A Range-Free Localization Algorithm for Wireless Sensor. Networks .... similar to a routing table (we call it 'anchor table') to keep information about anchor ..... Conference of the IEEE Computer and Communications Societies. IEEE,. 2003, pp.
A Range-Free Localization Algorithm for Wireless Sensor Networks Qiqian Huang and S. Selvakennedy School of Information Technologies, Madsen Bldg. F09, University of Sydney, NSW 2006, Australia. {qhuang1|skennedy}@it.usyd.edu.au
Abstract-Distributed localization in wireless sensor networks has attracted significant interest in recent years. In this paper, we propose two improvements towards the DV-Hop algorithm: the anchor placement strategy and the Weighted DV-Hop algorithm. It is demonstrated that our proposals ensure better location estimations and the Weighted DV-Hop is expected to perform even better in actual implementations.
I. INTRODUCTION The wireless sensor technology is an emerging technology attracting considerable research interest in recent years. Recent development in MEMS technology has made it possible to produce cheap, small and smart sensor nodes. There are many interesting sensor network applications such as earthquake monitoring, target tracking and surveillance etc. These new applications require deployment of large number of sensor nodes over large geometrical areas, and their utility are dependent on an automatic and accurate location estimation of these nodes. This would lead to proper identification of significant event locations. In addition, accurate location estimation could also aid in sensor network services such as routing, information processing, tasking and querying [1], [2]. In distributed localization, there could be a small number of nodes, which have a priori knowledge about their coordinates. These nodes are usually called anchor nodes or landmarks. Apart from the anchor nodes, most of the other nodes (regular nodes) do not know their location at the outset. These nodes may have the capability to measure the distance or angle from their local neighboring nodes. Due to their limited power, communication between nodes is restricted to local neighbors. Based on such estimation, these nodes could realize their location through trilateration or triangulation. A feasible distributed localization algorithm should be easy to deploy, have good accuracy, promotes scalability, and be energy efficient. Among many of the distributed localization algorithms, APS DV-Hop [3] is a neat scheme which worth further investigation. It shows good accuracy, and is independent of distance measurement error. In this paper, we will focus on the DV-Hop algorithm and propose two enhancements: the anchor placement strategy and the Weighted DV-Hop algorithm. II. RELATED WORKS There has been significant research into distributed localization. For example, the ad hoc localization system
(AHLoS) [4] can be used when the percentage of anchor nodes are high. In AHLos sensor nodes discover their locations using a set of distributed iterative algorithms. This system represents three major types of multilateration: atomic, iterative and collaborative. This method can produce high quality estimation, when a good distance measurement technique is used. The disadvantages are that it needs high percentage of anchor nodes [2] and is dependent on distance measurement errors. The Ad Hoc Positioning System (APS) [3, 5] is also a distributed algorithm, which implements a method to forward range measurement so that all the nodes in the network could infer their distance to the anchor nodes and hence compute their positions. This algorithm aims to provide location estimates for all the nodes in the network with only limited number of anchor nodes. There are three methods of propagation: DV-Hop, DV-distance and Euclidean. In DVHop distances are propagated as number of hops, while in DVdistance the actual measured distances known from received signal strength are propagated, whereas in Euclidean the geometrically computed Euclidean distances between nodes are propagated. The detail of DV-Hop will be explained later in this paper. Hop-TERRAIN and Refinement proposed by Savarese et al [6] could be seen as an improvement over the DV-Hop algorithm. This algorithm aims to address the two primary obstacles to positioning in an ad-hoc network: the sparse anchor node problem and the range error problem. There are two phases in this algorithm: Hop-TERRAIN and Refinement. The Hop-TERRAIN is the start-up phase to get initial estimation of positions and is equivalent to DV-Hop. The Refinement phase is an iterative algorithm to increase the accuracy of position estimations done in the start-up phase. Overall, the performance of this method is comparable to other algorithms in the case of “easy” networks (high connectivity and many anchors), and performs better in difficult networks (where the sparse node and range error problems are more prevalent). There are also other distributed algorithms and they are somewhat similar. III.
