LocaToR: Locating Passive RFID Tags with the Relative Neighborhood Graph

Yiyang Zhao, S. C. Cheung and Lionel M. Ni Department of Computer Science and Engineering

The Hong Kong University of Science and Technology Hong Kong, China

{zhaoyy, scc, ni}@cse.ust.hk

Abstract—Passive tags are widely used in many applications, for example, the supply chain, the food industry and ware-house management. In such applications, the location informa-tion of tags is very important. However, the uncertain proper-ties of Received Signal Strength Indicators (RSSI), various backscattering events on different power levels and the direc-tivity of readers prevent traditional ranging-based approaches working well in passive RFID systems. In accordance with our observations during experiments, we create a novel approach to locate a specific tag among objects. Although absolute posi-tions are difficult to obtain, we can estimate locations by build-ing a relative relationship between tags. To reduce the effect of the above limitations, we propose a range-free approach named LocaToR to establish a relative neighborhood graph. We implement our method on a real passive system. Taking environmental factors into consideration, we look at two situa-tions: a controlled chamber and a semi-open space. Experi-mental results show that our approach can obviously improve the accuracy of the localization system as well as save readers’ energy.

Keywords- Range-free localization; Passive RFID system; Relative location

I. INTRODUCTION

Radio Frequency Identification (RFID) is a type of auto-matic identification system. It is widely used in various ap-plications, such as supply chain management, inventory tracking, transportation payments, mobile payment, people and animal tracking, access control, warehouse management, health care, food safety guaranties and so on [1]. Since an RFID system not only provides identification information, but also generates extra information to help in location sens-ing, such as RSSI [2], RF phase status [3], reading range [4] and identification rate [5], the information can be directly applied in Real Time Locating Systems (RTLS), which sup-ports the tracking and locating of objects. In a general case, some inexpensive nodes, such as badges or tags, are attached to or embedded in objects. At the same time, readers receive wireless signals from those tags and calculate their locations.

RFID technology has a number of advantages for loca-tion sensing. First of all, RFID enables the identification of objects from a distance out of the line of sight. Secondly, RFID storage is larger than that of its counterpart, the bar code, and can incorporate additional information. This capa-bility allows RFID to adapt the requests of many applications. Thirdly, because tags can be rewritten in a short period, they can satisfy some applications which require frequent data

modification. Those features have enabled RFID technology to become a popular choice for object tracking.

One typical application is locating merchandise in a large warehouse. Generally, we put things on a particular shelf. If we want to find something, we need to know its location. Otherwise, we need to make a big effort to find it. Another application scenario is in a supermarket. When a customer checks out, the salesperson may want to check some dubious goods, the commodity location then becomes very important information. In a large scale warehouse or during a stock take of goods, if we want find a specific object, an intuitive way is to scan all tags and guess the position of the target. However, the cost of this method is too high.

Existing approaches for locating a specific object suffer the following drawbacks: cost, latency and inaccuracy. For example, there are two types of reader deployments used to detect a tag. One is to deploy many fixed readers or antennas, which cover particular regions. The deployment fee of this method is very costly. Another way is to use a handheld reader to do location sensing. Recently, some handheld RFID readers are available on the market. Since those types of readers are portable and easy to use, it is suitable for loca-tion sensing in a large warehouse. In general, the reading range of a handheld reader is around a few meters with an additional modular [6]. In the near future, the ability of read-ers will have improved due to new antenna designs and backing materials. Therefore, the mobile localization scheme based on passive systems may become a widely used ap-proach.

Our work is driven by observations during experiments. To estimate the localization performance of a passive RFID system, we conduct several preliminary studies. By analyz-ing experimental results, we have made a few interesting observations as follows.

� The readability of passive tags is sensitive to the transmission power of the reader. For a given dis-tance, the reading state of a tag under different pow-er levels of a reader is different. For example, a tag can either be read or not within a 1 dBm range.

� Incomplete reading of tags refers hidden information. From the physical layer viewpoint, even if a tag is not recognized by a reader, some information still can still be sent to the reader.

� The antenna of the reader is directional, which is dif-ferent to RFID systems. . Although it means that the traditional disc model does not work for directional

2010 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing

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DOI 10.1109/EUC.2010.31

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localization, the angle of the directional signal can give hints about locations of tags.

