Efficient 3-dimensional localization for RFID systems using jumping probe

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Efficient 3-dimensional localization for RFID systems using jumping probe Honglong Chen a,∗ , Guolei Ma a , Zhibo Wang b , Jiguo Yu c , Leyi Shi d , Xiangyuan Jiang a a

College of Information and Control Engineering, China University of Petroleum, Qingdao, PR China

b

School of Computer, Wuhan University, Wuhan, PR China

c

School of Information Science and Engineering, Qufu Normal University, Rizhao, PR China

d

College of Computer and Communication Engineering, China University of Petroleum, Qingdao, PR China

article

info

Article history: Available online xxxx Keywords: Jumping probe Localization efficiency RFID 3-dimensional localization

abstract Radio Frequency Identification (RFID) technology manifests its potential in widespread applications, such as warehouse management, library maintenance and product tracking, etc. One of the most important characteristics for RFID-based applications is their 3Dimensional localizability. Recently, researchers have proposed some 3-Dimensional RFIDbased localization schemes, but most of them suffer from low efficiency. In this paper, we target at improving the efficiency of RFID-based localization, including energy efficiency and time efficiency, without sacrificing localization accuracy. The main idea is to adopt a ‘‘jumping probe’’ in distance estimation, based on which we propose the 3-Dimensional RFID-based localization schemes called JumpLoc, including a passive scheme two active schemes. In the passive JumpLoc scheme, a target tag will be located based on the estimated distances between itself and some reference readers. While the active schemes include basic and enhanced active JumpLoc schemes to locate a target reader. We numerically analyze the localization efficiency improvement of the proposed JumpLoc schemes. We also conduct simulations to validate their effectiveness, the results of which show that the passive JumpLoc scheme can improve the energy efficiency and time efficiency by at least 56% and 34% respectively, and the active JumpLoc schemes can improve the energy efficiency and time efficiency by at least 82% and 83% respectively. © 2016 Published by Elsevier B.V.

1. Introduction Radio Frequency Identification (RFID) [1–3], as an emerging technology, has gained increasingly widespread applications in industry [4,5], especially with the explosive development of Wireless Sensor Networks (WSNs) [6–11] and Internet of Things (IoTs) [12]. An RFID system typically consists of two basic components—reader and tag, the communication between which does not rely on line-of-sight. Moreover, RFID tag becomes smaller and smaller with a very low price. The above features make the large-scale RFID applications [3] possible, and many applications, such as health monitoring [13], library maintenance [14] and product tracking [15] can greatly benefit from utilization of RFID systems with security and privacy [16–18] considerations.

∗

Corresponding author. E-mail address: [email protected] (H. Chen).

http://dx.doi.org/10.1016/j.pmcj.2016.12.002 1574-1192/© 2016 Published by Elsevier B.V.

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Localizability [19,20] is one of prerequisites for many location-based services. However, one of the most challenging issues in RFID-based applications is the acquisition of location information of either the tags or readers [3]. Thus, RFIDbased localization [21–24] (especially 3-dimensional localization) has been an active research topic recently. The traditional RFID-based localization approaches adopt the received signal strength indicator (RSSI) to either estimate the rough distance between the target tag and reference reader [25] or rely on the fingerprinting method [26]. However, RSSI may fluctuate severely due to various environmental factors such as temperature and humidity, making the localization accuracy of these approaches unsatisfied. An RFID-based 3-Dimensional (3D) positioning scheme is then proposed in [21], which does not rely on RSSI. In [21], some reference tags or readers are deployed with fixed locations in advance, then the distance between a target tag and reference reader can be approximated as the distance between a reference reader and a reference tag, which can be obtained easily via Euler distance calculation. Following the research work in [21], there are two main directions to either improve the localization accuracy [27–29] or improve the localization efficiency [30]. In this paper, we will focus on improving localization efficiency without sacrificing accuracy. RFID-based localization efficiency includes energy efficiency and time efficiency [30]. Energy efficiency can be measured by the number of tag responses, while time efficiency can be measured by the execution time of the localization procedure. The efficiency will dominate the localization performance in large-scale RFID systems. Our main objectives are threefold: (1) improving the energy efficiency, i.e., reducing the number of reference tags involved in localization; (2) improving the time efficiency, i.e., reducing the number of time slots to complete the localization process; (3) improving the accuracy or at least not deteriorate the accuracy. Our main idea is to adopt a ‘‘jumping probe’’ in the distance estimation, which is the basis of the localization procedure. We firstly propose a passive scheme to locate a target tag based on estimated distances between itself and some reference readers. Then we propose two active localization scheme to locate a target reader. The main contributions of this paper are summarized as follows.

• We propose to adopt a ‘‘jumping probe’’ to estimate distance between a tag and a reader, which can effectively improve the localization efficiency in RFID systems;

• We propose a 3D localization scheme called JumpLoc, including a passive scheme to locate a target tag and two active schemes to locate a target reader;

• We numerically analyze the proposed JumpLoc schemes and other existing ones to illustrate their localization efficiency improvement;

• We conduct simulations to validate the effectiveness of our proposed JumpLoc schemes. The simulation results show that the passive scheme can improve the energy efficiency and time efficiency by at least 56% and 34% respectively, and the active schemes can improve the energy efficiency and time efficiency by at least 82% and 83% respectively. The rest of this paper is organized as follows. Section 2 reviews the existing RFID-based 3D localization schemes. Section 3 describes the proposed jumping probe based passive 3D localization scheme with the numerical analysis on localization efficiency. In Section 4, the proposed jumping probe based active 3D localization schemes are presented and the localization efficiency is numerically analyzed. Section 5 evaluates our proposed jumping probe based 3D localization schemes with other existing ones through simulations. Section 6 concludes this paper. 2. Preliminary work One of the earliest 3D RFID-based localization schemes is the SpotON [25], which measures the distance between an AIR ID tag and an AIR ID reader based on the receive signal strength. SpotON includes off-line phase and on-line phase. In off-line phase, the RSSIs corresponding to different known distances are measured by the reference reader, the location of which is fixed and known. In on-line phase, the target tag moves with a periodical broadcast, then its nearby reference readers can measure the received signal strength, which can be used to estimate the distance by searching the distance-to-RSSI relationship built in the off-line phase. The location of the target tag can then be easily estimated through least squares fitting [31]. LANDMARC [26] is a fingerprinting-based localization scheme in RFID systems, which also includes off-line phase and on-line phase. In off-line phase, an RSSI map is built. And in on-line phase, k nearest neighboring reference tags are selected by matching the current RSSIs with the RSSI map, after which the weighted centroid of the selected k nearest neighboring reference tags is considered as the reader’s position. The common limitation of the SpotON and LANDMARC schemes is the instability of RSSI in communications, which may fluctuate greatly due to various environmental factors such as temperature and humidity, making the localization accuracy of these approaches unsatisfied. To get rid of the negative effects of the RSSI’s instability on the distance measurement, Wang et al. [21] propose a passive and an active RFID-based localization schemes, the distance measurement in which does not rely on RSSI. In the passive scheme, some reference readers and reference tags are deployed at known locations on the ceiling as shown in Fig. 1. It is named ‘‘passive’’ scheme because the target to locate is a passive tag, which will passively wait for the reference readers’ queries. The readers are equipped with tunable transmission power levels, which can be up to 38 [21]. To estimate the distance between a reference reader Rr to a target tag Tt , Rr can read tags with an increasing transmission power level until it firstly reads Tt with level l. Table 1 lists the frequently used notations in this paper. Then the reference tags, which can be read by Rr with level l + 1 but cannot be read with level l, can be identified by Rr , and then the average distance between each of them and Rr can be considered as the distance estimation between Rr and Tt . After getting the distance estimations from Tt to at least three reference readers, the location of Tr can then be estimated using the Simplex method [32].