BASIC MECHANISM OF DV-HOP
Although DV-Hop was introduced in some detail in earlier papers such as [3, 6], none of them are complete for others to reproduce and test in the same way to obtain similar results. Some details were missing, which may appear trivial but are crucial for others to fully implement this algorithm. For
example, Hop-TERRAIN [6] in principle is equivalent to DVHop, but Hop-TERRAIN authors were not clear about the reason why they obtained quite different accuracy performance compared with the results presented in [3]. Basically, in DV-Hop, all the regular nodes calculate shortest paths to all the anchor nodes and the shortest paths are represented in number of hops (no distance measurement involved here). Each anchor node also computes shortest paths to other anchor nodes. Once an anchor gets the information about all the other anchors, it can compute the Average Hop Size (AHS), which is the average ratio of distance and hop count to all the other anchors. The actual distance to other anchors can be easily computed using the true location of those anchors, which are broadcasted by anchors themselves. It then broadcast it to the regular nodes. The AHS value is used by regular nodes to obtain rough distance estimation to those anchors. For example, node A is 8 hops away to anchor B and its AHS is equal to 3.5 m, the rough distance of A to B would be 28 m. When a regular node knows the AHS value and paths to at least 3 anchors, it could perform a location estimation using trilateration. And this estimation will be updated each time new information becomes available, such as information of a new anchor node, a shorter path to a known anchor, or a new AHS value etc. The estimation will terminate (i.e. localization is done) when there are no more updates and the whole network becomes stable. There will be no more updates when all the shortest paths are formed, all anchors have calculated new AHS values based on the shortest paths to all the other anchors, and each regular node has received one of those final AHS values and did its final trilateration. Details about the shortest path formation, and subsequent message forwarding are introduced in following sub-sections. A. Shortest Path Formation From above it is clear that each node needs something similar to a routing table (we call it ‘anchor table’) to keep information about anchor nodes including IDs, locations and number of hops to each of them. Now let us look at how this table is formed and updated. At the beginning of the localization process, each anchor broadcasts a message stating its ID number, its location and a hop count of 0. We term it the ‘hop message’. Upon reception of such a message, the receiving node will check it against the information that already exists in its anchor table. If this is an anchor without an entry, it will simply increment the hop count by 1 then insert a new entry and rebroadcast the message to its neighbors. If this message is about a known anchor, it will compare it against the entry of the same anchor: (a) if this message indicates a shorter path to that anchor, it will update the entry and also rebroadcast this message after incrementing the hop count by 1; (b) if this message has an equal or larger hop count, it will be ignored and neither update nor forwarding will be done. Such updates and further broadcast will continue until all the shortest paths are found.
B.
AHS Forwarding and Update Another important type of message used in the scheme is the messages sent by anchors containing AHS values (termed the ‘AHS message’). It is observed empirically that an anchor needs to compute its AHS value more than once during the whole localization process. However so far none of the previous paper ever mentioned about the update and forwarding of AHS values that contribute to further overhead, and this makes it necessary for us to discuss this issue here. An anchor will compute the AHS value for the first time when information of all the other anchors is available, and then it will re-compute the value whenever there is an update in its anchor table. The AHS value is passed around the network in a controlled manner as explained in [3]. Each regular node will only keep and re-broadcast the first value it receives and ignore all consequent messages to avoid endless flooding. Usually a regular node will receive the first value from its closest anchor. In addition, an anchor node should ignore forwarding such AHS messages from other anchors. Even if an anchor forwards the message, its neighbors will most likely ignore it, because they may have already received a value from that anchor and any consequent messages are wasteful. The above process will stop when all the anchors have calculated AHS values based on the final shortest paths, and all the regular nodes have received the final updates. C. Location Estimation A regular node can calculate its location when there is known estimated distance to at least three anchors (in 2D) and an AHS value. A re-estimation of its location will be triggered when: (a) a new entry is added to its anchor table; (b) one of the existing shortest paths is update; or (c) a newer AHS value is received. It is obvious that location estimation of the whole network will terminate when there are no more updates. Since the location estimation is performed iteratively during the whole process, we term this approach the ‘iterative approach’. In the following section, we propose some enhancements to DV-Hop that could improve the estimation accuracy. IV. ENHANCEMENTS TO DV-HOP The main task of DV-Hop is the computation of shortest paths and the AHS value that are used by a regular node to obtain estimation of distance to anchor nodes. In trilateration, those estimated distances and anchor locations are used as inputs. Since true locations of anchors are known, the major and only source of localization error comes from the calculation of the AHS values. If we can find ways to improve the accuracy of estimation of AHS, the distance estimation could be improved, and this will results in smaller localization errors. Following are detailed descriptions of two strategies to improve the estimation of AHS: the anchor placement strategy and the Weighted DV-Hop algorithm. We term the DV-Hop algorithm we introduced before as the ‘standard DV-Hop’.