Based on our empirical studies, we propose a novel range-free approach named ‘LocaToR’ to determine the rela-tive positions of tags. In our approach, the identification rate (IR) is introduced as a localization parameter. At same time, the incomplete reading and directional property of the reader antenna provides extra information for localization. The con-tributions of this paper are listed as follows:

� We measure and analyze the relationship between the distance and identification rate. Instead of exist-ing approaches employing RSSI for estimation of distance, we apply a new statistic criterion, the identification rate of a tag, to build the distance re-lationship between tag and reader. An ordered set of tags represents the distances of tags in the reading range. The relative distance estimation scheme can increase the efficiency of the localization algorithm, as well as reduce the computational efforts and cost.

� According to our observations, we first present a rel-ative positioning approach using the incomplete reading information of passive RFID tags. The pro-posed scheme can reduce the energy cost. At the same time, the estimation error can be reduced too.

� Introducing the rigidity theory, we analyze the ener-gy efficiency and give a lower bound of the mini-mum scanning time. Although our approach is a coarse granularity method, the rigidity theory can still provide the lower bound.

To verify our method, we conduct real implementations in two representational scenarios: an anechoic chamber and an indoor room. The environmental factors are considered in both tests. The experimental results show that our approach can reduce the estimation time and provide a more accurate than intuitive solution. For different environments, the esti-mation error trend is similar, which means the proposed scheme not only works in ideal situations, it also operates under complicated circumstances.

The structure of this paper is organized as follows. The related state-of-the-art work is introduced in Section II. Ob-servations from preliminary experiments are explained and the problem is defined in Section III. In Section IV, some parameters used in our approach are discussed. In Section V, we use an example to illustrate our ‘LocaToR’ approach. The experimental setup and results are demonstrated in Sec-tion VI. Finally, we conclude our work and discuss future work in Section VII.

II. RELATED WORK

For obtaining the location of an object, many wireless technologies and techniques are proposed in the literature, especially for RF techniques, such as Wi-Fi, wireless sensor [7-10], bluetooth and RFID [11]. In classifying existing techniques, state-of-the-art approaches can be either of two categories: ranging techniques and range-free techniques. In ranging approaches, precise ranging parameters are com-monly used. For example, angle-of-arrival (AOA) methods use the accurate angle measurements of radio signals to cal-

culate the position of objects. On the other hand, range-free methods do not require precise estimators. Rough informa-tion is utilized, such as hop information and any severe changes to the RF signal. Since passive RFID systems work in a short range, a lot of works applying passive RFID tags as landmark points are proposed in robot control systems to control the movements of a robot [12].

A. Ranging Techniques Ranging techniques include the Time of Arrival (TOA),

Time Difference of Arrival (TDOA), Angle of Arrival (AOA) and RSSI based methods, which employ the ranging parame-ters. LANDMARC [13] is one attractive solution for locali-zation using RSSI information of active RFID systems. However, ranging approaches suffer some constraints, such as the high cost, long estimation delays and synchronization difficulty.

A simultaneous localization and mapping (SLAM) sys-tem for robot navigation based on RFID tags was presented by Haehnel et al [14]. A mobile robot carried a pair of direc-tional antennas, which can determine the range and angular position of detected tags relative to its current position. A Bayesian filter has been used for position estimation, when the angular dependence range of the RSSI is modeled statis-tically. The system was measured in a 780 m2 environment while passive reference tags were deployed at known loca-tions. The robot’s location can be estimated with a typical error of less than 2 m, by combining the range measurements with data obtained by odometry.

Besides the RSSI based approaches, the phase informa-tion of passive RFID systems has also been used in localiza-tion. In [15], the authors discussed three main techniques based on the phase difference of arrival, which are time do-main, frequency domain and spatial domain. The I-Q plane constructs a phasor space. The phase ϕ can be calculated by two vertical vectors. To examine the localization effect of TD-PDOA approaches, the authors deployed an experimen-tal portal. The results showed that the direction of movement and the point of center can be determined easily. Another work focused on active systems [16]. Using USRP for cap-turing the phase difference of two antennas, the authors ar-gued that the active tag can be traced reliably. Experimental results showed the motional detection based on the phase difference is accurate. However, phase based methods re-quire extra devices to monitor the channel. B. Range-free Techniques

Range-free techniques apply read range or communica-tion range information, such as hop count for wireless sensor network and reading range for an RFID system. Proximity based methods estimate the shape of the communication range.

