The Beacon Movement Detection Problem in Wireless Sensor Networks for Localization Applications

The Beacon Movement Detection Problem

in Wireless Sensor Networks

for Localization Applications

Sheng-Po Kuo, Member, IEEE Computer Society, Hsiao-Ju Kuo, and

Yu-Chee Tseng, Senior Member, IEEE Computer Society

Abstract—Localization is a critical issue in wireless sensor networks. In most localization systems, beacons are being placed as references to determine the positions of objects or events appearing in the sensing field. The underlying assumption is that beacons are always reliable. In this work, we define a new Beacon Movement Detection (BMD) problem. Assuming that there are unnoticed changes of locations of some beacons in the system, this problem concerns how to automatically monitor such situations and identify such unreliable beacons based on the mutual observations among beacons only. Existence of such unreliable beacons may affect the localization accuracy. After identifying such beacons, we can remove them from the localization engine. Four BMD schemes are proposed to solve the BMD problem. Then, we evaluate how these solutions can improve the accuracy of localization systems in case there are unnoticed movements of some beacons. Simulation results show that our solutions can capture most of the unnoticed beacon movement events and thus can significantly alleviate the degradation of such events.

Index Terms—Context awareness, localization, location-based service, pervasive computing, positioning, wireless sensor network.

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of wireless ad hoc and sensor networks. Ad hoc networking technologies enable quick and flexible deploy-ment of a wireless communication platform. A wireless sensor network typically adopts the ad hoc communication architecture and is capable of exploiting context information collected from sensors. Many applications of wireless sensor networks have been proposed [2], [5], [6].

Sensor networks are promising because they support context-aware and location-aware services. The success of this area may greatly benefit human life. One essential research issue in sensor networks is localization, whose purpose is to determine the position of an object or event. In most localization systems, they assume that there are sets of beacon sensors (or simply beacons), which may or may not be aware of their locations and can periodically transmit/ receive short broadcast packets. By evaluating the distances, angles of arrival, or signal strengths of these broadcast packets, we can estimate the locations of objects by triangulation [24] or pattern matching [3]. Under such an

architecture, we observe that most existing works have an underlying assumption that beacons are always reliable. Based on this observation, this paper points out a new Beacon Movement Detection (BMD) problem that may occur in most beacon-based localization systems. No matter if beacons know or do not know their own locations, we define a beacon movement event as one where a beacon is migrated to a location different from where it is supposed to be (or where it was at the training stage). However, our localization system is unaware of this event. With unnoticed beacon movement events, the topology of the sensor network may be different from what it is supposed to be, and thus a localization algorithm may lose its accuracy or even incorrectly estimate an object’s location. In this work, we assume that beacons are static under normal circum-stances, but occasional beacon movement events are not unusual. This is true especially in a wireless sensor network. For example, a beacon node may be moved by unexpected forces, such as those from animals being monitored, or by manual errors, because beacon nodes are normally quite tiny.

The BMD problem involves two issues. First, we need to determine those beacons that are unexpectedly relocated. Second, the result has to be forwarded to the positioning engine to reduce the impact of movement on localization accuracy. To solve the first issue, we will allow beacons to monitor each other to identify those moved beacons automatically. This is nontrivial work because we do not have a trust model among beacons. In this paper, we show that without any assumption, it is impossible for a general BMD problem to correctly identify those moved beacons because an ambiguity situation will always exist. However, if we assume that the number of moved beacons is relatively small, we can relieve the BMD problem using some

. S.-P. Kuo is with Telcordia Applied Research Center, Suite E-453, 4F, No. 19-13, SanChung Rd., Taipei 115, Taiwan.

E-mail: kuopo@research.telcordia.com.

. H.-J. Kuo is with the Wireless Communication Technology BU, MediaTek, Inc., 5F, No. 22, Lane 35, Jihu Rd., Neihu District, Taipei 11492, Taiwan. E-mail: sherry.kuo@mediatek.com.

. Y.-C. Tseng is with the Department of Computer Science, National Chiao Tung University, Hsin-Chu 30010, Taiwan, and with the Department of Information and Computer Engineering, Chung-Yuan Christian University, Taiwan. E-mail: yctseng@cs.nctu.edu.tw. Manuscript received 14 Nov. 2007; revised 15 Sept. 2008; accepted 9 Dec. 2008; published online 6 Jan. 2009.