A. The Anchor Placement Strategy As anchors computes the AHS values, it is beneficial if the anchors can estimate more accurately. Here, we highlight how the placement of anchors improves this estimation. While experimenting with random placement of anchors, we observed that some anchors might end up placed too close to each other. As anchors add up the number of hops in all the shortest paths to other anchors, if some anchors are too close to each other, we will have unrealistic hop counts and the accuracy of AHS will be affected. The basic idea here is to place the anchors as far away as possible, so that there are many other nodes between each pair of anchors, and hence there will be more hops in the shortest path. Another phenomenon observed is that random placement of anchors also makes some regular nodes very close to some or even many of the anchors. This leads to worse estimation of distances to those anchors, since they are too close and the hop metric is not able to describe the distance between them. To resolve the above problems, we place the anchors on the boundary of the network, since the anchors are furthest apart from each other when they are placed such. The anchors are also equally spaced on the boundary. Furthermore, a regular node will no longer be too close to many of the anchors. Actually, if the density of anchors on the boundary is not high, a regular node will be close to only one or two of the anchors and all the other anchors would be far away from it in different directions. Adopting such placement strategy also obviates the need to a high density of anchors. Through experiments, it is found that fewer anchors are needed to achieve a better accuracy when the anchors are placed as indicated. It is feasible and inexpensive to fix just a few anchors on the boundary of the network. B.
Weighted DV-Hop This algorithm also seeks to improve the calculation of the AHS values. Using this strategy, a regular node computes a weighted AHS based on all the AHS values it receives from the anchors, instead of just taking the first received AHS message. In the standard DV-Hop, most of the regular nodes will receive an AHS value from the closest anchor, but this is not guaranteed in reality due to some unpredictable physical phenomena. Also from our observations, when there are many anchors, the AHS messages from some anchors are just wasted. Since each piece of information brings its own knowledge, it would be better if we can make full use of it. In order to make the AHS from the closest anchor have the greatest influence, we give each AHS a weight which is the inverse of the number of hops to that anchor. While adopting this strategy to the iterative standard DVHop, we found that it is not efficient both in terms of energy and storage space. Each regular node would have to store all the AHSs, as the anchors will re-calculate and re-broadcast AHSs, and each AHS value has the chance to be updated for several times. To overcome those inefficiencies, we implemented the Weighted DV-Hop algorithm in two steps, and we term it the ‘two-step approach’. The two steps are: the
messaging step where the shortest paths are calculated, and the location estimation step where each anchor computes AHS once and each regular node calculates its location once. It is obvious that this two-step approach will significantly reduce the amount of overhead and time to do estimation. And it also simplifies the estimation of our weighted AHS. Using this approach, each regular node calculates weighted AHS value in an incremental fashion and does not need to keep all the values. V. SIMULATION MODEL In order to verify the performance of above strategies, a simulator is developed in C++ using the discrete event approach. In our simulations, we could control several parameters (such as number of anchors used etc.) easily and fully due to its careful design. Furthermore, the simulator could be readily modified and extended for testing other distributed localization algorithms. Trilateration is the core task in most of the localization algorithms. All the location estimation depends on this step. The trilateration problem is the problem to solve a set