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Fig. 1. Passive 3D localization in RFID system. Table 1 Terminology. Notation

Description

Rr /Rt Tr /Tt i ,j Rt

Reference reader/tag Target reader/tag Reference tag in ith row jth column Radius of reader’s on-floor/on-ceiling communication region Length/width/height of the localization space Spacing distance of the grid topology Number of reference tags in each row/column Number of reference readers/tags Transmission range of reader with power level l Estimation of Rl Actual distance between reference reader and target tag Estimation error of dl /d Midpoint of vi and vj Distance between vi and vj Density of reference tags Number of involved tags/time slots of JumpLoc scheme Number of involved tags/time slots of collect all scheme Number of involved tags/time slots of probe some scheme

Rf /Rc L/W /H d Nr /Nc Nrr /Nrt Rl dl d el /e Mid(vi , vj ) d(vi , vj )

ρ

Njl /Njlts ts Nca /Nca ts Nps /Nps

The other scheme proposed in [21] is named ‘‘active’’ scheme, since it aims to locate a target reader, which can actively read the reference tags. As shown in Fig. 2, only reference tags are necessary, which are deployed at known locations on both the ceiling and floor. When localization is required, the reader can activate some tags on both the ceiling and floor with a high enough transmission power level, for example, l. Then the radius of the reader’s communication region on the ceiling Rc (and on the floor Rf ) can be estimated. Assume the coordinates of the target reader are (x, y, z ), then the coordinates (x, y) can be easily obtained as the center of the reader’s communication region on the ceiling or floor. The coordinate z of the target reader can be estimated by solving the following equation: z 2 + R2f = (H − z )2 + R2c = R2l . R2c −R2 +H 2

(1)

f , where H represents height of the ceiling and Rl represents transmission radius Then z can be obtained as z = 2H of the target reader with transmission power level l. Two main research directions tightly follow the work in [21]: improving the localization accuracy [27–29] or improving the localization efficiency [30]. In [27], a degree of irregularity (DOI) denoting the maximum variation of the transmission range per unit degree is considered in the RFID system, which is more applicable to the real wireless environment. The

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Fig. 2. Active 3D localization in RFID system.

approaches proposed in [27], which can tolerate to some permanent faults due to environment interference or hardware failures, aim to improve the RFID-based localization accuracy with a complex radio propagation model. In [28,29], additional hardware is employed to improve the localization accuracy in the RFID systems by using the phase difference. After pointing out the significance of localization efficiency in the large-scale RFID systems, Bu et al. propose to probe some instead of collection all in [30]. They can improve the localization efficiency effectively since fewer tags are involved in the localization. However, the distance estimation error produced in [30] is considerable, which has not been correctly analyzed. In this paper, we focus on improving the localization efficiency, during which a concern we have to consider is: Can the localization efficiency be improved greatly without sacrificing the localization accuracy? The answer is positive. In this paper, we will propose the efficient 3D RFID-based localization schemes called JumpLoc which can achieve the above objective. 3. Passive JumpLoc scheme In this section, we will firstly describe the procedure of the proposed passive JumpLoc scheme, which can greatly improve the localization efficiency. After that we will numerically analyze the localization efficiency of the proposed passive JumpLoc scheme and compare it with other existing ones [21,30]. 3.1. Procedure of passive JumpLoc For the passive localization, we consider a sample RFID system as shown in Fig. 1. The RFID system includes reference readers, reference tags and a target tag. The reference readers and reference tags are deployed on the ceiling, the locations of which can be manually obtained in advance. An Nr × Nc grid topology with a space of d is adopted, the number of reference readers is Nrr and the number of reference tags is Nrt = Nr Nc .1 Each of the reference readers, which are connected with the background server, can be aware of the location-to-ID relationships of all the reference readers and reference tags. The target tag locates between the ceiling and floor and does not know its current location, which can be estimated with the assistance of the reference readers and reference tags. The localization of target tag requires the distance measurements to at least three non-collinear reference readers, which can be achieved by the following three stages. Stage I: Minimum transmission power level determination. Each reference reader can adopt the method in [21] to determine the minimum transmission power level, with which it can communicate with the target tag. Initially, reference reader Rr queries target tag Tt by its tag ID with transmission power level 1 (the lowest one). If Tt does not respond to Rr , Rr will gradually increase its transmission power level and try the query until it receives the response from Tt with transmission power level l. Then Rr can determine the minimum transmission power level as l.

1 Note that N + N > N N , indicating that each of the reference readers is deployed at the same location with some reference tag. rr rt r c

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Fig. 3. Estimation of Rl−1 using jumping probe.

Fig. 4. Relationship between the actual distance d and transmission radii.

Stage II: Distance estimation using jumping probe. After determining the minimum transmission power level l, as shown in Fig. 4, Rr can determine that the actual distance between itself and the target tag, denoted as d, satisfies Rl−1 < d ≤ Rl , where Rl−1 and Rl are Rr ’s transmission radii with transmission power level l − 1 and l. Thus, Rr can R +R estimate d as l−12 l . Since Rl−1 and Rl may be affected by time-varying environmental factors such as temperature, Rr can estimate each of them with assistance of the reference tags. To efficiently estimate Rl−1 , Rr can probe the reference tags using a jumping way. Rr first chooses the neighboring reference tags in one of its diagonal lines, which can be achieved based on its knowledge of the reference tags’ deployment i,j information. We use Fig. 3 to aid the description of the estimation of Rl−1 using jumping probe. In Fig. 3, we use Rt to denote i,j i ,j the reference tag in the ith row and jth column, and the distance between Rr and Rt is denoted as d(Rr , Rt ). Without loss of generality, we assume Rr is deployed in row 0, column 0, and Rl−1 = 5d, Rl = 8d, where d presents the spacing 2,2 distance between two adjacent reference tags within the same row or column. Then, Rr first √ probes Rt with transmission 2,2 2,2 power level l − 1, i.e., it sends a probe query with Rr ’s ID. Since d(Rr , Rt ), which is 2 2d, is smaller than Rl−1 , Rt can receive the probe query from Rr (q1 in√ Fig. 3), after which it will send a response to Rr (r1 in Fig. 3). When receiving r1 from 2,2 Rt , Rr can determine that Rl−1 ≥ 2 2d and then continues to probe the farther reference tags. In order to improve the 4,4 3 ,3 4,4 4 ,4 efficiency, Rr can jumpingly probe the reference tags, i.e., it will probe Rt instead of Rt . Since d(Rr , Rt ) > Rl−1 , Rt 4,4 cannot receive the probe query and Rr cannot receive the expected response. Thus, Rr can determine that Rt is out of its 3 ,3 current transmission range. To improve the resolution of distance estimation, Rr can continue to probe Rt , after which it can receive a response r3 . Finally, the estimation of Rl−1 , denoted as dl−1 , can be obtained as follows: 3,3

d l −1 =

2 3,3

√

4 ,4

d(Rr , Rt ) + d(Rr , Rt )

√ 3,3 Rr Rt

= d(

3,3

√

,

)+

2d 2

.