For information on obtaining reprints of this article, please send e-mail to: tmc@computer.org, and reference IEEECS Log Number TMC-2007-11-0341. Digital Object Identifier no. 10.1109/TMC.2009.15.

heuristic algorithms. Based on this assumption, we propose four schemes. The first location-based (LB) scheme tries to calculate each beacon’s current location and compares the result with its predefined location to decide if it has been moved. In the second neighbor-based (NB) scheme, beacons will keep track of their nearby beacons and report their observations to the BMD engine to determine if some beacons have been moved. In the third signal strength binary (SSB) scheme, the change of signal strengths of beacons will be exploited. In the last signal strength real (SSR) scheme, the BMD engine will collect the sum of reported signal strength changes of each beacon to make decisions. Note that only the first scheme assumes that the original locations of beacons are known in advance. The other three schemes do not assume any a priori knowledge on the original locations of beacons.

The noise-prone signal strengths are another challenge to the BMD problem. In real environments, signal strengths may be influenced by many factors, such as hardware difference, remaining battery, multipath propagation, and dynamic signal fading. When combining these factors, it is even harder to correctly determine a beacon movement event. To relieve this influence, we import the concept of tolerable regions in the proposed schemes. To evaluate the proposed BMD schemes, we adopt a close-to-reality radio irregularity model (RIM) [28] to simulate the decay of signal strengths. This model has been shown to be able to reflect the propagation of radio signals, especially in indoor environments. In our simulation study, we have tuned the parameters of RIM to evaluate the performance of LB, NB, SSB, and SSR under different conditions. The results show that the SSB and SSR schemes perform well under most situations. The NB scheme is easy to implement but has limited movement detection capability. Compared to SSB, SSR, and NB, the LB scheme has higher computation complexity and is quite sensitive to the density of beacons. When there are many beacons, LB can have excellent detection results. However, its performance degrades quickly when there are not enough beacons to provide a good localization service.

The remainder of this paper is organized as follows: Section 2 gives a formal definition of the BMD problem. Related works and motivations are given in Section 3. Section 4 presents our solutions to the BMD problem. Then, in Section 5, we evaluate the proposed schemes and examine their capability to improve the localization accuracy in events of beacon movement. Finally, Section 6 draws our conclusions.

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Before we formally define the BMD problem, we illustrate an example to demonstrate how movement of some beacons may affect the accuracy of localization results. Let us consider Fig. 1a, where we use three beacons to determine a target’s position via typical triangulation approaches. If beacon b3 is moved to the location marked

in gray without being noticed, the system may incorrectly estimate the target’s location, as shown in Fig. 1b. Note that the circle centered at b3 has a radius equal to the distance

from the real location of b3to the target. Also note that the

results proposed in this paper are applicable not only to the unnoticed movement of beacons, but also to the unexpected behaviors of some beacons (for example, a beacon may be unexpectedly covered by an obstacle, thus lowering the observed signal strengths).

We are given a sensing field, in which a set of beacons B¼ fb1; b2; . . . ; bng is deployed for localization purposes.

Depending on different schemes, we may or may not assume that the locations of these beacons are known in advance. Periodically, each beacon will broadcast a HELLO packet. To determine its own location, an object will collect HELLO packets from its neighboring beacons and send a signal strength vector S ¼ ½s1; s2; . . . ; sn to an external

positioning engine, where si is the signal strength of the

HELLO packet from bi. If it cannot hear from bi, we let

si¼ smin, where smin denotes the minimum signal strength

and any signal strength lower than this value is not detectable by a receiver. The positioning engine can then estimate the object’s location based on S (for example, in the

case of RADAR [3], S is compared against a location database obtained in the training phase based on a pattern-matching method).

Suppose that a set of unreliable beacons BM B is

moved or blocked by obstacles without being noticed. The BMD problem is to compute a detected set BD that is as

similar to BM as possible. The result BD may be used to

calibrate the positioning engine to reduce the localization error (for example, in the case of RADAR, the entry si in S

may be ignored if bi is detected to be unreliable).

