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PAPER
Special Section on Challenges in Ad-hoc and Multi-hop Wireless Communications
A Localization Scheme for Sensor Networks Based on Wireless Communication with Anchor Groups∗ Hiroyuki OCHI† , Shigeaki TAGASHIRA† , Nonmembers, and Satoshi FUJITA†a) , Member
SUMMARY In this paper, we propose a new localization scheme for wireless sensor networks consisting of a huge number of sensor nodes equipped with simple wireless communication devices such as wireless LAN and Bluetooth. The proposed scheme is based on the Point-InTriangle (PIT) test proposed by He et al. The scheme is actually implemented by using Bluetooth devices of Class 2 standard, and the performance of the scheme is evaluated in an actual environment. The result of experiments indicates that the proposed scheme could realize a localization with an error of less than 2 m. key words: sensor networks, localization, range-freeness, point-intriangulation test, Bluetooth
1. Introduction According to the recent advancement of network technologies, an expectation for location-aware services such as intelligent house and location-aware security services is rapidly growing [8], [10]. Those location-aware services are based on an identification of real-world environments, and such an identification is generally realized by a localization process, which tries to acquire the location information of user devices such as PDA and notebook PC, and associates them to a virtual space artificially organized in a computer network; i.e., by realizing a “bridge” connecting a physical space and a logical space [6]. As a means to identify the physical location of each user device, wireless communication with small IC chips, such as sensor nodes and IC tags, has attracted considerable attentions in recent years. In such systems, a user device can acquire its precise location through a short range communication with its nearby IC chips that have already been informed their precise location information, and this localization process naturally motivates another localization problem for those IC chips; i.e., the problem of how to deliver precise location information to a huge number of IC chips distributed over the given physical space. In this paper, we will consider this important and challenging localManuscript received May 30, 2005. Manuscript revised November 24, 2005. † The authors are with the Graduate School of Engineering, Hiroshima University, Higashihiroshima-shi, 739–8527 Japan. ∗ Earlier versions of some results contained in this paper appear in H. Ochi, S. Tagashira, S. Fujita, “A Localization Scheme for Sensor Networks based on Wireless Communication with Anchor Groups,” Proc. of the 11th International Conference on Parallel and Distributed Systems (ICPADS 2005), Fukuoka, pp.299–305 (2005). This research was partially supported by the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research. a) E-mail:
[email protected] DOI: 10.1093/ietisy/e89–d.5.1614
ization problem. More concretely, we propose a new localization scheme for networks consisting of a huge number of sensor nodes distributed over a given physical space such as market, library, factory, and so on. In recent years, there have been proposed a lot of techniques for the localization of mobile devices, which includes the utilization of trace logs [7] and the combination of several measurement techniques such as RF and ultrasonic pulse [9]. The localization scheme proposed in this paper is based on the Point-In-Triangle (PIT) test proposed in [3]. The PIT test is a basic tool to realize a localization with a range-free wireless communication; i.e., a localization of devices without measuring concrete distance and/or direction to specific devices called anchors. It should be noted that, as will be shown in Sect. 2, range-free localization schemes have a lot of advantages compared with rangebased localization schemes, including low hardware cost, low power consumption, and so on. The proposed localization scheme was actually implemented by using Bluetooth devices of Class 2 standard, and the performance of the scheme was experimentally evaluated in an actual environment. The result of experiments indicates that the proposed scheme could realize a localization with a sufficiently small error of less than 2 m. It improves the performance of a previous scheme [3] by about 25% to 65%, and in addition, we found that an increase of the computation time due to such an improvement is very small, i.e., less than 1%. The remainder of this paper is organized as follows. Section 2 is devoted to a review of related work. Section 3 describes our proposed localization scheme, and Sect. 4 outlines a prototype system implemented based on the proposed method. The result of experiments conducted on the prototype system is illustrated in Sect. 5. Finally, we conclude the paper with future problems in Sect. 6. 2. Related Work In a localization system based on wireless communication, the location of devices, which will be referred as nodes hereafter, could be acquired by directly communicating with several dedicated devices with their correct location information, which will be referred to as anchors hereafter. Anchors could be a satellite as in global positioning systems (GPS), or a kind of base stations as in cellular phone systems. Such wireless localization systems could be classified into two categories by the capability of communication devices, i.e., range-based type and range-free type, as will be