Since d(Rr , Rt ) ≤ Rl−1 < d(Rr , Rt )+ 2d, we can guarantee the estimation error el−1 satisfies el−1 = |dl−1 −Rl−1 | ≤

2d . 2

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The above estimation error el−1 can be further reduced by probing one more reference tag as follows: when Rr gets 3,3 3 ,4 3,4 3,4 response from Rt , it can continue to probe Rt (q4 in Fig. 3. As d(Rr , Rt ) = 5d = Rl−1 , Rt is within transmission range of Rr , indicating that it will receive the probe message and then reply a response. Thus Rr will receive the response 3,4 3 ,4 from Rt and determine that Rt is within its current transmission range. Finally, Rr can estimate Rl−1 as: 3 ,4

dl−1 =

4,4

d(Rr , Rt ) + d(Rr , Rt ) 2

.

The pseudocode of the estimation of Rl−1 based on jumping probe is shown in Algorithm 1. Algorithm 1 Estimation of Rl−1 Based on Jumping Probe 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27:

Input: Reference reader Rr locating in ith row and jth column with transmission power level l − 1, reference tags. Output: dl−1 as estimation of Rl−1 , k = 0. while true do i+k+2,j+k+2 Rr probes Rt . if Rr gets the corresponding response then k = k + 2. else Break. end if end while i+k+1,j+k+1 Rr probes Rt . if Rr gets the corresponding response then i+k+1,j+k+2 Rr probes Rt if Rr gets the corresponding response then d l −1 = else

i+k+1,j+k+2 i+k+2,j+k+2 d(Rr ,Rt )+d(Rr ,Rt ) 2

d(Rr ,R

i+k+1,j+k+2

)+d(Rr ,R

i+k+1,j+k+1

)

t t d l −1 = 2 end if else i+k,j+k+1 Rr probes Rt if Rr gets the corresponding response then

d l −1 = else d l −1 = end if end if

i+k,j+k+1 i+k+1,j+k+1 d(Rr ,Rt )+d(Rr ,Rt ) 2 i+k,j+k+1 i+k,j+k d(Rr ,Rt )+d(Rr ,Rt ) 2

Theorem 1. The estimation error of dl−1 using jumping probe is upper bounded by 2d . Proof. Without loss of generality, we consider a scenario as shown in Fig. 5. When the reference reader A probes reference tag B, it can receive the response. After that A will probe D, which is out of its transmission range and A will not receive the response. Then A will continue to probe C, which is also out of A’s transmission range. A will not receive the response from C, then it will continue to probe E. If Rl−1 < d(A, E ), then A cannot receive the corresponding response. Thus, A will estimate d(A,E )−d(A,B) d(A,B)+d(A,E ) . Since d(A, B) ≤ Rl−1 < d(A, E ), we can get el−1 = |dl−1 − Rl−1 | satisfies el−1 ≤ . Rl−1 as dl−1 = 2 2

According to the property of triangle 1ABE, we can get d(A, E ) − d(A, B) < d(B, E ) = d. Thus, el−1 ≤ cases, such as A can receive response from C, we can also easily prove that el−1 ≤

d 2

d . 2

Similarly, for other

using the above method. Therefore, we

can conclude that the estimation error of dl−1 using jumping probe is upper bounded by 2d .



Reference reader Rr can continue to estimate Rl . As shown in Fig. 3, after estimating Rl−1 , Rr will√ increase its transmission power level to l and begin to probe the reference tag, which is on the diagonal line with a space of 2 2d and did not respond 4 ,4 4,4 6,6 5,5 5 ,6 to Rr ’s probe when estimating Rl−1 (i.e., Rt ). Similarly, Rr will sequentially probe Rt , Rt , Rt and Rt . Since Rr will 5,6 6,6 5,6 6,6 get response from Rt but not Rt , it can determine that d(Rr , Rt ) ≤ Rl < d(Rr , Rt ). Finally, Rr can estimate Rl as: 5,6

dl =

6 ,6

d(Rr , Rt ) + d(Rr , Rt ) 2

.

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Fig. 5. Illustration of error bound of distance estimation using jumping probe.

Corollary 1. The estimation error of dl using jumping probe is upper bounded by 2d . After estimation of Rl−1 and Rl , Rr can estimate the actual distance d from itself to the target reader as  d=

dl−1 +dl . 2

We

denote the estimation error of the actual distance d as e, i.e., e = | d − d|, then we have the following theorem. Theorem 2. The estimation error of  d using jumping probe is upper bounded by Proof. According to Theorem 1 and Corollary 1, we can get Rl−1 −

 d=

dl−1 +dl , 2

d 2

Rl −Rl−1 +d . 2

≤ dl−1 ≤ Rl−1 +

d 2

and Rl −

d 2

≤ dl ≤ Rl + 2d . Since

we can get:

Rl−1 + Rl − d 2

≤ d≤

Rl−1 + Rl + d 2

.

Furthermore, the actual distance between the reference reader and target tag d satisfies Rl−1 < d ≤ Rl . Therefore, we can get: Rl−1 + Rl − d 2

− Rl ≤  d−d≤

Rl−1 + Rl + d 2

− Rl−1 ⇒ −

Rl − Rl−1 + d 2

⇒ e = | d − d| ≤

≤ d−d≤

Rl − Rl−1 + d 2

Rl − Rl−1 + d 2

.

Thus, we can conclude that the estimation error of  d using jumping probe is upper bounded by

(2) Rl −Rl−1 +d . 2



Based on Theorem 2, it can be observed that increasing the density of reference tags, i.e., reducing d, can really improve the distance estimation accuracy. However, when d is reduced to a small enough value, then the distance estimation error R −R will be dominated by l 2 l−1 . Stage III: 3D localization based on estimated distances. The position of target tag Tt can be estimated when the distances from itself to at least three non-collinear reference readers are obtained. Assume that reference readers {Rr1 , Rr2 , . . . , Rrm } (m ≥ 3) estimate the distances between each of them and Tt as {d1 , d2 , . . . , dm }, and their coordinates are (x1 , y1 , z1 ), (x2 , y2 , z2 ), . . . , (xm , ym , zm ) respectively, then the estimated coordinates of Tt , denoted as (x0 , y0 , z0 ), can be obtained by solving the follow equation [32]: min s.t .

m 1  

2 (xi − x0 )2 + (yi − y0 )2 + (zi − z0 )2 −  di

m i=1 0 ≤ x 0 ≤ L, 0 ≤ y0 ≤ W , 0 ≤ z0 ≤ H

(3)

where L, W and H are the length, width and height of the localization space respectively. Note that in our deployed RFID system, zi = H for i = 1, 2, . . . , m, since all the reference tags are deployed on the ceiling.

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3.2. Numerical analysis In this section, we will compare the localization efficiency, including energy efficiency and time efficiency of the passive JumpLoc scheme with that of collect all [21] and probe some [30] schemes. For the energy efficiency, we will investigate the number of reference tags involved during Stage II, since there is only 1 reference tag involved during Stage I and none is involved during Stage III. Similarly, the number of time slots required in Stage I depends on Rl and no time slot is required in Stage III, we will analyze the time efficiency by investigating the number of time slots required in Stage II for simplicity. 3.2.1. Energy Efficiency We denote Njl , Nca and Nps as the numbers of involved reference tags during Stage II by JumpLoc, collect all and probe some schemes respectively. We also denote ρ as the density of deployed reference tags, then we can get:

ρ=

Nrt

(Nr − 1)(Nc − 1)

d2

=

Nr Nc

(Nr − 1)(Nc − 1)

d2

≈

1 d2

.