Range-free techniques are widely used in RF based loca-lization algorithms [17]. Although the blocking effect of the signal of the active RFID system [18] is considered to be an interfering noise in normal applications, it provides the clue that an object is crossing the sensing area. The data mining approach was applied to find the frequent trajectory. Similar to this idea, the diversity of RSSI values of wireless sensors

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was a parameter of the range-free localization. Lot experi-ments showed that the proposed algorithm was suitable for many situations. The accuracy of range-free approaches can only be approximate, because the moving object may influ-ence more than one tag or node.

CRR [19] is a robot guiding scheme, which recognize the edges of the communication range of an RFID reader. The localization algorithm decides the position by estimating the intersection points of the directional traverses. Since the communication range of an antenna is an ellipsoid, the azi-muth centerline of two angles of the antenna can narrow down the possible position of a tag. This work employs prox-imity information to decide the position of the robot. Since passive tags are only deployed as reference points, the robot carries a reader, which increases the cost of the system.

III. PRELIMINARY EXPERIMENTS AND OBSERVATIONS Lot applications utilize passive RFID tags. This is be-

cause the tag is cheap and contains identification information. In general cases, each box or object is attached a tag to iden-tify. When a stack of boxes passed a gate, three antennas will try to read all the tags. However, the position and angle of antennas can affect the results. Therefore, we need to find the best position for the antenna to guarantee all the tags are rec-ognized. However, this generates the problem of how to find the position of a tag with little power.

If we want to locate a tag on a shelf in a large scale ware-house, one of the intuitive ways is to install lot of fixed read-ers. Each reader covers a determinate area, however this is way too costly and since it is a proximity-based approach, the precision is only approximate. Normally, each reader or antenna can only cover one shelf, so the reading field is close. Hence we suggest using a hand-held reader, which is a mo-bile device and can obtain all IDS of tags in reading range. One constraint is that the energy of the reader is limited.

When we conducted our preliminary experiments, we made three interesting observations: Different reading per-formances under different power levels, incomplete reading, and directional properties of antennas of tags and readers. We will explain these observations as follows.

A. Reading Performance under Different Power Levels The passive RFID system is a backscattering system.

When the energy emitted by a reader is received by a tag, it will bounce the id back to the reader. In this process, we de-fine the transmitting signal as the forward link and the back-scattering signal as the backward link. Since the path loss of

each link is related to the distance, the identification reada-bility of passive tags is sensitive to the reading power level.

The transmission power level can be adjusted according to the requirements of the working distance. For commercial readers currently on the market, the power level is usually from 15 to 30 dBm. In our study, we compare the perfor-mance of several power levels. Our experimental results show that the trend of the relationship between the distance and identification rate is similar except that the effective working distances are different. Another interesting observa-tion is that we can increase the power level of a reader to identify more tags in a fixed distance.

B. Incomplete Readings Normally, if a tag is in the reading range of an interroga-

tor, it will send its ID to the reader. To the contrary, when the power is not enough, the tag does not reply to the reader. However during our experiments we find some tags occasio-nally return incomplete EPCs. As shown as Fig. 1, a success-ful reading has information, such as ‘QueryRep’ and ‘ACK’ illustrated in (a). In contrast, an incomplete reading has the same information as (b), where the EPC of a tag is not com-plete.

The energy insufficient of passive tags is the main con-straint behind why incomplete readings exist. For a passive RFID tag, two power levels, as shown in Figure 2, determine its performance. The first one is the turn on power. We con-cern whether there is enough power to turn on a tag. The interception point of the red and white lines (two top lines) is the turn on power. The second is the backscattering power. We want to know backscattered RF signal reached the re-ceiver of the reader is strong enough to be detected correctly

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which is the interception point of the blue and green lines (two bottom lines). The green line gives the path loss of the backscattered RF signal. The blue line indicates the threshold level of the reader receiver. Eventually, the shorter range among these two ranges determines the read range of the tag by the reader.