c 2006 The Institute of Electronics, Information and Communication Engineers Copyright
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briefly overviewed in this section (a detailed survey is given in [6]). 2.1 Range-Based Localization In range-based localization schemes, the location of each node is identified by using several metrics such as the distance to an anchor and its direction. An estimation of such metrics is carried out based on a theoretical model of signal propagation, with a concrete value of physical characteristics such as the strength of signals received from anchors (RSSI: Received Signal Strength Indicator), the time of arrival (TOA) of signals, and so on. GPS is a typical rangebased localization system based on TOA, which has been widely used in many application fields including car navigation systems and location-aware security systems. On the other hand, examples of RSSI-based localization systems include RADAR [1] and SpotON [5], which have been used to realize an alignment of materials in modern automated factories. Range-based localization schemes realize an accurate localization in many realistic situations. For example, the error of GPS is about few meters, and that of SpotON is reported to be few micrometers. However, it needs a special hardware to acquire precise values of several physical characteristics, and in addition, such a special hardware consumes a lot of electronic power compared with simple wireless communication devices [3]. Thus, we could not directly apply those schemes to a network consisting of a huge number of nodes fabricated as a small IC chip with a limited size and a limited battery capacity. 2.2 Range-Free Localization In range-free localization schemes, in contrast to rangebased schemes, the location of a node can be identified without directly estimating the distance and/or the direction to anchors. Thus far, several range-free schemes have been proposed in the literature [3], [4], and most of them are based on the communication with several anchors and the history of such communications. Among them, APIT [3] realizes an accurate localization of a node by approximating the Point-In-Triangle (PIT) test, a detail of which will be outlined in subsequent subsections. In general, the hardware cost for the range-free localization schemes is significantly low compared with that for range-based schemes, since it needs no additional hardware except for simple wireless communication devices. In addition, the amount of power consumption by the resultant system is expected to be very low, since it does not try to extract an accurate physical information from the received signals as in range-based schemes. Thus, range-free schemes are suitable to the localization in sensor networks, provided that the accuracy of localization could be as good as that of range-based schemes.
2.3 PIT Test Suppose that three anchors A, B, and C form a triangle in the given space. Let us denote this triangle as ∆ABC. The basic idea of the PIT test is to examine the inclusion of the location M of a node to ∆ABC by evaluating the change of the strength of signals received from three anchors around location M, where we are assuming that the strength of received signals monotonically decreases as increasing the distance to the senders. It should be stressed that this test merely tries to evaluate the relative strengths of two signals observed at two nearby points, and does not try to derive a concrete distance as being done in range-based schemes. By conducting such inclusion test for every triangle formed by anchors located in the given space, and by appropriately integrating those test results, we could realize a precise localization of a node (an integration method proposed in the previous paper will be outlined in Sect. 2.5). More concretely, inclusion of a node to a triangle could be tested by using the following proposition [3]: Proposition 1: The location M of a node is not contained in ∆ABC if and only if there exists at least one point M around M such that the strength of signals received from anchors A, B, and C at M simultaneously decrease, or equivalently, simultaneously increase compared with the signal strengths observed at M. See Fig. 1 for illustration. As is shown in the figure, if M is contained in the triangle, there are no direction in which the strengths of signals received from three anchors simultaneously increase or decrease (see (a)), while if M is not contained in the triangle, there is a direction in which the strengths of signals simultaneously decrease (see (b)). However, it should be noted that in practice, we cannot examine the change of signal strength for every direction around M, and have to make a decision by examining merely a finite number of directions. In addition, two observing points (i.e., M and its nearby point M ) cannot be closer than a threshold determined by the sensitivity of receivers. In other words, we have to introduce a kind of approximations to realize the PIT test in practice, even if we could directly realize it by moving the location of each node to its nearby points (of course, such a direct approach is not feasible if the system consists of a huge number of sensor nodes). The outcome of such an approximation inherently involves some error, especially when we could not find an evidence that M
(a) Fig. 1
(b) Explanation of proposition 1.