of equations in the form: (1) ( x − x i ) 2 + ( y − y i ) 2 = d 2i where x and y are the unknowns, xi and yi are the coordinates of the ith anchor node, and di is the estimated distance between the unknown node and the ith anchor node. By subtracting the first equation from the others and rearranging, such system of equations can be reduced to the linear form of (2) 2 ( x i − x 1 ) x + 2 ( y i − y 1 ) y = d 12 − d i2 + x i2 − x 12 + y i2 − y 12 In our implementation, we choose to solve this problem using least squares by singular value decomposition [7]. Another point need to be mentioned here is the topology generation. In all the experiments, we used 100 regular nodes plus a specified number of anchors in a 100 mx100 m region. In order to make sure all the regular nodes would be distributed uniformly throughout the network, we divide the whole region into four quadrants and then randomly place 25 regular nodes in each quadrant. VI. RESULTS AND DISCCUSSION Each implementation is tested using different number of anchors (in the range from 3 to 50 anchors) and different radio ranges (from 18 m to 50 m). The reason why we choose 18 to be the smallest radio range is because this radio range will give us an average node degree greater than or equal to 7.5. According to [8], this connectivity will make the Noisy-Disk radio model sufficient and valid for simulation. This model has a disk like connectivity and a Gaussian ranging noise. Since DV-Hop is independent of range error, we only used the disk connectivity. A. Standard DV-Hop Firstly, we implemented and tested standard DV-Hop. Fig. 1 shows the estimation error vs. radio range. The anchor ratio for these simulations is about 0.09. As expected, the estimation decreases when radio range (i.e. connectivity) is
placement strategy, we plotted a random network topology together with errors in Fig. 5 and Fig. 6. In these graphs, small dark circles are anchor nodes and each circle is centered at the true location of each node. The size of each circle represents the amount of localization error, but the size of the circles in these two graphs is not to scale. We can see that for the same topology, when we increased the radio range from 18 m to 25 m, the error dropped dramatically from 93.95% to 39.47%, and variation of errors between nodes also became smaller. One more thing needs to be mentioned here is that the error is usually larger for nodes that are too close to anchors. This is because when a regular node is within one hop to an anchor, hop count is not an accurate metric to represent the distance. Error (in % of radio ran ge)
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increased. But the error tends to stabilize when the radio range is more than 30 m. Thus, in order to achieve the best estimation as well as avoid collision, 30 m seems to be appropriate. Fig. 2 shows the average estimation error vs. number of anchors with a fixed radio range of 25 m. As expected, accuracy increases quickly when number of anchors is increased from 3 to 10, while the improvement is much slower when there are more than 20 anchors. Overall, these results are not as good as those presented in [3], but are better than [6]. For example, Hop-TERRAIN obtained an estimation error of 69% with 10% anchors and an average node degree of 8%, while our result is 50% error when there are 9% anchors with radio range at 20 m. 80% 60% 40% 20%
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Figure 1: Accuracy vs. radio range with 10 anchors and 100 regular nodes. (Standard DV-Hop)
Figure 3: Accuracy vs. radio range with 10 anchors and 100 regular nodes. (The Placement Strategy)
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The Placement Strategy From Fig. 3, it is obvious that with the anchor placement strategy, we get much better results than standard DV-Hop. For example, when the radio range is increased from 20 m to 25 m, there is approximately a 10% reduction in estimation error compared to Fig. 2. When we fixed the radio range to 25 m, Fig. 4 shows much smaller variation in error when number of anchors is changed, compared with results shown in Fig. 2. This means that with such strategy, we only need use a small number of anchors and this could result in cheaper implementations. In order to show that connectivity has significant effect on the localization error and errors are larger at the boundary in
