance. In order to improve the localization accuracy, the unknown node uses distances to part of anchor nodes to locate. Furthermore, anchor nodes are treated as unknown when obtaining their coordinate correction values which are used to correct the localization results of unknown nodes. The simulation results show that each step of coordinates correction-distance vector-hop can increase the localization accuracy effectively; coordinates correction-distance vector-hop is better than the traditional distance vector-hop and some existing improved algorithms both in localization accuracy and in localization stability. Keywords Wireless sensor networks, distance vector-hop, node localization, average hop distance, pseudo-range error factor Date received: 19 May 2017; accepted: 17 October 2017 Handling Editor: Roberto Casas Introduction Wireless sensor networks (WSNs) are composed of plenty of sensor nodes deployed in the monitoring field. A multi-hop self-configured network can be further formed by means of wireless communication. 1 The sensor nodes with perception, processing, and communication ability need to locate themselves not only for reporting events but also for the target tracking in many applications. Examples include environmental monitoring, medical care, and military target tracking services. Sensory data will make no significance without the position information in many applications. Hence, node localization is a key issue of WSNs, and accurate and stable localization algorithm is essential for WSNs. Currently, many localization algorithms have been proposed to calculate the position of individual nodes. Based on the criteria whether it requires to measure the actual distances between nodes, the localization algorithms of WSNs can be classified into two categories, that is, range-based and range-free schemes. The range-based algorithms, such as time difference of arrival (TDOA), 2 received signal strength (RSS), 3 angle of arrival (AOA), 4 and time of arrival (TOA), 5 need to use the distance or angle information between neighbors to locate, and some of them may even need precise clock synchronization. These algorithms present very accurate results. However, the specialized hardware required makes them expensive in large networks, and in some applications, these algorithms are greatly School of Information Engineering, Nanchang HangKong University, NanChang, China Corresponding author: Yunfeng Nie, School of Information Engineering, Nanchang HangKong University, NanChang , China. nieyunf@gmail.com Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License ( which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages ( openaccess.htm).

2 2 International Journal of Distributed Sensor Networks influenced by the surrounding environment, which has limited the application of such methods to some extent. Due to the limitations of hardware and restrictions on high power consumption of the range-based algorithms, the rang-free algorithms, such as centroid algorithm, 6 approximate point-in-triangulation (APIT), 7 distance vector-hop (DV-Hop), 8 and multidimensional scaling-map (MDS-MAP), 9 are recommended as they use the estimated distance instead of the metrical distance to locate. In terms of accuracy, the range-free algorithms are not as good as those based on range, but they can still satisfy a number of applications requirements. With the advantages of relatively simple implementation, low power consumption, and low cost, rang-free algorithms are being pursued as a feasible alternative to the range-based algorithms in large-scale practical applications. The DV-Hop algorithm, as a range-free localization algorithm, aims to use the connectivity information to compute the shortest paths and the average hop distance (AHD) applied by the unknown nodes to obtain the estimated distances to anchors. 10 Then, those estimated distances and anchor locations are used as inputs in trilateration to locate unknown nodes. Since actual locations of the anchors are known, the major source of localization error comes from the AHD calculation. If the distribution of nodes across the network is uniform, DV-Hop can obtain a reasonable AHD, so as to achieve the appropriate positioning accuracy. 11 On contrary, as the networks where the nodes are disposed stochastically, the AHD is always bigger than the actual due to the shortest paths may be not straight-line between anchor nodes and unknown nodes. 