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is really contained in ∆ABC; i.e., the fact that “we could not find an evidence” does not imply the non-existence of such directions. 2.4 APIT Scheme In the same paper with the PIT test [3], He et al. proposed a practical localization method, called APIT, to approximate the PIT test in sensor networks with a large number of sensor nodes. The basic idea of APIT is to emulate the observation of signals at nearby locations of M by the observation of nearby nodes that have been distributed over the given sensor network. Although it could well approximate the PIT test provided that the observing nodes are distributed over the given space uniformly at random, it involves several problems listed below: 1. The resolution of the resultant localization scheme critically depends on the density of sensor nodes distributed around the observing node, and such a distribution could not be controlled in general. 2. Every node in the system must be equipped with a capability of scattering structured messages to the nearby nodes, which include a list of signal strengths received from each anchor. 3. Such a scattering of messages must be supported by an appropriate conflict resolution protocol such as CSMA/CA, which generally causes a significant increase of the hardware cost and the power consumption, compared with a simple signal receiver. 2.5 SCAN Integration Scheme Next, we will review the SCAN algorithm, which was proposed in [3] to efficiently integrate the result of several PIT tests into a localization information. SCAN is a procedure that is locally executed by each node. In addition, it assumes that a complete coordinate system is given to each node a priori; i.e., upon receiving a message from an anchor including its correct location in the space, the receiver could associate the received message with a point in the (locally held) coordinate space. The algorithm first partitions the given entire space into cells by a two dimensional regular grid of an appropriate resolution. Let C = {c1 , c2 , . . . , cm } be the set of resultant cells. Note that a signal transmitted by an anchor may not be observed by the node (i.e., several anchors may be invisible to the node) due to several physical constraints such as the transmission radius, the effect of noises, and so on. In other words, we do not consider a sensor network in which each pair of sensor and anchor nodes can communicate with each other, and we (implicitly) assume an infrastructure that enables multi-hop communication among those nodes although we will not use it in the proposed localization process. Let T be the set of triangles constructed by the set of visible anchors, and T (⊆ T ) be the set of triangles that are judged to contain the location of the node in it.
For each ci ∈ C, SCAN counts the number of triangles in T to have a non-empty intersection with the cell. Let ni denote the number of triangles intersecting with ci , and let C˜ be the set of cells c j such that n j = maxi ni . The scheme then outputs the centroid of cells contained in C˜ as the estimated location of the node. 3. Proposed Method Recall that the objective of the PIT test is to determine if the location M of a given node is contained in a triangle formed by three anchors, according to the change of signal strength measured around M. In the previous method, such a measurement of signal strengths around M is approximated by the exchange of measured strengths among nearby nodes, and an integration of those test results is realized by using a simple counting scheme. In this paper, we propose an alternative way to approximate the PIT test and a new integration method called ISCAN, which is an improvement of the SCAN algorithm. 3.1 Another Approximation of the PIT Test In this subsection, we propose a new method to approximate the PIT test. Consider a group of anchors, which will be referred to as an anchor group (AG, for short) in what follows. The anchor located at the center of the group will be referred to as the center anchor (C-anchor, for short), and the other anchors will be referred to as peripheral anchors (P-anchors, for short). In the proposed scheme, we assume that all anchors contained in the same AG can simultaneously move to any point in the space by keeping their relative distance and their relative direction; i.e., we do not allow an expansion and a rotation of AG while it could be shifted to any point in the space. Anchors contained in an AG (almost simultaneously) transmit signals including their concrete location to nearby nodes, where the position of an AG is represented by that of C-anchor. In other words, in the proposed scheme, C-anchors play the role of anchors in the original PIT test, and P-anchors emulate the observation at nearby locations. Note that since we are assuming that each AG can move to any point in the space, we could significantly reduce the number of anchors if it is allowed to spend a (relatively) long time duration for the localization process. In addition, it is possible to generate an appropriate schedule for each AG, which includes a set of points at which signal transmissions take place and an appropriate route connecting those points. Such a schedule could be calculated, for example, by the shape of the given space (i.e., a convex hull of node locations), the required resolution of localization, and the number of available AG’s† . A main reason of adopting the notion of AG’s in our proposed scheme is the temporal instability of the received † Probably a simplest schedule for a single AG is to move along the boundary of the space, and to transmit signals at points on the route with a fixed interval.