(4)

Thus, for collect all scheme, since all the reference tags within Rr ’s transmission range Rl participate in the distance estimation, we can get: Nca = π R2l ρ ≈

π R2l d2

.

In probe some scheme, Rr will estimate the distance between itself and the farthest reference tag, which can be probed, with the same row (or column) as Rl . Therefore: Nps = ⌊

Rl d

⌋.

For the proposed passive JumpLoc scheme, we can get the following theorem. Theorem 3. The number of involved reference tags during the estimation of Rl−1 in the passive JumpLoc Scheme is:

N =

  Rl−1    , √    2 2d         Rl−1   + 1,  √ 2 2d

      Rl−1   + 2, √     2 2d       R√l−1 + 3, 2 2d

√

 2

if

Rl−1 2d

2

√ if

 2

≤

√

  if



√

2 2d

√

2d

d

2

R l −1

Rl−1

Rl−1

 ≤

<

  2

  + 2

Rl−1 d

<

R l −1 2 2d

2

2 2d

+1

√

2 2d

   2 Rl−1 + 2 √ +1 ;

2



R l −1

 

2

√

R l −1

√

2 2d

≤

Rl−1

2

 +1

d

<

√

  + 2



Rl−1

2

√

Rl−1



√

2 2d



 +1 ;

2d

(5)

2 +2

;

elsewhere.

Proof. During the estimation of Rl−1 in the proposed passive JumpLoc √ scheme, Rr will probe the reference tags from the nearest one to the farthest one on the same row with a spacing of 2 2d with transmission power level l − 1. Without loss √ R of generality, we will prove the correctness of Eq. (5) using the example in Fig. 5. Assume that d(A, B) = 2 2d⌊ √l−1 ⌋, which means that d(A, B) ≤ Rl−1 < d(A, D). Then, when d(A, B) ≤ Rl−1 < d(A, E ), i.e.,

√

R

2 2d Rl−1 d

< 2d  R Rl−1 l − 1 (2⌊ 2√2d ⌋)2 + (2⌊ 2√2d ⌋ + 1)2 , reference tag E is out of Rr ’s current transmission range Rl−1 and only the reference tags √ R between A and B (including B) will be involved with a space of 2 2d in the localization. Thus, N = ⌊ √l−1 ⌋. Similarly, when 2 2d  √ R R R R d(A, E ) ≤ Rl−1 < d(A, C ), i.e., (2⌊ √l−1 ⌋)2 + (2⌊ √l−1 ⌋ + 1)2 ≤ ld−1 < 2(⌊ √l−1 ⌋ + 1), then the reference tags between 2 2d 2 2d 2d √ R R R A and B together with reference tag E will be involved, we can get N = ⌊ √l−1 ⌋ + 1. Similarly, when 2⌊ √l−1 ⌋ ≤ ld−1 < 2 2d 2d   √ R 1 R 1 R 1 R 1 R 1 R R (2⌊ 2√l−2d ⌋ + 1)2 + (2⌊ 2√l−2d ⌋ + 2)2 , N = ⌊ 2√l−2d ⌋ + 2, and when (2⌊ 2√l−2d ⌋ + 1)2 + (2⌊ 2√l−2d ⌋ + 2)2 ≤ ld−1 < 2⌊ √l−2d1 ⌋, R N = ⌊ √l−1 ⌋ + 3. 2 2d

2⌊ √l−1 ⌋ ≤



R Corollary 2. The number of involved reference tags in the proposed passive JumpLoc Scheme satisfies: Njl ≤ ⌊ √l ⌋ + 6. 2 2d

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√ Proof. Basically the reference reader Rr will probe the reference tags on the diagonal line with a space of 2 2d, during R which ⌊ √l ⌋ reference tags will be involved. Furthermore, according to Theorem 3, at most 3 other reference tags will be 2 2d

involved in estimation of Rl−1 to not on the √ reduce the estimation error. Similarly, at most 3 other reference tags, which are R diagonal line with a space of 2 2d, will be involved when reducing estimation error of Rl . Therefore, Njl ≤ ⌊ √l ⌋ + 6.  2 2d

Thus, when Rl ≫ d, we have:

 Njl Nca

≈

Njl

 = √

d2 Rl √

d

2 2π Rl

π R2l

 Nps

Rl √ 2 2d

.

(6)



2 2d

1

Rl d

2 2

≈   ≈ √ .

(7)

Eqs. (6) and (7) illustrate that the proposed passive JumpLoc scheme can greatly reduce the number of reference tags involved in the localization process, i.e., it can achieve a much higher energy efficiency. 3.2.2. Time Efficiency ts ts and Nps as the numbers of required time slots during Stage II by JumpLoc, collect all and probe We denote Njlts , Nca some schemes respectively. In collect all scheme, Rr has to query all the reference tags within its transmission range, in which response from different tags may interfere with each other. To solve the response collision problem, a framed slotted Aloha [33,10] protocol can be adopted. In the slotted Aloha protocol, when the reader wishes to read a set of tags, it will first power up and transmit a continuous wave to energize the tags. It then initiates a series of frames, each of which has a number of slots and each tag will randomly select one of the slots to respond to the reader. In each time slot within the frame, the reader can correctly receive the response only if one tag replies. The slotted Aloha protocol can only partially solve the collision problem since the scenario that multiple tags send the response in the same time slot may still happen. However, in our proposed JumpLoc scheme, Rr only needs to query one reference tag each time although lots of reference tags are deployed in the system. Therefore, the scenario that several tags respond to the reader simultaneously will not happen and the interference of reference tags in our proposed JumpLoc scheme can be ignored. It is proved that the slotted Aloha will obtain the highest efficiency of 1e when the length of frame is set to the number of ts tags to read. Therefore, Nca can be estimated as [30]: ts Nca ≈ eNca =

eπ R2l d2

.

In probe some scheme, since Rr will query the reference tags one by one until the one outside its transmission range, the number of required time slots always equals the number of reference tags involved plus 1. The additional one refers to the one outside Rr ’s transmission range and will not receive the probe query, consequently it will not be involved during the localization. Thus we can get: ts Nps = Nps + 1 =

  Rl d

+ 1.

For the passive JumpLoc scheme, we can get the following theorem. R

Theorem 4. The number of required time slots during estimation of Rl−1 in the passive JumpLoc Scheme is: N ts = ⌊ √l−1 ⌋ + 3. 2 2d Proof. Similarly, we that √ will prove the correctness of the above claim using the example in Fig. 5. WeR also√assume R R d(A, B) = ⌊ √l−1 ⌋2 2d, i.e., d(A, B) ≤ Rl−1 < d(A, D). Then, when d(A, B) ≤ Rl−1 < d(A, E ), i.e., ⌊ √l−1 ⌋ 2 ≤ ld−1 < 2 2d



R

2d

R

1 1 (2⌊ 2√l−2d ⌋)2 + (2⌊ 2√l−2d ⌋ + 1)2 , reference tag E is out of Rr ’s current transmission range Rl−1 and only the reference tags √

between A and B (including B) will be involved with a space of 2 2d in the localization. However, according to Algorithm 1, R Rr will try to sequentially probe reference tags D, C and E, which requires additional 3 time slots. Thus, N ts = ⌊ √l−1 ⌋ + 3. 2 2d