12 In such cases, using the hopping distance to replace the straightline distance will cause a larger error and unsatisfactory positioning accuracy. Hence, an efficient way to improve the calculation accuracy of AHD has a crucial impact on distance estimated and localization accuracy. In this article, we propose an improved DV-Hop algorithm named coordinates correction-dv-hop (CC- DV-Hop). First, the pseudo-range error factor is defined to remove anchor nodes which may cause a larger calculation error of the AHD, through this way to improve the calculation accuracy of AHD, as well as to reduce the influence of random topology. Second, the anchor node broadcasts the corrected AHD together with its corrected coordinate values calculated by trilateral or multilateral measurement with the premise of being treated as the unknown node. Finally, the coordinates of each unknown node are corrected through the weighted average value of the coordinate correction values which are received from the corresponding anchors. We also present the simulations to demonstrate the effectiveness of CC-DV-Hop. The rest of this article is organized as follows. Section Related work gives a survey of the related works. Section DV-Hop localization algorithm describes the original DV-Hop algorithm. Section CC-DV-Hop algorithm presents the derivation of the proposed improved algorithm CC-DV-Hop. In section Simulation results and discussion, simulation results are shown and localization performances are discussed. In section Conclusion, conclusions are presented. Related work Since the AHD and the hop-count between the destination and the anchor nodes have essential impact on the localization accuracy of traditional DV-Hop algorithm, a number of approaches have been studied to improve the accuracy of AHD and hop-count. It is often considered that algorithms increase the accuracy of the AHD based on the selection of anchor nodes. Gui et al. 13 checked out DV-Hop algorithm and proposed the selective three-anchor DV-Hop algorithm. In this algorithm, the normal node first selects any three anchors to form a three-anchor group; then, it calculates the candidate position based on each threeanchor group; finally, according to the relation between candidate positions and the minimum hop anchor nodes, the normal node chooses the best candidate position. Wang et al. 14 calculated and optimized the coordinates of the unknown node that was set as the anchor node to increase the anchor node density, so as to improve the localization accuracy of DV-Hop. Xia et al. 15 proposed an improved algorithm based on regional division of hop-count. The received signal strength indication (RSSI) location technology and the hop-limitation mechanism are introduced to optimize the combination of anchor nodes to determine the coordinates of unknown nodes. Some previous works improve the accuracy of the AHD by weighting method. Hu and Li 16 used a hop threshold M that limits the unknown nodes to receive the beacon nodes with M hops. Then, the AHD is calculated using the weighting method, and the distances between nodes are also calculated to improve the localization precision under the limitation of M hops. Zhang et al. 17 introduced the weighted mean method to calculate the AHD. Instead of trilateration method, the centroid method is used to calculate the coordinate. Hou et al. 18 proposed differential DV-Hop (DDV-Hop) algorithm to improve the AHD applied by each locating node for estimating its own location through weighting the N received AHD from anchor nodes. The results show that DDV-Hop algorithm has higher localization accuracy compared with DV-Hop algorithm and Hop-count algorithm. However, some studies have been made on the correction of hop-count. Zhang et al. 19 proposed RSSI

3 Wang and Nie 3 and average hopping distance modifying DV-Hop (RADV-Hop) algorithm through using RSSI to subdivide one hop into several grades and modify AHD to reduce the locating error. Wen et al. 20 subdivided the first hop into several grades based on RSSI. The rest hops are modified to achieve higher location precision than traditional DV-Hop algorithm with the distance ratio of adjacent nodes which is transformed into the corresponding relationship of RSSI. Xiao and Liu 21 refined and made sure the hops between anchor nodes were not only integer but also decimal between all anchor nodes and unknown nodes. Simulation results show that it has obviously better localization performance in positioning accuracy than the traditional DV-Hop algorithm. Recently, considering the need of high localization accuracy along with energy consumptions has become a research hotspot. Kumar and Lobiyal 22 proposed a power-efficient range-free