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signal strengths, which is commonly observed even if the locations of two communicating nodes are rigidly fixed. See Fig. 2 for illustration. This figure shows the temporal transition of RSSI values (of Bluetooth), where the distance from the anchor was ranged from 5 m to 20 m. Note that the unit for RSSI values is dB, and the measurement of the values starts from different time point for each fixed distance; e.g., the measurement for 5 m did not start simultaneously with that for 20 m. As is shown in the figure, due to temporal instability of RSSI values, two curves for different distances frequently cross; i.e., an assumption that the signal strengths monotonically decreases as increasing the distance to the anchor, no longer holds. Hence, in order to accurately emulate observations of the same signal at two different nearby points by the signal transmissions from two nearby points, those two signals must be transmitted almost simultaneously; i.e., they must be issued by distinct devices. On the other hand, it is also true that the transmissions from different anchor points in the original PIT test must not be issued simultaneously; in fact, in the proposed scheme, it is possible to simulate the transmissions from several anchor points by a single AG by repeating shift and transmission operations.
dition, since such an extension could degrade the accuracy of estimation for cells intersecting with a small number of triangles, we introduce an explicit noise reduction by using a median filter; i.e., by replacing the value of each cell by a median of its neighboring values including itself. A concrete procedure for ISCAN is described as follows. ISCAN (Improved SCAN) 1. Partition the given space into cells by a two dimensional regular grid. Let C = {c1 , c2 , . . . , cm } be the set of resultant cells. 2. For each ci , let αi (resp. βi ) denote the number of triangles in T (resp. T ) intersecting with ci , where T is the set of triangles visible from the observing node, and T (⊆ T ) is the set of triangles that are judged to contain the location of the node in it. 3. For each ci , γi ← 0 if αi = 0, and γi ← βi /αi , otherwise. 4. Apply the median filter to the resultant two dimensional data {γ1 , γ2 , . . . , γm }, and output the centroid of cells with a maximum value as the estimated location of the observing node.
3.2 ISCAN Integration Scheme 4. Implementation of the Proposed Method Next, we propose a new method to integrate the result of approximated PIT tests. Recall that in the SCAN algorithm, the number of intersecting triangles containing the observing location will be counted for each cell, and the centroid of those cells with a maximum count will be output as the result of localization. Hence, a cell intersecting with many triangles is likely to be selected as a cell with a maximum count, regardless of the actual inclusion of the observing location to triangles. To overcome such a problem of SCAN, in the proposed method, we focus on the ratio of the number of intersecting triangles containing the location as an interior point, to the total number of triangles intersecting with the cell. In ad-
Fig. 2 Temporal instability of signal strength. The horizontal axis is the elapsed time [sec], and the vertical axis is the RSSI value [dB] for each fixed distance to the anchor.
4.1 Hardware We implemented the proposed localization scheme by using Bluetooth devices of Class 2 standard [2]. Since Bluetooth devices have a unique identifier BD ADDR, the implementation is based on an assumption that each node can distinguish signals from different anchors. In the prototype system, an anchor group (AG) consists of one C-anchor and four P-anchors. Four P-anchors are located at the boundary of a circle centered at the Canchor with a uniform interval; i.e., four P-anchors form a square in an AG. The distance between C-anchor and a Panchor is fixed to 1.5 m according to the result of our preliminary experiments (see Sect. 5.1 for the detail). The system configuration is illustrated in Fig. 3. The behavior of a AG is controlled by a notebook PC; i.e., C-anchor is directly connected to a USB port of the notebook PC through
Fig. 3
System configuration of an anchor group (AG).