Similarly, when d(A, E ) ≤ Rl−1 < d(A, C ), i.e.,



R

R

1 1 (2⌊ 2√l−2d ⌋)2 + (2⌊ 2√l−2d ⌋ + 1)2 ≤

Rl−1 d

√ R R 1 < ⌊ √l−2d1 ⌋ 2, ⌊ 2√l−2d ⌋+1 reference tags

R will be involved. Besides that, Rr will attempt to probe reference tags D and C with two time slots. Thus, N ts = ⌊ √l−1 ⌋ + 3. 2 2d

R We can also prove that under the other conditions, it still satisfies N ts = ⌊ √l−1 ⌋ + 3. 2 2d



R Corollary 3. The number of required time slots in the passive JumpLoc Scheme satisfies: Njlts ≤ ⌊ √l ⌋ + 7. 2 2d

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Proof. The proof is similar to that of Corollary 2. The main difference is that there may exist a reference tag on the diagonal √ line with a space of 2 2d, which will be probed by Rr twice, resulting in requiring one more time slot. For the example in 4 ,4 Fig. 3, Rr will spend a time slot on probing Rt when estimating Rl−1 and spend another time slot on probing the same R ts reference tag when estimating Rl . Therefore, Njl ≤ ⌊ √l ⌋ + 7.  2 2d

Consequently, when Rl ≫ d, we can get the following equations: Njlts ts Nca

Njlts ts Nps



Rl √



2 2d

≈

= √

d2



Rl √

d

2 2eπ Rl

eπ R2l

.

(8)



2 2d

1

Rl d

2 2

≈   ≈ √ .

(9)

Therefore, it is illustrated that our proposed passive JumpLoc scheme can achieve a much higher time efficiency compared with collect all and probe some schemes according to Eqs. (8) and (9). 4. Active JumpLoc schemes In this section, we will present the active JumpLoc localization schemes for 3D RFID system. We will first propose a basic active JumpLoc scheme, in which the determination of three concyclic points is conducted to estimate the radius of communication region. After that we will propose an enhanced active JumpLoc scheme to improve the localization efficiency. Finally we conduct numerical analysis on localization efficiency of the proposed active JumpLoc schemes and other existing schemes. 4.1. Basic active JumpLoc Different from passive JumpLoc scheme, active JumpLoc scheme is to locate a target reader and no any reference reader is necessary. We can borrow the idea from collect all [21] scheme as shown in Fig. 2 to locate the target reader. However, collect all scheme suffers from low localization efficiency, in which all the reference tags within the target reader’s communication region will be probed, resulting in more involved reference tags. In the basic active JumpLoc scheme, we will use the jumping probe to determine the three concyclic points, based on which the radius of the target reader’s communication region can be estimated. The localization of the target reader in the basic active JumpLoc scheme includes the following two stages. Stage I: Concyclic points determination using jumping probe. A simple solution to estimate the radius of the target reader’s communication region is to determine at least three concyclic points [34]. We adopt the Reader Talks First mode [35] in this paper, in which the reader first powers up and transmits continuous wave to energize tags and then each tag replies to reader’s command. The communication procedure between the target reader and reference tags can be simply designed as follows. Tr has three types of query, i.e., ‘‘floor’’, ‘‘ceiling’’ and ‘‘floor&ceiling’’, which are illustrated in Table 2.2 Initially, the target reader Tr has to select a starting tag for the floor and ceiling respectively. Tr firstly sends a query with the type of ‘‘floor&ceiling’’ with transmission power level 1, i.e., the lowest one. After that any reference tag on the floor or ceiling receiving the query will reply a response to Tr . If Tr receives no response, it will gradually increase the transmission power level and query the reference tags until it receive the first response. If the first responding reference tag is from the ceiling, it will be the ceiling’s starting tag.3 Tr will continue to query the reference tags by gradually increasing the transmission power level with the query type of ‘‘floor’’. Therefore, only the reference tags on the floor receiving the query will respond to Tr . When Tr receives the first response from the floor, it will consider the responding tag as the floor’s starting tag. Similarly, if the first response comes from a reference tag on the floor, Tr will consider it as the floor’s starting tag and continue to query the reference tags on the ceiling by gradually increasing transmission power level with query type of ‘‘ceiling’’. The framed slotted Aloha protocol [33] can be used here to avoid the interference. By using such a scheme, Tr can determine the starting tags for both the ceiling and floor. Moreover, each of the starting tags should locate near the center of corresponding 3,3 communication region. As shown in Fig. 6, Tr can determine reference tag Rt as the starting tag. After selecting the starting tag, Tr can find out at least three concyclic points by querying the reference tags one-byone deployed in the same row or column with the selected starting tag. However, in the real indoor application, Tr may locate near a wall or corner, making its on-floor or on-ceiling communication region not a complete one. Under such a scenario, it will be difficult for Tr to find the concyclic points since even the reference tag on the boundary may be within

2 Note that the types of query can be signed using at most 2 bits in the query message, which is easy to implement. 3 There may be multiple responding tags, then we will randomly select one from them as the starting tag.

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Table 2 Illustration of different types of queries from target reader. Query type

Illustration

Floor Ceiling Floor&ceiling

Only the reference tags on the floor will reply Only the reference tags on the ceiling will reply Reference tags on both the floor and ceiling will reply

Fig. 6. Concyclic points determination using jumping probe.

Tr ’s communication range and Tr cannot determine whether it lies on the transmission circumference. We define the above negative effect caused by the boundary as boundary effect. To overcome the boundary effect, Tr can just query the reference tags which is farther away from the boundaries than the starting tag. Therefore, Tr can avoid querying the reference tags 3,3 near the boundaries. For example, as shown in Fig. 6, after determining Rt as the starting tag, Tr will query the reference 3,3 tags below or on the right side of Rt with a high enough power transmission level since they are farther away from the 3,0 0,3 boundaries than Tr . Thus it will not query the reference tags near the boundaries, such as Rt and Rt , which are on its up side or left side (the opposite directions of query). Similarly, Tr can query the reference tags using a jumping probe based on its knowledge of the reference tags’ deployment 5,3 information to improve the localization efficiency. For example, as shown in Fig. 6, Tr will first query reference tag Rt , 5,3 3,3 which is two hops below Rt . Since Rt is within Tr ’s transmission range, it will reply a response to Tr . After that Tr 7,3 continues to query Rt , which is outside Tr ’s transmission range and will not respond to Tr . Therefore, Tr can conclude 6 ,3 7 ,3 5,3 that the communication circumference crosses between Rt and Rt . Then to increase the accuracy, Tr can query Rt to 7 ,3 6 ,3 6,3 check if Rt is within its transmission range. If yes, as shown in Fig. 6, Tr can consider the midpoint between Rt and Rt as the first concyclic point. Similarly, Tr can also determine the second concyclic point on the right side of the starting tag 3,6 3 ,7 using the above jumping probe based method, which will be the midpoint of Rt and Rt as shown in Fig. 6. Since three concyclic points are the basic requirement to locate the center of a circle, Tr has to find another concyclic point. Inspired by the idea that the midpoint between two concyclic points is near the circumference, Tr can initially query the reference tag nearest to the midpoint of the previously found two concyclic points. As shown in Fig. 6, based on its 5,5 knowledge, Tr can determine that Rt is the nearest reference tag to the midpoint between the found concyclic points. Tr 5 ,5 5,5 will first query Rt . Since Rt is within transmission range of Tr , it can receive the query message and reply a response. 6 ,6 7,7 After that, Tr will query Rt , which will send back a response. Then Tr can query Rt , which is outside the transmission 7,6 range and will not respond. Finally, Tr will query Rt and get no response. Consequently, Tr can estimate the midpoint 6,6 6,7 between Rt and Rt as the last concyclic point. i ,j Assume the starting tag is Rt , which is near the upper left corner, the pseudocode of determining the three concyclic points A(xA , yA ), B(xB , yB ) and C (xC , yC ) is listed in Algorithm 2. Note that Tr has to respectively determine three concyclic points of its on-floor and on-ceiling communication regions. Stage II: Radius estimation and 3D localization of target reader. After determining the three concyclic points, Tr can estimate the centers of the communication regions on both the floor and ceiling, after which the radii of communication regions can also be estimated. Assume the center of Tr ’s on-floor communication region is (xf , yf ), and the three concyclic points are A(xA , yA ), B(xB , yB ) and C (xC , yC ) respectively. Then, according to [34], (xf , yf ) can be estimated as:

α1 (yB − yC ) + α2 (yC − yA ) + α3 (yA − yB ) , β α1 (xC − xB ) + α2 (xA − xC ) + α3 (xB − xA ) yf = , β xf =

(10)

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Algorithm 2 Jumping Probe Based Concyclic Points Determination 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48:

i,j

Input: Tr with a high enough power transmission level. Reference tags with starting tag Rt near the upper left corner. Output: Coordinates of three concyclic points: A(xA , yA ), B(xB , yB ) and C (xC , yC ). %Determination of point A% k = 0. while true do i+k+2,j Tr probes Rt . if Tr gets the corresponding response then k = k + 2. else Break. end if end while i+k+1,j Tr probes Rt . if Tr gets the corresponding response then i+k+1,j i+k+2,j A is the midpoint between Rt and Rt . else i+k+1,j i+k,j A is the midpoint between Rt and Rt . end if %Determination of point B% k = 0. while true do i,j+k+2 Tr probes Rt . if Tr gets the corresponding response then k = k + 2. else Break. end if end while i,j+k+1 Tr probes Rt . if Tr gets the corresponding response then i,j+k+1 i,j+k+2 B is the midpoint between Rt and Rt . else i,j+k+1 i ,j + k B is the midpoint between Rt and Rt . end if %Determination of point C% m,n Tr finds the reference tag nearest to the midpoint between A and B as Rt . k = 0. while true do m+k+1,n+k+1 Tr probes Rt . if Tr gets the corresponding response then k = k + 1. else Break. end if end while m+k,n+k+1 Tr probes Rt . if Tr gets the corresponding response then m+k,n+k+1 m+k+1,n+k+1 C is the midpoint between Rt and Rt . else m+k,n+k+1 m+k,n+k C is the midpoint between Rt and Rt . end if

where

α1 = x2A + y2A , α2 = x2B + y2B , α3 = x2C + y2C , β = 2[xA (yB − yC ) + xB (yC − yA ) + xC (yA − yB )].

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Then the radius of Tr ’s on-floor communication region, denoted as Rf , can be calculated as: C   (xf − xi )2 + (yf − yi )2

Rf =

i =A

.

3

(11)

Similarly, the center of Tr ’s on-ceiling communication region (xc , yc ) can be estimated based on Eq. (10) and the corresponding radius Rc can be calculated using Eq. (11). Assume the coordinate of Tr is (x, y, z ), then we can get: x=

xf + xc 2

,

y=

yf + yc 2

,

(12)

and z can be obtained using Eq. (1), where H is the height of the ceiling, i.e., the distance from the floor to ceiling. 4.2. Enhanced active JumpLoc We can observe that by using the starting tag searching method in the basic active JumpLoc scheme, Tr tends to select the nearest reference tag as the starting tag, which will be near the center of Tr ’s communication region. Based on this observation, we can directly consider the location of starting tag as the center of Tr ’s communication region. In this section, we will propose an enhanced active JumpLoc scheme to improve the localization efficiency. In the enhanced active JumpLoc scheme, Tr will adopt the starting tag searching method in basic active JumpLoc scheme to sequentially determine the starting tags on both the floor and ceiling. Assume the coordinate of the center of Tr ’s on-floor 3 ,3 communication region is (xf , yf ), which can be estimated as the location of the starting tag on the floor, such as Rt as shown in Fig. 6. Tr can then determine a point Pc near the circumference of communication region and the radius Rf can be estimated as the distance between Pc and the center. Algorithm 3 Jumping Probe Based Radius Estimation 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28:

i ,j

Input: Tr with a high enough power transmission level. Reference tags with starting tag Rt near the upper left corner. Output: Pc and Rf (or Rc ). k = 0. while true do i+k+2,j+k+2 Rr probes Rt . if Rr gets the corresponding response then k = k + 2. else Break. end if end while i+k+1,j+k+1 Rr probes Rt . if Rr gets the corresponding response then i+k+1,j+k+2 Rr probes Rt . if Rr gets the corresponding response then i+k+1,j+k+2 Pc = Mid(Rt , Rti+k+2,j+k+2 ). else i+k+1,j+k+2 Pc = Mid(Rt , Rti+k+1,j+k+1 ). end if else i+k,j+k+1 Rr probes Rt . if Rr gets the corresponding response then i+k,j+k+1 Pc = Mid(Rt , Rti+k+1,j+k+1 ). else i+k,j+k+1 Pc = Mid(Rt , Rti+k,j+k ). end if end if i ,j Rf (or Rc ) = d(Rt , Pc ).

In determination of Pc ’s location, Tr will probe the reference tags with a high enough transmission power level along a 7,7 diagonal line to the farthest corner to avoid the boundary effect. As shown in Fig. 6, Rt is the tag on the farthest corner 3 ,3 5 ,5 5 ,5 of starting tag Rt . Therefore, Tr will probe Rt first. Since Rt is within the communication range, Tr can receive the 7,7 response. Then Tr continues to query Rt , which is outside the communication range and there will be no response. Tr can

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)

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7,7

6 ,6

determine that Pc lies between Rt and Rt . To improve the accuracy, Tr will then probe Rt and receive no response. 6,5 Finally, Tr will probe Rt , which is within its communication range and will respond to Tr . Therefore, Tr will consider the 6,5 6,6 3,3 3,3 midpoint between Rt and Rt as Pc . And the distance between Rt and Pc , i.e., d(Rt , Pc ), as Rf . Estimation of Rc is similar to the above process. i ,j Assume the starting tag on the floor (or ceiling) is Rt , which is near the upper left corner, then the pseudocode of estimating Rf (or Rc ) is listed in Algorithm 3. Note that the probe direction can be adjusted by Tr according to the position of the starting tag. Assume the coordinate of Tr is (x, y, z ). After determining the centers of Tr ’s on-floor and on-ceiling communication regions, x and y can be estimated according to Eq. (12). And z can be estimated using Eq. (1) based on the estimated Rf and Rc . Note that the enhanced active JumpLoc scheme can greatly improve the localization efficiency based on the basic active JumpLoc by reducing the number of reference tags involved into the localization, which will be numerically evaluated in next section. 4.3. Numerical analysis In this section, we will compare the energy efficiency and time efficiency of the proposed basic active JumpLoc and enhanced active schemes with that of collect all [21] and probe some [30] schemes. For simplicity, we only consider that the communication region of Tr on the floor or ceiling is within the boundaries, that is, we ignore the boundary effect in the numerical analysis. 4.3.1. Energy efficiency We denote Njl , Njl′ , Nca and Nps as the numbers of involved reference tags by the basic active JumpLoc, enhanced active JumpLoc, collect all and probe some schemes respectively. For simplicity, we only compare the number of involved reference tags on the floor.4 For the collect all scheme, all the reference tags within Tr ’s transmission range will be probed and involved. Thus, we can get: Nca = π R2f ρ ≈

π R2f

d2 where Rf presents the radius of Tr ’s on-floor communication region. In the probe some scheme, the reference tags on two perpendicular chords of Tr ’s communication region will be involved. Since it can be easily proved that the length of two perpendicular chords is larger than the diameter, we can get:

 Nps ≥

2Rf



d

.