localization algorithm (PERLA) for WSNs. In PERLA, the anchor node floods packet just once, and one complete communication is eliminated to reduce the energy consumption. To improve the localization results of unknown nodes, PERLA adopts a new procedure to reduce error propagation. Simulation results show that PERLA is more computationally efficient and localization performance is superior to the traditional DV-Hop algorithm. Li 23 proposed an improved DV-Hop localization algorithm based on energy-saving non-ranging optimization. In this algorithm, only one anchor node broadcasts its position coordinate information to other node, thus reducing the energy consumption. To improve the localization accuracy, non-ranging energy-saving optimization algorithm is used to locate unknown nodes and the ratio of position is used to reduce the localization error. Simulation results show that compared with the traditional DV-Hop, the proposed algorithm has better results in localization accuracy and energy-solving performance. Liu et al. 24 restricted the hop-counts between unknown nodes and anchors to reduce the energy consumption. Moreover, they use the scheme of upgrading positioned nodes and a new weighted average one-hop distance processing method to guarantee the localization accuracy. Simulation and analysis results show that the new algorithm can effectively decrease the positioning error and total localization rounds to take account of both the energy consumption and the localization accuracy. In the first phase, each anchor node broadcasts a message to be flooded throughout the network which contains its location information and a hop-count parameter initialized to zero. Each receiving node maintains a table (x i, y i, hop i ), where x i and y i are the coordinates of anchor nodes it received and hop i is the minimum hopcount to the particular anchor node. If a received message contains lower hop-count to a particular anchor node, the corresponding item in the table will be replaced by the information in this message. And this message is flooded outward with hop-count values incremented by one. On contrary, if a received message contains a higher hop-count to a particular anchor node, this message will be ignored. Through this mechanism, all nodes in the network get the minimal hopcount to every anchor node. In the second phase, once an anchor i gets location and hop-count to other anchor nodes, the AHD of anchor i is estimated as in equation (1) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 2 x i x j + yi y j j6¼i HopSize i = P h ij j6¼i ð1þ where (x i, y i ) and (x j, y j ) are the coordinates of anchor i and anchor j, respectively; HopSize i is the estimated AHD of anchor i; and h ij is the hop-count between anchor i and anchor j. Once the HopSize i is calculated, each anchor node broadcasts its HopSize i to the network with controlled flooding. Unknown nodes receive HopSize i information and only save the first one. They transmit the HopSize i to their neighbor nodes at the same time. This scheme could assure that most nodes receive the HopSize i from the anchor node that has the least hops between them. When an unknown node u accepts the information from one anchor node, it computes the distance between itself and the anchor node as in the following formula d uk = HopSize i 3 hop uk ð2þ where hop uk is the minimum hop-count between the unknown node u and the anchor node k and HopSize i is the AHD that the unknown node u obtains from the nearest anchor node. DV-Hop localization algorithm The original DV-Hop algorithm is a distributed, hop-by-hop localization algorithm. The algorithm implementation is composed of three non-overlapping stages. In the third phase, each unknown node location can be estimated by the polygon method. Let (x u, y u ) be the unknown node u location, (x i, y i ) be the known location of the ith anchor node receiver, and d i be the ith anchor node distance to the unknown node u. We suppose that n