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USB cable, and P-anchors are connected to another USB port through USB hub and USB cables. Nodes receiving signals from AG are also realized by a Bluetooth device connected to other PC. The basic characteristics of each PC are as follows: CPU Pentium II 300 MHz, Memory 256 MB. 4.2 Procedure In the following exposition, we assume that the system contains exactly one AG. In the prototype system, AG transmits the following messages to its nearby nodes after moving to its next position: 1) C-anchor transmits a message containing its current location, and 2) each P-anchor transmits a message containing an instruction to measure the RSSI value. After receiving those messages, each node records the location of the C-anchor and the signal strength for each P-anchor in a table described below. Note that the above operations will be repeated until AG sends a termination message. The received information will be recorded by each node as in Table 1. Each row in the table corresponds to a location of AG, and the first column of the table corresponds to the location of the C-anchor. The remaining four columns correspond to the relative signal strength received from each P-anchor; i.e., the second column records value 1 if the signal strength received from the first P-anchor is greater than that from the C-anchor, and takes 0 otherwise. Note that each column in the table contains relative signal strengths received from the same P-anchor. After completing the communication with AG (by receiving a termination message), each node starts the PIT test for each triangle constructed by all the examined locations of AG; i.e., for each combination of three rows in the table. More concretely, if there exists i ∈ {2, 3, 4, 5} such that all of the three rows do not agree in the ith column, then the location of the node is judged to be contained in the triangle formed by the three anchor locations, and otherwise, it is judged to be an exterior point of the triangle. Finally, the outcome of those PIT tests is integrated by using ISCAN algorithm described in Sect. 3.2. Thus, by increasing the number of P-anchors that is fixed to four in our current implementation, the possibility of existing such a column i will increase, which implies that more nodes will be judged as interior points compared with the case of small number of P-anchors. Although such an increase of the number of Table 1 Table recorded by each node in the proposed localization scheme (each row corresponds to a location of AG). Location of C-anchor
P1
Relative RSSI P2 P3 P4
(x1 , y1 ) (x2 , y2 ) (x3 , y3 ) .. .
0 1 0 .. .
1 0 0 .. .
1 1 1 .. .
1 0 1 .. .
(xk , yk )
1
1
0
0
P-anchors could increase the accuracy of an approximated PIT test, it is not clear whether it actually increases the accuracy of the overall localization process since it also depends on the correctness and the stability of the received signal strength indicator (RSSI) and the accuracy of the integration process (i.e., ISCAN in our scheme), and thus, we will leave a detailed evaluation of such an improvement as a future work. 5. Experiments 5.1 Preliminary Experiment This section describes the result of experiments conducted to evaluate the goodness of the proposed scheme. At first, we conducted a preliminary experiment to determine an appropriate distance between C- and P-anchors in an AG. The objective of the experiment is to identify the minimum distance between C- and P-anchors that enables receiver nodes to correctly identify their relative position from the difference of RSSI values. First, locate two nodes, node 1 and node 2, in this order on a straight line starting from a signal transmitter. See Fig. 4 for illustration. Note that it models a situation in which node 1 receives signals from C-anchor and node 2 receives signals from a P-anchor. Under this setting, we conducted the following experiment: • The distance x from the anchor to node 1 was varied from 3 m to 9 m, and the distance y between nodes 1 and 2 was varied from 0.125 m to 4 m. • For each fixed x and y, each node measures the RSSI value of received signals ten times with a fixed time interval 0.1 sec, and outputs an average of them as the result of the measurement. We repeat the above measurement 100 times (for each pair of locations), and counted the number of measurements in which the output correctly reflects the relative location of the nodes. The result is summarized in Table 2. As shown in the table, if the distance y between nodes 1 and 2 is no smaller
Fig. 4
Environment for the preliminary experiment.