To solve the BMD problem, we will enforce beacons to monitor each other from time to time. Let us denote the local observation vector of bi at time t by Oti¼ ½o

t i;1; o t i;2; . . . ; o t i;n, where ot

i;j is bi’s observation on bj at time t. The content of

an observation will depend on the corresponding BMD scheme (refer to Section 4). We use the observation vector at time t ¼ 0 to represent the original observation where all beacons stay at their original locations. The observation matrix at time t is denoted by Ot_{¼ ½O}t

1; Ot2; . . . ; Otn T

. Note that ideally the observation matrix Ot_{should be symmetric (in the}

sense that Ot_{½i; j ¼ O}t_{½j; i). However, in practice, due to the}

asymmetry of radio propagation, it is possible that Ot _is

asymmetric (our BMD schemes are able to handle asym-metric Ot_{). Given O}t_{, the BMD engine is capable of calculating}

a set BD. The result is then sent to the calibration algorithm in

the positioning engine. Fig. 2 illustrates our system model. Considering the following reasons, we define the tolerable region Ri of each beacon bi as the geographic area within

which a slight movement of bi is acceptable. First, radio

signal tends to fluctuate from time to time. Second, slight movement of a beacon should not change the signal strength much unless an obstacle is encountered (if so, this should be discovered by our BMD engine). Third, ignoring the data of a slightly moved beacon in the location database will decrease the localization accuracy due to fewer beacons helping the localization procedure. So the slight movement of beacons is constrained by the tolerable regions. As a result, the unreliable set BM only contains those beacons

which are moved out of their tolerable regions. The sizes of tolerable regions are application dependent, which is beyond the scope of this work. For simplicity, tolerable regions are assumed to be circles centered at beacons of the same radius.

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There are two main approaches for localization: multi-lateration and pattern matching. Multimulti-lateration is a process of finding the location of an object based on measuring the distances or angles of three or more signal sources at known coordinates. A special case of multilateration is triangula-tion. For example, the Bat sentient system [1] is composed of a set of sensors for 3D localization. Sensors are installed at known positions, such as ceilings, to measure the signal traveling time from a user badge to them. Then, a triangulation algorithm calculates the location of the badge. Localization by the signal’s angle of arrival is addressed in [17], [20], [21]. In Cricket [21], ultrasonic sensors are used to estimate the location and orientation of a mobile device. In [24], a distributed positioning system called Ad Hoc Localization System (AHLoS) is proposed, where some beacons are aware of their own locations while others are not. The former are used to determine the positions of the latter. A similar work based on a probability model is proposed in [22].

All the above systems require special hardware to support localization. Recently, indoor localization, using pattern-matching techniques [3], [4], [14], [23], [25], is gaining popularity because the localization task can be achieved by off-the-shelf communication hardware, such as WiFi-enabled mobile devices. Such localization systems are more cost-effective. Pattern-matching localization does not rely on any range estimation between mobile devices and infrastructure networks. For example, a system can be based on WiFi access points at unknown locations to serve as beacons [3]. Then a training phase is exploited to learn

the possible signal strengths of these beacons at locations of our interest. The training results will be stored in a location database. Then, in the positioning phase, an object to be localized will compare the strengths of received signals against the location database to estimate its location. Extensive research has been dedicated toward this direction [7], [9], [12], [13], [14], [19], [25].

While the above works assume that beacons are static, some works have considered mobile beacons [16], [18], [22], [26]. It is typically assumed that a mobile beacon cannot only move around but also locate itself through a special device or mechanism. With periodic broadcast, these mobile beacons can also help conduct localization. The trajectory of the locations where broadcast messages are sent can be regarded as a sequence of static sensors.

All the above works assume that beacons are reliable. In reality, some beacons may be moved to locations where they are not supposed to be without being noticed. Some beacon signals may be blocked by new obstacles deployed after the training phase, making their signal strengths untrustworthy. Some beacons may even conduct malicious attacks if they are compromised. To address the reliability issue, Olson et al. [18] mention the concept of beacon movement. The authors propose using a powerful mobile device to relocate those moved beacons. How to detect malicious beacons in a localization system is addressed in [15], [27]. A malicious beacon is one which is tampered or compromised by an adversary and which can provide false distance or angle measurements. A malicious attack can be conducted individually or cooperatively. In this work, we do not consider intelligent malicious beacons. Instead, we assume that beacons are tiny and lightweight. The major sources of unreliability come from unnoticed movement of some of these tiny beacons or unnoticed deployment of obstacles after the training phase, which may lower some beacons’ signal quality. However, signal quality from beacons can always be correctly measured, unless they are being interfered by noise. Based on these assumptions, we discuss our BMD problem.