4 4 International Journal of Distributed Sensor Networks sensors are to determine the location of unknown node. Then, the unknown node u location can be acquired by equation (3) 8 ðx u x 1 Þ 2 + ðy u y 1 Þ 2 = du1 2 ðx u x 2 Þ 2 + ðy u y 2 Þ 2 = d >< u2 2 ð3þ >: ðx u x n Þ 2 + ðy u y n Þ 2 = dun 2 The system is solved to use a standard least-squares approach by the following formula 2 3 2ðx 1 x n Þ 2ðy 1 y n Þ 2ðx 2 x n Þ 2ðy 2 y n Þ A = 6 ð4þ ðx n 1 x n Þ 2ðy n 1 y n Þ 2 x 2 1 x2 n + y2 1 y2 n + d2 un 3 d2 u1 x 2 2 x2 n + y2 2 y2 n + d2 un d2 u2 B = ð5þ x 2 n 1 x2 n + y2 n 1 y2 n + d2 un d2 un 1 ð Þ U = x u y u CC-DV-Hop algorithm = A T 1A A T B ð6þ In this section, we use the traditional DV-Hop algorithm to calculate the initial AHD of each anchor node and propose to use the following additional steps added in order to improve localization accuracy, thus forming CC-DV-Hop algorithm. Correction of AHD Under the premise of DV-Hop idea, the number of hops among nodes is generally fixed. In order to obtain the minimum error between the estimated distance and the actual distance, CC-DV-Hop manages to adjust the AHD. According to the second phase of DV-Hop introduced in section DV-Hop localization algorithm, there will be a big error that each anchor node selects all the other anchors as the reference nodes to estimate an AHD, because some of them may produce a large error especially in the random topology networks. Therefore, CC-DV-Hop provides an approach to remove the reference anchors which may produce a large error through this way to improve the calculation accuracy of AHD. First, we define pseudo-range error factor of each anchor node to its reference nodes. For example, anchor N i calculates the pseudo-range error factor to the jth reference anchor as follows d diff err ij = ~ ij d ij d ij ð7þ where d ij and ~ d ij are the actual distance and the estimated distance between anchor N i and anchor N j, respectively. And ~ d ij can be calculated by ~d ij = HopSize i 3 hop ij ð8þ where hop ij is the hop-count between anchor N i and anchor N j and HopSize i is the average hop size of anchor N i. The smaller the value of diff err ij, the closer the pseudo-range to the real distance. Then, we sort diff err ij in ascending order and choose the top k(k 3) reference anchors to form an optimal group of anchors (OGAs i, k )ofn i to recalculate the AHD of N i by equation (9). Finally, N i uses HopSize k i to replace HopSize i as its AHD HopSize k i = P k d ij j = 1 P k j = 1 hop ij ð9þ Calculation of the coordinate correction value of anchor nodes Supposing anchor N i is an unknown node, N i locates itself by estimating its distances to each anchor among OGAs i, k. The distance between N i and the jth (1 j k) anchor node N j within OGAs i, k is calculated by equation (10) ~d ij = HopSize k i 3 hop ij ð10þ Since true location of N i is known, we can calculate the position correction values of N i by equation (11) Dx i = x i ~x i Dy i = y i ~y i ð11þ where (x i, y i ) and (~x i, ~y i ) are the actual and estimated coordinates of N i, respectively. In a similar manner, each anchor node can obtain its corrected AHD and coordinate correction values. Afterwards, each anchor node broadcasts its message packages to its neighbors with controlled flooding. The format of the package is fid, OGAs i, k, HopSize k i,(dx i, Dy i )g. In the example in Figure 1, we assume that all nodes are deployed randomly across the network. 1. After the first step of DV-Hop, anchor 1 calculates its AHD (HopSize 1 ) based on the distances

5 Wang and Nie 5 and hops from itself to its neighbors and obtain the estimated distance to other anchors by equation (8). After that, we calculate the pseudorange error factors of anchor 1 to reference nodes by equation (7). 2. We sort the pseudo-range error factors in ascending order and select the top k reference nodes to form OGAs i, k of anchor 1. Here, we set k = 5 and assume that anchors 2 6 are selected as the OGAs 1, Anchor 1 adopts equation (9) to acquire the corrected AHD (HopSize 5 1 ) and uses HopSize5 1 to calculate the distances to each reference node among OGAs 1, 5 to obtain its estimated position (E1). Afterwards, anchor 1 uses equation (11) to calculate its coordinate corrections. In a similar manner, each anchor node can obtain its corrected AHD and coordinate correction values. Then, anchor 1 broadcasts its message packages to neighbors and the format is fid = 1, OGAs 1, 5, HopSize 5 1,(Dx 1, Dy 1 )g. Optimization of the coordinates of unknown nodes As what we have introduced above, in DV-Hop, unknown nodes take the nearest anchor s AHD as their own, so do they in CC-DV-Hop. However, different from DV-Hop, an unknown node uses the distances to each reference node among its nearest anchor node s OGAs to locate in CC-DV-Hop. For example, unknown node n u uses HopSize k i received from its nearest anchor N i to estimate the distances to each anchor among OGAs ik and then uses trilateration to acquire the estimated coordinate (~x u, ~y u ). In WSNs, the nodes in close proximity have very similar physical environment (e.g. the electromagnetic environment, the multi-path effect, and interference noise) and