Figure 4: Accuracy vs. number of anchors when radio range is 25 m. (The Placement Strategy)
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Figure 6: Visualization of topology and error (anchors = 10, radio range = 25 m, error = 39.47%)
Weighted DV-Hop Here, two graphs of the results of weighted DV-Hop are presented. From Figs. 8 and 9, it appears that the performance looks slightly better than the placement only strategy. We believe that weighted DV-Hop is superior if we take into account real world situations as in [9, 10]. Currently, as mentioned before, we use a disk like connectivity in simulation. It is obvious that in reality, the distribution of power is not like a disk and there is also no guarantee that a node can always hear from a specific neighbor. Error (in % of radio range)
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Figure 7: Accuracy vs. radio range with 10 anchors and 100 regular nodes (Weighted DV-Hop)
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Figure 8: Accuracy vs. number of anchors when radio range is 25 m. (Weighted DV-Hop)
In this paper we presented a complete description of standard DV-Hop and clarified some gaps in previous papers. Due to incomplete description of the algorithm and simulation scenarios, there is always a gap among different implementations. For example, our results of standard DVHop are both different from [3] and [6]. The results we obtained are not as good as in [3], but better than [6]. The major source of errors in standard DV-Hop is identified and two enhancements are proposed: the anchor placement strategy and Weighted DV-Hop. With the anchor placement strategy, we have achieved a better accuracy with less number of anchors and this will result in a cheaper implementation. In addition to the placement strategy, the two-step implementation of Weighted DV-Hop is more efficient both in energy and storage space. Weighted DV-Hop also promises better estimation in simulation, and it could make greater improvements if real world situations are taken into account. REFERENCES [1]
C.-Y. Chong and S. P. Kumar, "Sensor networks: evolution, opportunities, and challenges," Proceedings of the IEEE, vol. 91, pp. 1247-1256, 2003. [2] D. Niculescu, "Positioning in ad hoc sensor networks," Network, IEEE, vol. 18, pp. 24-29, 2004. [3] D. Niculescu and B. Nath, "Ad hoc positioning system (APS)," Proc. of Global Telecommunications Conference, 2001. GLOBECOM '01. IEEE, San Antonio, TX USA, 2001, pp. 2926-2931. [4] A. Savvides, C.-C. Han, and M. B. Strivastava, "Dynamic fine-grained localization in Ad-Hoc networks of sensors," Proc. of the 7th annual international conference on Mobile computing and networking, Rome, Italy, 2001, pp. 166-179. [5] D. Niculescu and B. Nath, "Ad hoc positioning system (APS) using AOA," Proc. of INFOCOM 2003. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies. IEEE, 2003, pp. 1734-1743 vol.3. [6] C. Savarese, J. Rabaey, and K. Langendoen, "Robust positioning algorithms for distributed ad-hoc wireless sensor networks," Proc. of USENIX Technical Annual Conf., Monterey, CA, 2002, pp. [7] W. T. Vetterling, S. A. Teukolsky, W. H. Press, and B. P. Flannery, Numerical Receipes in C, 2nd ed: Cambridge University Press, 2002. [8] K. Whitehouse, C. Karlof, A. Woo, F. Jiang, and D. Culler, "The effects of ranging noise on multihop localization: an empirical study," Proc. of The Fourth International Conference on Information Processing in Sensor Networks (IPSN '05), Los Angeles, California, 2005, pp. [9] I. Stojmenovic, A. Nayak, and J. Kuruvila, "Design guidelines for routing protocols in ad hoc and sensor networks with a realistic physical layer," Communications Magazine, IEEE, vol. 43, pp. 101-106, 2005. [10] J. Kuruvila, A. Nayak, and I. Stojmenovic, "Hop count optimal positionbased packet routing algorithms for ad hoc wireless networks with a realistic physical Layer," Selected Areas in Communications, IEEE Journal on, vol. 23, pp. 1267-1275, 2005.