Table 2 The number of trials in which the output of the measurement correctly reflects the relative location of the nodes, among 100 trials. x [m] 3.0 4.0 5.0 6.0 7.0 8.0 9.0
0.125 61 54 52 59 52 51 52
0.25 74 65 62 65 63 60 60
0.5 85 79 77 73 79 71 75
y [m] 1.0 96 98 97 98 97 96 97
2.0 98 98 98 99 98 99 –
3.0 99 100 100 100 100 – –
4.0 100 100 100 100 – – –
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than 1 m, each node could correctly identify the relative location of those nodes with more than 95% of success rate for all range of the distance x to the anchor, provided that the anchor and two nodes are arranged on a straight line. Of course, an actual arrangement of two anchors and an observing node may differ from the arrangement examined in this experiment; i.e., they may not be placed on a straight line. However, if the distance between C- and P-anchors is (slightly) larger than 1 m, e.g., fixed to 1.5 m, and the arrangement of node and anchors is (sufficiently) close to a straight line, each node could correctly identify the relative location of two anchors from the difference of RSSI values. According to the above discussion, in the following experiments, we fix the distance between C-anchor and each Panchor to 1.5 m. 5.2 Setting for Experiments Our main experiments were conducted on the roof of our department building (A1-building) of about 40 m height. The shape of the given two dimensional space is a square of 16 m × 16 m, and in a localization process, AG moves along the boundary of the square in the clockwise direction, i.e., starting from location (0, 0), it visits locations (16, 0), (16, 16), and (0, 16) in this order, and stops the move at the starting point (0, 0). The interval between two transmission points on the route is varied from 2 m to 8 m, and the effect of the interval to the accuracy of localization will be examined in Sect. 5.4 (see Fig. 5 for illustration, where the interval between two adjacent transmission points are selected as 2 m in this figure). In the experiments, three nodes are placed on locations (8, 8), (4, 4), and (8, 4), respectively, and each of them executes independent localization process five times (the accuracy and the computation time of a localization scheme will be evaluated by taking an average over those five localization processes). For each location of AG, each node measures the RSSI value of received signals ten times with a fixed time interval 0.1 sec, and records an average of them to a table as the result of measurement as was explained in Sect. 4.
It should be noted that in the following experiments we do not make a direct comparison of our proposed approximation scheme with APIT, because it is very difficult to have an efficient realization of APIT due to several critical reasons observed in Sects. 2 and 4. Instead, in the following, we will focus our attention to the performance of integration schemes, and compare the accuracy and the computation time attained by SCAN and ISCAN integration schemes in detail. 5.3 Basic Comparison First, we examine the performance of two integration schemes by fixing parameters as follows: 1) the interval between two transmission points on the route is fixed to 2 m, and 2) the size of each cell used in the integration scheme is fixed to 0.5 m × 0.5 m. The result is summarized in Table 3 (note that this is an average over five localizations). We can easily see from the table (a) that the accuracy of the overall localization scheme apparently improves by using ISCAN instead of SCAN; in particular, the (average) error reduces to about 35% of SCAN for a corner location (4, 4), whereas it reduces to only 75% for the center location (8, 8). This result implies that the proposed integration scheme is particularly effective to improve the accuracy of localizations executed by a node located close to the boundary of the given space. On the other hand, an increase of the computation time due to such a significant improvement of accuracy is found to be very small. As is shown in Table 3 (b), although it slightly increases the computation time, the amount of increase is less than 1% of the computation time of SCAN, i.e., it could be neglected in practice. 5.4 Effect of Transmission Schedule Next, we examine the effect of the transmission schedule of AG to the overall performance. Table 4 summarizes the result. In the experiment, we adopted three transmission schedules for AG; in the first schedule, it transmits signals for every 2 m on the route (i.e., the total number of “anchors” is 32), in the second schedule, it transmits signals for every 4 m (i.e., the number of “anchors” is reduced to 16), and in the third schedule, it transmits signals for every 8 m (i.e., the Table 3 A basic comparison of SCAN and ISCAN (the interval between two transmission points is fixed to 2 m and the size of each cell is fixed to 0.5 m times 0.5 m). (a) Average error [m]. SCAN ISCAN
(8,8) 1.06 0.78
(4,4) 4.26 1.46
(8,4) 3.34 1.70
(b) Average computation time [sec].
Fig. 5
Environment for the experiment.