topological structure. Therefore, if each unknown node and its nearest anchor node use the same OGAs to estimate their own coordinates, the coordinate correction values of them are similar. So, it is reasonable that the unknown node s coordinates are corrected by its nearest anchor node s coordinate correction values. Moreover, since the correction values of nodes obey Gaussian distribution under the topology random networks, the anchor node with the closer distance has a greater effect on the positioning accuracy of the unknown node. Thus, we define weights p i = 1=hop ui (hop ui is the hop-count between anchor N i and unknown node n u, N i within OGAs i, k ) to ensure the closest anchor node that will mostly affect the localization result. Then, we modify the coordinates of n u by equation (12). And (x u, y u ) is the final estimated coordinates of n u Figure 1. The concept of sections Correction of AHD and Calculation of the coordinate correction value of anchor nodes. 8 >< x u = ~x u + 1 k >: y u = ~y u + 1 k P k i = 1 P k i = 1 p i Dx i p i Dy i ð12þ Continue the example in Figure 1 and the example in Figure 2, suppose that we need to estimate the position of unknown node U. We assume that anchor node 1 is the nearest anchor node of unknown node U. 1. Unknown node U receives message package from anchor node 1. Then, U uses ranges between U and each anchor node among OGAs 1,5 to calculate the estimated coordinates U1 (shown in Figure 2(a)). 2. Finally, the coordinates of U1 and the coordinate correct values of OGAs 1,5 are used as inputs in equation (12) to acquire the localization result U2 (shown in Figure 2(b)). Simulation results and discussion Assuming nodes with the same communication radius are randomly distributed in the square region area with the fixed size of m 2, and we use Matlab2013a as the simulator to evaluate the performance of algorithm. The metric for comparison in evaluating localization algorithms is the average location error, which is shown as follows ave error = Xn i = 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (x i X i ) 2 +(y i Y i ) % ð13þ n 3 R

6 6 International Journal of Distributed Sensor Networks Figure 2. The concept of correcting estimated coordinates: (a) locating unknown node U and (b) correcting U s estimated position. where (x i, y i ) is the estimated coordinates, (X i, Y i ) is the actual coordinates, R is the communication radius, and n is the number of unknown nodes. In all of our graphs, each data point represents the average value of 200 trials with different random seeds. Validation of the improved effect in each step In this section, two new algorithms named CC-DV- Hop_1 and CC-DV-Hop_2 were proposed. For CC- DV-Hop_1 algorithm, only use the method in section Correction of AHD to correct the AHD and then use the procedure same as DV-Hop to locate unknown node. For CC-DV-Hop_2 algorithm, different with CC-DV-Hop, the last step (uses the coordinate correction values of anchor nodes to correct the coordinates of unknown nodes) of CC-DV-Hop is not employed. Compared to the localization results of the traditional DV-Hop with CC-DV-Hop_1, CC-DV-Hop_2, and CC-DV-Hop, we can learn the improved effect in each step of CC-DV-Hop. And the simulation results are given as follows. Figure 3 shows the comparison of the average localization errors in four algorithms. As shown in Figure 3(a), with the increase in ratio of anchors, the average localization accuracy of CC-DV-Hop_1 is about 10% lower than DV-Hop, that of CC-DV- Hop_2 is about 20% lower than DV-Hop, and that of CC-DV-Hop is about 5% lower than CC-DV-Hop_2; as shown in Figure 3(b), with the increase in node number, the average localization accuracy of CC-DV- Hop_1 is about 15% lower than DV-Hop, that of CC- DV-Hop_2 is about 17% lower than DV-Hop, and that of CC-DV-Hop is about 5% lower than CC-DV- Hop_2; as shown in Figure 3(c), with the increase in communication radius of anchor node, the average localization accuracy of CC-DV-Hop_1 is about 13% lower than DV-Hop, that of CC-DV-Hop_2 is about 15% lower than DV-Hop, and that of CC-DV-Hop is about 3% lower than CC-DV-Hop_2. It is obvious that CC-DV-Hop_1 can improve the localization accuracy of traditional DV-Hop, CC-DV-Hop_2 can do it better than CC-DV-Hop_1, and CC-DV-Hop can achieve the best localization accuracy. We can conclude that each step (e.g. correct the AHD and locate unknown node by nearest anchor s OGAs and the correct unknown node s coordinates) of CC-DV-Hop can effectively improve the localization accuracy. Analysis of localization accuracy In this