There are three situations. If both the turn-on power and back-scattering power are strong enough, the tag will be rec-ognized successfully. In the second case, when the turn-on power is not enough, the tag will not respond to the queries from reader. Thirdly, if the turn-on power is higher than the threshold, and the backscattering power is not strong enough, an incomplete reading will occur. From the physical layer point of view, even when the signal is not complete, we still can recover some information, such as the tag ID, by decod-ing methods. For our approach, the tag ID can also be ob-tained by increasing the transmission power. C. Directional Properties of Antennas of Readers

Differing from the disc model of other wireless tech-niques, the communication mode of a passive RFID system is directional. The real antenna radiation pattern can be de-picted as a beam, which is like a cone-spheroid or an ellipso-id with fixed angles.

In general, the beam of the pattern of antenna can be ca-librated in the laboratory. If a tag appears within the reading range, it will backscatter its ID to the reader. We can adjust the sending power level to change the read rate and the RSSI value for each tag. Also, the shape of the signal beam will provide clues to the neighboring relation.

To understand the pattern of the RFID antenna, we con-duct experiments in our chamber. Figure 3 shows the setup. In the experiments, the d is an adjustable parameter. When d is set, we rotate the antenna from 0° to 360°by 5 degrees. The identification rate of each angle is recorded. In Figure 4, we find the sensitive angles of the antenna are from 45°to 150°. The identification rates from the sensitive angles are 0%. D. Problem Definition and Challenges

To clarify the influences of the above observations, we define the problem as follows. A large number of tags are attached in boxes. We have a reader which can change the power level for reading and has directional antennas. Our goal is find the specific tag. With as few as possible reading attempts, we establish a relative neighborhood graph for tags. There are some challenges listed as follows.

� RSSI is frustrated to estimate positions directly in a passive RFID system. The reason is that the RSSI is more unstable due to double path-loss effect intro-duced by the backscattering of the passive RFID sys-tem. However, some hints can still help us to make the decision.

� Since traditional localization approaches based on the disc model of signal propagation, existing ap-proaches do not work under the directional model of signals.

� Tag collision of the RFID system may affect the identification rate. When a number of tags appear in

the same location, a collision may happen. Since the collision will occupy the reading time slots, it affects the identification rate. One possible way to deal with this problem is by applying an anti-collision me-chanism. Another way is to increase the time slots for each reading frame.

IV. EMPLOYED PARAMETERS In traditional approaches, the RSSI value is widely used

as an estimator of distance. We would like to employ other new parameters, such as identification-rate (IR), directional information and neighboring signature (NS), to find posi-tions of tags.

A. Identification-Rate (IR) As we discussed in the above sections, the RSSI informa-

tion does not directly provide a precise relationship, even in a semi-open area. In passive systems, the situation is even more severe than for its counterparts in active systems. The diversity of meanings for RSSI values of different vendors is also quite broad. Therefore, traditional RSSI-based ap-proaches are difficult to apply directly in passive RFID sys-tems.

In common applications, the RFID readers only report the status of a tag in a binary way, either found or not. Fortu-nately, we can find another parameter of an RFID system, which is sensitive with the distance. Readers can send the ‘Query’ commands, which can be retransmitted many times within a short time interval. Normally, a communication round is defined as being when the interrogator sends queries to a tag and the tag answers those queries. The average time of each round is very short. Since the reader has various op-erating ranges at certain transmission power levels, such as identification range, read range, write range and interference range, we focus on the most relevant range with location estimation. We define the ‘Identification-Rate’ (IR) to de-scribe the ration of successful identification to all command rounds. The IR is a statistic parameter for a passive RFID system rather than a snapshot of the RSSI value. Compared with RSSI, IR is more stable. Some researchers find that the IR for a set of passive RFID tags has a connection with dis-tance [5]. However, they only consider the IR of a set of tags. In our work, the IR of each tag is used for deciding the rela-tive relationship.