SCAN ISCAN
(8,8) 11.03 11.12
(4,4) 11.04 11.10
(8,4) 11.03 11.13
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(8,8) 1.06 / 0.78 2.59 / 1.28 3.02 / 1.87
(4,4) 4.26 / 1.46 5.09 / 2.33 5.12 / 3.81
(8,4) 3.34 / 1.70 3.42 / 2.52 4.02 / 3.40
(b) Average computation time (SCAN [sec] / ISCAN [sec]). Int. 2.0 m 4.0 m 8.0 m
(8,8) 11.03 / 11.12 1.39 / 1.39 0.18 / 0.18
(4,4) 11.04 / 11.10 1.35 / 1.36 0.19 / 0.20
(8,4) 11.03 / 11.13 1.42 / 1.43 0.18 / 0.19
(a) Map before applying median filter.
Table 5 Effect of the cell size (interval between two transmission points is fixed to 2 m). (a) Average error (SCAN [m] / ISCAN [m]). Size 0.25 m 0.50 m 1.00 m
(8,8) 1.02 / 0.79 1.06 / 0.78 1.10 / 0.93
(4,4) 4.25 / 1.40 4.26 / 1.46 4.68 / 1.62
(8,4) 3.20 / 1.66 3.34 / 1.70 3.75 / 1.81
(b) Average computation time (SCAN [sec] / ISCAN [sec]). Size 0.25 m 0.50 m 1.00 m
(8,8) 44.22 / 44.80 11.03 / 11.12 2.86 / 2.88
(4,4) 44.30 / 44.78 11.04 / 11.10 2.88 / 2.91
(8,4) 44.24 / 44.85 11.03 / 11.13 2.87 / 2.90
number of “anchors” is only 8). As is shown in the table (a), the effect of improvement by ISCAN is reduced by reducing the number of transmission points although it is still better than SCAN for all of the examined cases; e.g., in the third schedule, the error of localization reduces to 75% of the error of SCAN, while it was 35% in the first schedule. On the other hand, as is shown in the table (b), the computation time to integrate the result of PIT tests rapidly grows as increasing the number of transmission points; e.g., it increases to about 60 times by increasing the number of transmission points from 8 to 32. Note that such a rapid increase of the computation time is due to the increase of the number of triangles that should be examined in the integration scheme; in fact, the number of such triangles increases as 40, 280, and 2004, by increasing the number of transmission points as 8, 16, and 32 (it is almost proportional to a cube of the number of transmission points). The above results implies that we have to determine the interval of transmission points by carefully considering the trade-off between the accuracy and the computation cost. 5.5 Effect of the Size of Cells The accuracy of localization process also depends on the resolution of the two dimensional grid that is used to partition the entire space into a collection of small cells. Table 5 illustrates the effect of the cell size to the overall perfor-
(b) Map after applying median filter. Fig. 6
The effect of median filter to the γ values.
mance. It could be observed from the table (a) that we can really improve the accuracy of localization by reducing the size of each cell; e.g., the error of localization reduces to about 85% or 90% by reducing the cell size from 1 m × 1 m to 0.25 m × 0.25 m. Of course, such an improvement has been realized by spending more computation time. In fact, as is shown in Table 5 (b), the computation time increases to about 16 times by reducing the cell size from 1 m × 1 m to 0.25 m × 0.25 m. Hence, we have to take into account such a trade-off carefully when we apply the proposed scheme to actual localization processes. 5.6 Effect of Median Filter Finally, we demonstrate the effect of median filter used in the proposed integration scheme. See Fig. 6 for illustration. The vertical axis of the figure represents the γ value for each cell arranged in a two dimensional manner. As is shown in the figure, although the map of γ values contains several “peaks” immediately after being obtained by taking the ratio of triangles containing the node to the total number of triangles (see Fig. 6 (a)), such a peak will be “amortized” after applying the median filter to the map (see Fig. 6 (b)). This phenomena well explains the superiority of ISCAN to SCAN, since it indicates that an application of median filter well tolerates the flaw of the scheme that uses the ratio of triangles instead of a simple counting.