section, CC-DV-Hop is compared with the traditional DV-Hop, the algorithm in Xiao and Liu, 21 and DDV-Hop in Hou et al. 18 We set k = bn=3c in CC- DV-Hop (the reason for setting can be seen in section Analysis of localization accuracy ). Varying the ratio of anchors. In this scenario, 200 nodes (including anchor nodes) are randomly distributed in the sensor area. Vary the ratio of anchors from 0.05 to 0.45 and set the communication radius of each node as 20 m. Figure 4 shows the comparison of the average localization errors in four algorithms. We can see that the average localization errors of these four algorithms above tend to decline gradually when the anchor is in 5% 25% ratio and become stable when the anchor ratio is greater than 25%. Under the same condition, the average localization error of CC-DV-Hop is about 24% lower than that of the traditional DV-Hop, about

7 Wang and Nie 7 Figure 3. Localization error of DV-Hop, CC-DV-Hop_1, CC-DV-Hop_2, and CC-DV-Hop in different networks: (a) comparison with different ratios of anchor (300 nodes, R = 20 m), (b) comparison with different node numbers (ratio of anchor = 30%, R = 20 m), and (c) comparison with different anchor node communication radii (200 nodes, ratio of anchor = 30%). 4% lower than that of DDV-Hop, and about 10% lower than that of literature 21 algorithm. The reason is that the growth of the ratio of anchor nodes will reduce the distance between unknown nodes and the anchor nodes, decrease the information loss, and lead to a relatively high accuracy. Moreover, with the increase in anchor ratio, each anchor node has more reference nodes to choose to form more precise OGAs. Therefore, CC-DV-Hop can improve the localization accuracy better. Varying node number. In this scenario, the anchor ratio is set as 30% and communication radius is set as 20 m, and the node number is increased from 100 to 400. Figure 5 shows the contrast of four algorithms with different node numbers. To a certain extent, we observe that DDV-Hop and the algorithm in Xiao and Liu 21 improve the accuracy of the DV-Hop, while the CC- DV-Hop improves the accuracy on a much larger scale. The accuracy improvement of CC-DV-Hop is about Figure 4. Comparison with different ratios of anchor. 5% over than that of DDV-Hop, about 6% over than that of the algorithm in Xiao and Liu, 21 and about

8 8 International Journal of Distributed Sensor Networks Figure 5. Comparison with different node numbers. 24% over than that of the traditional DV-Hop. We can conclude that CC-DV-Hop has better localization precision than the other three and is more stable for its fluctuation range smaller than the other three algorithms with the variety of node numbers. The reason is that the increase in node number will change the network topology which may affect the localization accuracy of DV-Hop. However, CC-DV-Hop only selects k reference nodes with lower pseudo-range error factors to recalculate the AHD and others are removed, so as to reduce the influence of random topology. Therefore, the number of nodes has little influence on the location accuracy and stability of CC-DV-Hop. Varying communication radius. In this scenario, the ratio of anchor nodes is set as 30%, node number is set as 300, and the communication radius of anchor node is increased 5 m every time. Figure 6 shows that the average localization error of CC-DV-Hop is approximately 22% lower than that of the DV-Hop, approximately 4% lower than that of DDV-Hop, and approximately 3% lower than that of the algorithm in Xiao and Liu. 21 It is worth mentioning that the algorithm in Xiao and Liu 21 has better accuracy than DDV-Hop when the communication radius is larger than 35 m; however, CC-DV-Hop performs better in those environments. We conclude that the change in communication radius has minimal impact on CC-DV-Hop, which means CC-DV-Hop has better stability. The reason is that the AHD is always bigger than the actual distance, especially under random network. Normally, the greater the number of hops is, the greater accumulative error in the AHD calculation is and the bigger pseudo-range error factors are according to equation (2). The node s communication radius will change the network connectivity, so as to influence hops between nodes and the AHD calculation. CC- DV-Hop removes some reference nodes with bigger Figure 6. Comparison with different anchor node communication radii. pseudo-range error factor to reduce the accumulative errors in the distance estimated through this way to increase the accuracy of AHD calculation. Furthermore, fewer nodes