The definition of our IR is little bit different to that of the traditional read rate for RFID systems. Normally, the read rate is the parameter to measure the reading capacity of a reader. For example, to recognize all tags, the read rate of the reader is more than 100tags/s. Differing from this concept, our IR is the ratio of the number of successful reading rounds to the number of total reading rounds. The time of each read-ing round is related to the number of slots. Normally, the time of each round is 10-15ms.

Even if we have neighboring sets, it is still difficult to de-cide what the relative order is between tags. For example, which tag is located in the center and which tag is near the boundary of the reading area? To deal with this, we can bor-row statistical information, which is more reliable than one individual test. In experiments, we setup the signal generator

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Figure 5. The realationship between distance and IR in the chamber Figure 6. The relationship in a semi-opened space

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to run numerous rounds of reading. This gives us the rate from which we can find the status information of tags. Ac-cording to the IR, we can establish the order of tags in the neighboring set. On the other hand, we can still use the RSSI information to decide the near-far relationship. Although RSSI values do not directly provide location information, they represent the tendency of distance.

Shown in Fig. 5, we measure the relationship between the IR and the distance on a single tag in a controlled chamber. From the results in the figure, we can understand that the trend of relationships under different power levels is similar. The lines with different colors represent the different power levels of the reader. The scope of the transmission power is in a range from 15 dBm to 30 dBm.

For an estimation of the environmental factors, we con-duct the experiments in a semi-open space and an indoor office. Figure 6 shows the experimental results in a semi-open space. We can clearly see that the IR falls more sharply than its counterpart in the chamber. The reason is that the RF reflection effect by the grounding materials reduces the pow-er in 1400mm. Therefore, the power reached in tags is not enough to energy them.

In the indoor office, people may deploy a lot of furniture. Figure 7 illustrates the IR collected in an indoor office. There is an outlier at around 1300mm. When we investigate this outlier, we find that a metal box is deployed near the experi-mental area. Hence the signal may be enforced at 1300mm, which causes the IR of tags to increase sharply.

B. Directional Information As discussed in the previous section, the antenna of the

passive RFID system is directional. When we adjust the an-tenna to different read angles, the identification results will vary. For example, in Fig. 8, we put two tags in one location. The distance of the two tags is far. We virtually divided the whole area into four regions. When the reader initially sends in the read command, we can see that tag A in the top-right corner was identified. After that, we adjust the angle of the reader to the bottom-left corner. Then only tag B is recog-nized in the second scanning, which means the position of tag B is located to the bottom-left of tag A. In the third at-tempt, we rotate the antenna in the lower-right direction. Neither tag A nor tag B was identified. This is an indication

that the directional properties of the RFID antenna can only provide location information in an approximate way.

In a real situation, the cross section of the antenna pattern with the sensing area is similar to a circle. We assume that the projection of the beam of the reader is a circle in the above example. C. Neighboring Signature (NS)

As discussed in the previous section, the IR of passive tags is a distance sensitive variable. In the localization process, we employ this information to estimate the position of the tags. For example, if the IR of one tag is 98% and another one is 67%, we decide the position of the first tag is close to the center and the second tag is far away from the center.

When the reader makes many queries in a short period of time, a set of tags may reply to those queries. According to the different IRs of tags, we can give the order of each tag in the set. We term this ordered set of tags as ‘Neighboring Signature’ (NS). For example, a result of a single scanning is a set {a,b,c,d,e}. The IRs of those tags are different as shown in Table 1. According to the relationship of the IR and the distance, we define the neighboring signature NSa as the set {a,e,d,b,c}. In the neighboring signature, the highest IR means that the tag is located in the center part of the reading area. At the same time, the RSSI may be used as a reference to determine the ‘near-far’ relation of the tags. For example, the maximum RSSI may indicate the tag is in the center. For

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the tags on the border, the RSSI values are not accurate. Since the deployment of tags is sparse due to the size of

each box being large, for each scan, we can find different NSs. Those NSs have some important features.

� An NS is unique for each scan at a specific reading angle.

� The NS can present some hidden tag information of , such as incomplete reading information.

� The size of each NS may increase, when the trans-mission power of the reader is raised.

Table 1 the different IRs of tags

Tag ID a b c d e IRs(%) 100 44 7 56 97

Although the NS can represent the ‘near-far’ relationship of tags, the distribution of tags is still hard to decide. There-fore, directional information must be introduced for confirm-ing the deployment of tags.