For the proposed basic active JumpLoc scheme, Tr will probe the reference tags on three directions. We can get the following theorem. Theorem 5. When Rf ≫ d, the number of involved reference tags of the basic active JumpLoc scheme satisfies: Njl ≈

 √  ( 2 + 1)Rf 2d

.

(13)

Proof. As shown in Algorithm 2, to determine the location of Point A, Tr will probe from the starting tag to the reference tag outside its communication region with a spacing of 2d, the number of involved reference tags can be approximated as R

⌊ 2df ⌋ when Rf ≫ d since the starting tag is near the center of the communication region. Similarly, to determine the location R

of Point B, approximately another ⌊ 2df ⌋ reference tags will be involved. Furthermore, to determine the location of Point C, Tr will probe from the reference tag nearest to the midpoint between Points A and B to the one outside its communication √ region with a space of 2 2d. Since the distance from the center to the midpoint between Points A and B can be approximated √ √

as 22 Rf , the number of involved reference tags during this procedure approximates to ⌊ can get:

 Njl ≈ 2

Rf 2d



(1− 22 )Rf √ 2d

⌋. Thus, when Rf ≫ d, we

√      1− 2 R   √ f   2 ( 2 + 1)Rf   + ≈ .  √

2d

2d

4 Since the number of involved reference tags on the ceiling is similar to that on the floor, it is reasonable to only compare one of them.

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For the enhanced active JumpLoc scheme, only the reference tags in one direction are involved. When Rf ≫ d, the number of which can be formulized as:   Rf ′ Njl ≈ . √ 2 2d Thus, when Rf ≫ d, we have: Njl′ Nca





R

√f 2 2d

≈

≈ √

d2

Njl′ Nps Njl′ Njl



d

.

2 2π Rf

π R2f

(14)



Rf

√

1

2 2d

≤  2R  ≈ √ .  ≈ 

(15)

4 2

f

d



R

√f 2 2d

√ ( 2+1)Rf

1

 ≈

2+

2d

√ . 2

(16)

Note that ρ ≈ d12 according to Eq. (4). The above equations illustrate that our proposed active JumpLoc schemes can greatly improve the energy efficiency and also the enhanced active JumpLoc scheme outperforms the basic active JumpLoc scheme. 4.3.2. Time efficiency ts ts We denote Njlts , Njlts′ , Nca and Nps as the numbers of required time slots by basic active JumpLoc, enhanced active JumpLoc, collect all and probe some schemes respectively. ts Similarly, Nca can be estimated as: eπ R2f

ts Nca ≈ eNca =

.

d2 In the probe some scheme, besides the involved reference tags, Tr will also spend 4 time slots [30] on trying to probe 4 other reference tags which are outside its communication region. Thus, the number of required time slots equals the number of reference tags involved plus 4. Thus we can get: ts Nps = Nps + 4 ≥



2Rf



d

+ 4.

For our proposed basic active JumpLoc scheme, Tr will also spend several time slots on trying to probe some other reference tags outside its communication region besides the involved reference tags. Thus, when Rf ≫ d, we can get: Njlts

≈ Njl ≈

  √ ( 2 + 1)Rf 2d

.

Similarly, for the enhanced active JumpLoc scheme, when Rf ≫ d, we have:



Njlts′ ≈ Njl′ ≈

Rf



√

.

2 2d Then, when Rf ≫ d, we can get: Njlts′ ts Nca

Njlts′ ts Nps

Njlts′ Njlts





R

√f 2 2d

≈

≈ √

d2



d

2 2eπ Rl

eπ R2f

.



R

√f

1

2 2d

≈  2R  ≈ √ . d

≈ 

(18)

4 2

f



(17)

R

√f 2 2d



√ ( 2+1)Rf 2d

 ≈

1 2+

√ . 2

(19)

Eqs. (17)–(19) illustrate that our proposed active JumpLoc schemes can achieve a much higher time efficiency compared with the other schemes and the enhanced active JumpLoc scheme outperforms the basic active JumpLoc scheme.

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Fig. 7. Effects of spacing distance d on distance estimation error of our proposed passive JumpLoc scheme with varying transmission radius Rl . (a) d = 0.1 m; (b) d = 0.2 m; (c) d = 0.3 m.

5. Performance evaluation In this section, we will evaluate the performance of our proposed JumpLoc localization schemes in terms of localization efficiency, including energy efficiency and time efficiency. We will also analyze the effects of network parameters on the localization accuracy of JumpLoc. We have conducted the simulations in Matlab. The simulation parameters are set as follows: We simulate a hexahedron with size of 10 × 10 × 10 m3 as the 3D localization space, i.e., L = W = H = 10 m. There are two kinds of tags in the RFID systems, i.e., active and passive. In the simulations, we consider the passive tags, which can harvest the radio frequency energy from the reader to power their circuits. For the passive JumpLoc scheme, all the reference tags are deployed on the ceiling into a grid topology with a space of d, the default value of which is 0.1 m. There are totally nine reference readers (Nrr = 9) employed in the passive JumpLoc scheme: one reference reader is deployed in the center, four of them are deployed on four corners, and the other four are deployed on the midpoints between the center and corners. For the active JumpLoc schemes, the reference tags are deployed on both the ceiling and floor, and the space is also d. All the tags in the passive JumpLoc and active JumpLoc schemes are passive ones, which can reply to the reader only when it has been energized by the reader’s continuous wave. The transmission radius of each reader with transmission power level l is Rl = Kl, where 1 ≤ l ≤ 38 and the default value of K is 0.6. To make our simulations more suitable for the real applications, we employed a randomness in the simulations to reflect the non-ideal effects of the wireless communication procedure between RFID reader and tag. During the maximum transmission power level determination, by considering the non-ideal wireless communication in the real applications, the reader will have a probability Pr to get an incorrect maximum transmission power level, which is lower than the original one. In the simulations, we set Pr = 31 . 5.1. Passive JumpLoc scheme Fig. 8 illustrates the localization efficiency comparison of our proposed passive JumpLoc scheme and two other existing schemes—collect all [21] and probe some [30] with varying transmission radius Rl and spacing distance d. Fig. 8(a) shows the ratio of number of involved tags in JumpLoc scheme to that in each of other two schemes, which can reflects the energy efficiency performance. The transmission radius Rl varies from 4 to 14 m and the space d varies from 0.1 to 0.5 m. The simulation results show that there are less tags involved in probe some scheme than that involved in collect all scheme. But our proposed passive JumpLoc scheme can greatly improve the energy efficiency by reducing the number of involved tags by at least 56% compared with probe some scheme. Fig. 8(b) evaluates the time efficiency by comparing the number of required time slots. It illustrates that our proposed passive JumpLoc scheme can reduce the number of required time slots by at least 34% compared with probe some scheme, which performs better than collect all scheme. Therefore, Fig. 8 shows that our proposed passive JumpLoc scheme outperforms two other existing schemes on both the energy efficiency and time efficiency. Fig. 7 shows the effects of spacing distance d on estimation error of Rl of our proposed passive JumpLoc scheme. We vary Rl from 4 to 14 m with an increment of 0.1 m. The spacing distance d is set as 0.1 m, 0.2 m, and 0.3 m corresponding to Fig. 7(a), (b), and (c) respectively. The simulation results illustrate that increase of d will degrade the distance estimation accuracy. Furthermore, it validates our claim in Theorem 1 that the distance estimation error is upper bounded by 2d . Fig. 9(a) shows the cumulative distribution function (CDF) of the proposed passive JumpLoc scheme’s localization error R −R +d with different values of K when d = 0.1 m. According to Theorem 2, the estimation error of  d is upper bounded by l l2−1 . As Rl = Kl, we can get Rl − Rl−1 = K . Therefore, with increase of K , the estimation error of  d will increase, which will negatively affect the localization accuracy. The simulation results in Fig. 9(a) validate the above numerical analysis that when d increases, the localization error will increase. Fig. 9(b) compares the CDF of the proposed passive JumpLoc scheme’s localization error with different values of d when R −R +d K = 0.6. Since Theorem 2 claims that the estimation error of  d is upper bounded by l l2−1 and Rl − Rl−1 = K = 0.6 m,