participating in the AHD recalculation would reduce the computational complexity as well. Discussion about the value of k In CC-DV-Hop, the value of k is the key factor in the relationship between localization accuracy and energy consumption. If k is too small, the improvement of positioning accuracy may not be obvious enough although the computational complexity can be reduced. If the value of k is too large, it will lead overmuch reference nodes to be used for modifying AHD and cause a waste of sensor node resource. So, it is not good for the value of k to get too big or too small, and we must choose the k value suitably according to the actual situation of network. In this section, we investigate the effect of the value of k on the localization accuracy via extensive simulations. Figure 7 shows the effect of value of k on localizaiton accuracy. We can see that as a whole, when 3 k bn=3c, the localization accuracy appears an increasing trend; when bn =3c k bn=2c, the localization accuracy appears the most excellent; and when bn=2c k N, the localization accuracy appears a decreasing trend. Therefore, when bn =3ck bn=2c, CC-DV-Hop algorithm obtains the optimal localization accuracy. Discussion about performance For communication cost, the proposed CC-DV-Hop algorithm does not change the positioning process of the DV-Hop, and sense node does not require additional communication cost. Therefore, the communication cost

9 Wang and Nie 9 show that the localization precision and stability of CC- DV-Hop are better than the traditional DV-Hop, DDV- Hop, and the improved algorithm in Xiao and Liu. 21 Moreover, when bn =3c k bn=2c, CC-DV-Hop algorithm obtains the optimal localization accuracy. Future directions for this work may include reducing computational complexity for CC-DV-Hop which is the main downside of that algorithm and find the balance between localization accuracy and energy consumption. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (No ). Figure 7. Effect of the value of k on localization accuracy. of CC-DV-Hop is nearly the same as DV-Hop, the algorithminxiaoandliu, 21 and DDV-Hop. For the computational complexity, in CC-DV-Hop, anchor nodes only use the information of anchor nodes in the DV-Hop to calculate the corrected AHD and the coordinate correction values without additional hardware support, which will increase the computational complexity. However, less anchor nodes involved in the location of unknown node will decrease the computational complexity of CC- DV-Hop. Although the computational complexity of CC-DV-Hop is slightly higher than DV-Hop, it greatly improves positioning accuracy (about 25% 35%) and stability of DV-Hop. Compared with the algorithm in Xiao and Liu 21 and DDV-Hop, CC-DV-Hop improves the localization accuracy about 8% and 5% in the case of almost the same complexity. Conclusion In this article, CC-DV-Hop has been presented to enhance the positioning accuracy of DV-Hop under the random topology network scenarios. Simulation results References 1. Akyildiz IF, Su W, Sankarasubramaniam Y, et al. Wireless sensor networks: a survey. Comput Netw 2002; 38(4): Cheng X, Thaeler A, Xue G, et al. TPS: a time-based positioning scheme for outdoor wireless sensor networks. In: Proceedings of the 23rd IEEE annual joint conference of the IEEE computer and communications societies (INFOCOM 04), Hong Kong, China, 7 11 March 2004, pp New York: IEEE. 3. Shen H, Ding Z, Dasgupta S, et al. Multiple source localization in wireless sensor networks based on time of arrival measurement. IEEE T Signal Proces 2014; 62(8): Torrieri DJ. Statistical theory of passive location systems. IEEE T Aero Elec Sys 1984; 20(2): Girod L and Estrin D. Robust range estimation using acoustic and multimodal sensing. In: Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Maui, HI, 29 October 3 November 2001, pp New York: IEEE. 6. Bulusu N, Heidemann J and Estrin D. GPS-less low-cost outdoor localization for very small devices. IEEE Pers Commun 2000; 7: He T, Huang CD, Blum BM, et al. Range-free localization schemes for large scale sensor networks. In: Proceedings of the 9th annual international conference on mobile computing and networking, San Diego, CA, September 2003, pp New York: ACM. 8. Niculescu D and Nath B. Ad hoc positioning system (APS). In: Proceedings of the IEEE global telecommunications conference (GLOBECOM 01), San Francisco, TX, November 2001, pp New York: IEEE. 9. Shang Y, Ruml W, Zhang Y, et al. Localization from mere connectivity. In: Proceedings of the 4th ACM

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