V. PROPOSED LOCATOR APPROACH Applying the available parameters introduced in the pre-

vious section, we design a new localization approach called ‘LocaToR’ for passive RFID systems. In this section, we describe the whole process in detail by providing an example.

A. An Example of the Localization Process To explain the localization process roughly, we assume

eight tags are deployed in the sensing area. The deployment is shown in Fig. 9, where tags are attached to the same side of each box, and the property of each tag is calibrated in the chamber. Therefore we can say that the performance of each tag is the same. For positioning, we divide our algorithm into following steps. In the first step, the reader reads the tags once. As seen in Table 2, each tag has its own IR.

Table 2 the IRs of first snap shot

Tag a b c d e f g h IR(%) 98 90 85 85 85 57 0 0

According to the IR, we can build a relative map as in Figure 10. Since tag g and h are in a state of incomplete read-ing, we increase the reading power by 1dBm. After that, we have a new NS containing all eight tags. To reduce the scan-ning cost, we can also recover the information for tag g and h by obtaining physical information. The scanning range of the

reader is shown in Fig. 12. The dashed line means an incom-plete range.

The second step applies the directional characteristics of antennas. We adjust the direction of the antenna to one cor-ner. As shown in Fig. 11, the new NS will be obtained. We will analyze the relationship of two NSs. The relative map can be updated by adding directional information.

Now that the graph is 2-dimension, the tags in the NS may have the tag flip situation according to some probabili-ties. In our algorithm, we assume that there are four possible regions in the entire reading area. For example, if the inter-section of two NSs provides the relative relations of tags, there might be 3 possible positions for the ordered set {b,d} as seen in Fig. 13. We term this flip the possible flip. To confirm the positions of tags, more readings are required.

According to our assumption, the whole area can be di-vided into four possible areas. When two or more NSs have intersected, the positions of tags can construct a relative map. However, the map is rough because of the flips. By repeating the directional readings, we can eliminate any impossible branches of tag pairs and establish a relative graph. During this process, the precision of each directional reading is rough because the reading angle of a hand-held reader is difficult to control in real applications.

In this example, we adopt the Neighboring Signature for each reading. By adjusting the reading angle of the reader antenna roughly, we can establish the relative relations of tags by comparing different NSs. We call the graph representing the relative relationships of tags the ‘relative neighborhood graph (RNG)’.

B. Decision Positions based on the RNG

After we build the relative position graph for all tags, the real position of a tag can be calculated by introducing the size of each box. Since we assume that for each box only one tag is attached, the positions of the tags are changed to de-cide which tag is to be located in the boundary of which box. In our experiments, the size of each box is about 0.3 meter.

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According to neighboring relationships, tags can be put in different scopes of boxes. However, the error may be the size of a box. The estimation errors will be displayed in the fol-lowing section.

VI. EMPIRICAL STUDY To evaluate the performance of our method, we conduct

experiments under various conditions with several passive RFID tags. The experimental results are reported in this sec-tion. At the same time, the energy efficiency of readers is also considered. A. Experimental Setup

As shown in Fig. 14, 30 passive tags (operating frequen-cy is 915MHz) are deployed in a 700mm×600mm board as a 5×4 grid. The central height of two antennas is same as the central height of the board. The tag was held in the monorail system, which is an automation system. The system supports the linear movement of the board, and the linear and rotation movement of the two antennas. The precision of the system is 1mm for linear movement and 1 degree for the rotation.

To compare the influence of environmental factors, we conduct tests in two different environments: a chamber and an indoor aisle. In real situations, the handheld reader utilizes a single antenna, which combines the transmitter (TX) and receiver (RX) together. Isolated by software, signals are transmitted and received by the same antenna. Therefore, the precision of the signal is lower than the separate antenna, also called dual antenna. To obtain reliable information, in our experiment, we employ two types of dual antennas. One comes from CSL and the other one is an ‘enterprise Mobility Company’ product. As illustrated in Fig. 14, both antennas are calibrated before the experiments.