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Fig. 8. Localization efficiency comparison of the proposed passive JumpLoc scheme and two other existing schemes—collect all and probe some with varying transmission radius Rl and spacing distance d. (a) Comparison of energy efficiency; (b) Comparison of time efficiency.

Fig. 9. Effects of parameters K and d on the localization error of the proposed passive JumpLoc scheme. (a) Effects of K ; (b) Effects of d.

Fig. 10. Localization efficiency comparison of the proposed active JumpLoc schemes and two other existing schemes—collect all and probe some with varying transmission radius Rf and spacing distance d. (a) Comparison of energy efficiency; (b) Comparison of time efficiency.

the localization accuracy will be dominated by K when d is relatively small. The results Fig. 9(b) show that the effects of d on localization accuracy can be ignored. 5.2. Active JumpLoc schemes Fig. 10 illustrates the localization efficiency comparison of our proposed active JumpLoc schemes and two other existing schemes—collect all and probe some with varying transmission radius Rl and spacing distance d. Fig. 10(a) shows the ratio of number of involved tags in enhanced active JumpLoc scheme to that in basic active JumpLoc, collect all and probe some schemes respectively. The simulation results show that our proposed active JumpLoc schemes achieve a higher energy efficiency than the other two schemes and the enhanced active JumpLoc scheme outperforms the other schemes, which reduces the number of involved tags by at least 82% compared with probe some scheme. Fig. 10(b) evaluates the time efficiency by comparing the number of required time slots. It illustrates that the proposed enhanced active JumpLoc scheme can reduce the number of required time slots by at least 83% compared with probe some scheme.

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Fig. 11. Effects of parameters K and d on the localization error of the proposed enhanced active JumpLoc scheme. (a) Effects of K ; (b) Effects of d.

Fig. 11 shows the effects of K and d on the localization accuracy of the proposed enhanced active JumpLoc scheme. Fig. 11(a) shows the CDF of the proposed enhanced active JumpLoc scheme’s localization error with different values of K when d = 0.1 m. The results illustrate that increase of K will degrade the localization accuracy since a larger K indicates a larger Rl , which will negatively affect the estimation of Rf and Rc . In Fig. 11(b), the CDFs of the proposed enhanced active JumpLoc scheme’s localization error with different values of d when K = 0.6 are compared. Similarly, increase of d indicates a lower density of reference tags, which will increase the estimation error of Rf and Rc , thus the localization error will increase. 6. Conclusions and future work In this paper, we target at improving the localization efficiency including the energy efficiency and time efficiency without sacrificing the localization accuracy. We adopt a ‘‘jumping probe’’ in the distance estimation, based on which we propose a 3D RFID-based localization scheme called JumpLoc, including a passive scheme and two active schemes, to effectively improve the localization efficiency. In the passive localization scheme, a target tag will be located based on the distance estimations between itself and some reference readers. While the active schemes include basic active JumpLoc and enhanced active JumpLoc schemes, in which the target will be a reader and only reference tags are required. We conduct numerical analysis to show the localization efficiency improvement of our proposed JumpLoc schemes. The simulation results illustrate the effectiveness of the proposed JumpLoc schemes. In this paper, we just validate the effectiveness of our proposed JumpLoc localization schemes by simulations. In our future work, we intend to implement a real RFID system to evaluate the proposed localization schemes. Acknowledgments This work was supported in part by NSFC grants (No. 61309023, No. 61502352, No. 61373027, No. 61672321, No. 61503413, No. 61309024), Shandong Provincial Natural Science Foundation (No. ZR2013FQ032, No. ZR2015FL027), Shandong Provincial Key Program of Research and Development (No. 2015GGX101045), Qingdao Fundamental Research Project (No. 15-9-1-79-jch, No. 16-5-1-1-jch), the Fundamental Research Funds for the Central Universities of China (No. 16CX02059A), Natural Science Foundation of Hubei Province (No. 2015CFB203), Natural Science Foundation of Jiangsu Province (No. BK20150383) and The National Basic Research Program of China (No. 2014CB340600). References [1] M. Chen, W. Luo, Z. Mo, S. Chen, Y. Fang, An efficient tag search protocol in large-scale RFID systems with noisy channel, IEEE/ACM Trans. Netw. 24 (2016) 703–716. [2] H. Yue, C. Zhang, M. Pan, Y. Fang, S. Chen, A time-efficient information collection protocol for large-scale RFID systems, in: Proc. of IEEE INFOCOM, 2012, pp. 2158–2166. [3] L. Yang, Y. Chen, X.-Y. Li, C. Xiao, M. Li, Y. Liu, Tagoram: Real-time tracking of mobile RFID tags to high precision using COTS devices, in: Proc. of ACM MOBICOM, 2014, pp. 237–248. [4] L. Wang, L.D. Xu, Z. Bi, Y. Xu, Data cleaning for RFID and WSN integration, IEEE Trans. Ind. Inf. (2014). [5] Y. Qiao, S. Chen, T. Li, S. Chen, Energy-efficient polling protocols in RFID systems, in: Proc. of ACM MobiHoc, 2011. [6] H. Chen, W. Lou, On protecting end-to-end location privacy against local eavesdropper in wireless sensor networks, Elsevier Pervasive Mob. Comput. 2015 (16) (2015) 36–50. [7] Y. Zhang, S. He, J. Chen, Data gathering optimization by dynamic sensing and routing in rechargeable sensor networks, IEEE/ACM Trans. Netw. 24 (3) (2016) 1632–1646. [8] Y. Zhang, X. Sun, B. Wang, Efficient algorithm for K-Barrier coverage based on integer linear programming, China Commun. 13 (7) (2016) 16–23. [9] J. Shen, H. Tan, J. Wang, J. Wang, S. Lee, A novel routing protocol providing good transmission reliability in underwater sensor networks, J. Internet Technol. 16 (1) (2015) 171–178.

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