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6. Concluding Remarks In this paper, we proposed a new localization scheme for sensor networks consisting of a huge number of sensor nodes distribute over a given physical space. The proposed scheme was actually implemented by using Bluetooth devices of Class 2 standard, and the performance of the scheme was experimentally evaluated in a realistic environment. The result of experiments indicates that the proposed scheme could realize a localization with a sufficiently small error of less than 2 m. It improves the performance of a previous scheme based on the SCAN integration scheme by about 25% to 65%, and in addition, we found that an increase of the computation time due to such an improvement is very small. An important open problem is how to generate an optimal schedule for a given instance of the localization problem. Although it seems to be computationally hard to minimize several metrics such as the length of route and the number of transmission points, it should be a reasonable and a necessary approach to propose a heuristic scheme to provide a practically good solution to the scheduling problem. Another interesting problem is to improve the accuracy of the proposed localization scheme. We are now trying to do so, by increasing the number of P-anchors in an AG, and by increasing the number of signal transmissions for each fixed location. References [1] P. Bahl and V.N. Padmanabhan, “Radar: An in-building RF-based user location and tracking system,” Proc. IEEE INFOCOM, pp.775– 784, 2000. [2] Bluetooth: The Official Bluetooth Website. http://www.bluetooth.com/ [3] T. He, C. Huang, B.M. Blum, J.A. Stankovic, and T. Abdelzaher, “Range-free localization schemes for large scale sensor networks,” Proc. 9th MOBICOM, pp.81–95, 2003. [4] J. Heidemann, N. Bulusu, and D. Estrin, “GPS-less low cost outdoor localization for very small devices,” IEEE Pers. Commun. Mag., vol.7, no.5, pp.28–34, Oct. 2000. [5] J. Hightower, G. Boriello, and R. Want, “Spoton: An indoor 3D location sensing technology based on RF signal strength,” University of Washington CSE Report #2000-02-02, Feb. 2000. [6] J. Hightower and G. Borriello, “Location systems for ubiquitous computing,” Computer, vol.34, no.8, pp.57–66, Aug. 2001. [7] J.H. Kang, W. Welbourne, B. Stewart, and G. Borriello, “Extracting places from traces of locations,” Proc. 2nd ACM International Workshop on Wireless Mobile Applications and Services on WLAN Hotspots (WMASH’04), pp.110–118, 2004. [8] Q. Li, M.D. Rosa, and D. Rus, “Distributed algorithms for guiding navigation across a sensor network,” Proc. 9th MOBICOM, pp.313– 325, 2003. [9] N.B. Priyantha, A.K.L. Miu, H. Balakrishnan, and S. Teller, “The cricket compass for context-aware applications,” Proc. 7th MOBICOM, pp.1–14, 2001. [10] A. Ranganathan, R.H. Campbell, A. Ravi, and A. Mahajan, “ConChat: A context-aware chat program,” IEEE Pervasive Computing, vol.1, no.3, pp.51–57, 2002.
Hiroyuki Ochi received the B.E. degree in electrical engineering, M.E. degree in information engineering from Hiroshima University in 2003 and 2005, respectively. His current research interests include mobile computing and web-based computing.
Shigeaki Tagashira received the B.E. degree from Ryukoku University in 1996, and the M.E. degree and Dr. E. degrees in information science from Nara Institute of Science and Technology (NAIST) in 1998 and 2000, respectively. He is a Research Associate at Graduate School of Engineering, Hiroshima University. His current research interests include system software and mobile computing. He is a member of the Information Processing Society of Japan (IPSJ) and IEEE Computer Society.
Satoshi Fujita received the B.E. degree in electrical engineering, M.E. degree in systems engineering, and Dr. E. degree in information engineering from Hiroshima University in 1985, 1987, and 1990, respectively. He is an Associate Professor at Graduate School of Engineering, Hiroshima University. His research interests include communication algorithms on interconnection networks, parallel algorithms, graph algorithms, and parallel computer systems. He is a member of the Information Processing Society of Japan, SIAM Japan, IEEE, and SIAM.