To obtain the physical layer information, we use Labview software, which is short for ‘Laboratory Virtual Instrument Engineering Workbench’, to simulate the reader. It is a graphical programming environment containing two remark-able features: Graphical programming and Data flow repre-sentation. We can find the time waveform includes both the command and response signal. There might be several seg-ments of command and response in a real-time inventory sequence. The IR information can also be acquired directly from the software. B. Energy Efficiency

Since the hand-held reader is battery assisted, the energy consumption is a major concern. The optimal approach uses

as short as possible scanning time to do the localization. To estimate the scanning time, we define two scanning types as the scanning time. One is the power adjustment and the other is directional change.

According to the rigidity theory, for a network containing n nodes, a rigid graph requires at least 2n-3 edges. These edges are effective edges, without any redundancy. To en-sure global rigidity, the graph must have at least 2n-2 edges. If each scan can cover m tags, we assume the most effective edges are 2m-2. Hence, the lower bound to reach the global-ly rigid is

�N − 1m − 1� + λ

where the λ is a constant. If we consider the k factor, which means that k tags are in an incomplete reading state, the low-er bound is changed to the following equation.

� N − 1m + k − 1 − ξ� + λ′

where the λ’ is a constant and the ξ is a is a variable to adjust effective edges introduced by k.

According to discussion in previous sections, we analyze the lower bound of the energy consumption by using the rigidity theory. Figure 15 shows the results. The blue bar represents the intuitive scanning scheme. The green bar is the lower bound of our method, which does not consider the k factor. The brown bar is the lower bound with k factor. C. Localization Performance

We evaluate our approach by comparing the scanning time and the accuracy of localization. We define the estima-tion error as the disparity of the distance from real position of a tag to its estimated position. Figure 16 demonstrates the relationship between the estimation error and the number of scans. When the scanning time is larger, the localization re-sult is more accurate, unless the scanning time is larger than a certain threshold. In our evaluation, one scanning time in-cludes the power adjustment and the directional change.

To compare the performance of various location methods, we use the RSSI based triangulation method to calculate the position of tags. Figure 17 shows the experimental results. The red line is the RSSI approach. With the increase in the number of tags, the error of the RSSI based approach is in-creased. In contrast, our method is stable. Since the relative map ensures the measuring error within the size of one box, the maximum error is about 0.3m. We also estimate the situ-

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Figure 16. The relationship between scanning time and correct ratio Figure 17. Comparision of performences of different appoaches

0 1 2 3 4 5 6 7 80

10 %

40 %

60 %

80 %

100 %

Scanning Time

Cor

rect

Rat

io (%

)

10 15 20 25 300

0.3

0.6

0.9

1.2

Number of Tags

Max

imum

Est

imat

ion

Err

or (m

)

With k factorWithout k factorRSSI based approach

ation without k factor. The estimation error is higher than our method with k factor.

VII. CONCLUSION AND FUTURE WORK RFID systems are deployed almost everywhere, especial-

ly for passive systems. To support location based services, various approaches have been proposed. In this paper, we present a novel relative positioning scheme employing statis-tical information of a passive RFID system. Our approach uses the Identification Rate of tags (IR) to decide the rough relationship of their positions. The directional characteristics and the incomplete reading information help us build the relative graph of tags.

We implement our method in two different environments: a controlled chamber and a semi-open piazza. The experi-mental results show that our method has better accuracy than the RSSI based algorithm. Since the energy of the reader is limited, we analyze the energy efficiency with scanning time based on the rigidity theory. The total energy will be reduced if the k factor is introduced.

In our model, we assume that tags are deployed in one layer. For many applications, the deployment of tagged box-es is a type of multiple layers. The blocking effect of tags in the frontal layers is severe. Also, the irregular deployment is normal in real situations. Therefore, we need to build a new localization model for both deployments in the future.

ACKNOWLEDGMENT This research was supported in part by Hong Kong RGC

Grants HKUST617710, the RGC/GRF grant 612309, the ITF grant ITP/022/08LP from Hong Kong, China NSFC Grants 60933011 and 60933012, the National Hi-Tech R&D Pro-gram of China (863 Program) under Grant No. 2008AA01A324, the Science and Technology Planning Project of Guangdong Province, China under Grant No. 2009A080207002.

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