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To solve the BMD problem, we propose four detection schemes, namely LB, NB, SSB, and SSR schemes. These schemes differ in their local processing rules of beacons and the corresponding decision algorithms at the BMD engine. In the LB scheme, each beacon reports its observed signal strengths, which are used by the BMD engine to compute each beacon’s current location. The result is used to compare against its original location. In the NB scheme, each beacon locally decides if some neighboring beacons have moved into or out of their communication coverage range and reports its binary observations to the BMD engine. The SSB scheme is similar to the NB scheme, but the definition of movement is according to a threshold of signal strength change. In the SSR scheme, a beacon does not try to determine whether a neighboring beacon has been moved or not. Instead, each beacon reports the amount of signal strength change of each neighbor; the sum of all reported values is used by the BMD engine to make a global decision.

4.1 Location-Based Scheme

The LB scheme assumes that the initial locations of beacons are known by the BMD engine in advance and utilizes localization techniques to monitor the locations of beacons. Techniques such as trilateration or pattern matching can be used in the BMD engine. Each beacon is in charge of reporting the observed signal strength values of its neighbors to the BMD engine. Hence, the observation ot

i;jis defined as oti;j¼ sti;j, where sti;j is the observed signal

strength by bion bj. The engine then estimates the position

of each beacon through any localization technique. Let the estimated location of bjat the current time t be ‘tj. Then the

tolerable region Rj will be used to decide whether bj has

been moved. If ‘t

jis out of the tolerable region Rj, then bjis

determined to be unreliable.

An example using the trilateration technique is shown in Fig. 3. Beacon b4 is moved out of its tolerable region R4.

Since beacons b1, b2, and b3 are unmoved, they can help to

determine b4’s new location. One point worth mentioning is

that because of b4’s movement, the estimated locations of b1,

b2, and b3 may also be changed by a certain degree. So the

outcome depends on the observations of the beacons in BM.

Intuitively, the LB scheme is sensitive to the performance of the adopted localization system. If the density of beacons is too low or signal strengths are too unstable, the results of movement detection cannot perform well.

Since this scheme uses beacons (including unreliable ones) to localize each other, moved beacons will also contribute some errors to the mutual localization process and thus influence our decisions. Here we propose to use a simple greedy approach as follows. After the BMD engine receives the observations from all beacons, it estimates their possible locations under current mutual observations. Then the beacon bi with the longest moved distance will be

selected. If bi’s current location is out of its tolerable

region, it will be included in BD and any observations

contributed from bi will be removed from Ot. This greedy

process will be repeated until the most suspicious one is found and is regarded as an unmoved one. Our experience

Fig. 3. An example of movement detection in the LB scheme where b4is

the only beacon being moved. A trilateration technique is used in this example.

shows that this greedy strategy can identify most of the unreliable beacons.

4.2 Neighbor-Based Scheme

In the previous LB scheme, we report the observations according to the received signal strengths directly. It is sensitive to any slight movement. Hence, the NB scheme is designed to hide the information of signal strengths and just report binary observations to the BMD engine. In this scheme, each beacon bi monitors the change of

neighbor-hood relations with other beacons in its coverage area. The neighborhood relation of bi at time t is defined as

nt i;j¼ 1; if bican hear bj; 0; otherwise:  Let n0

i;j be the original neighborhood relation when the

system was first configured. Then the observation ot

i;jof bion

bj at time t is oti;j¼ nti;j n0i;j, where  is the “exclusive-or”

operator. An example with four beacons is shown in Fig. 4a, where the coverage of each beacon is a circle of radius one. Initially, each beacon is in the coverage of two neighboring beacons. Suppose that at time t, beacons b3and b4are moved

as shown in Fig. 4b. If the tolerable regions are defined in such a way that each beacon can only move no more than one grid length, then the observation matrix Ot_{is as shown}

in Fig. 4c. Note that due to the asymmetric property of radio propagation, ot

i;j¼ 1 does not imply otj;i¼ 1. Hence, the

matrix Ot_{could be asymmetric.}

Unfortunately, given an observation matrix Ot_{, it is}

possible to come up with other beacon movement scenarios that result in the same Ot_{. For example, the movement}

scenario in Fig. 4d also has the same observation matrix as shown in Fig. 4c. In fact, we can prove a stronger result that such ambiguity always exists.

Definition 1. An observation matrix Ot _{obtained in the NB}

scheme is ambiguous if there exist two different movement scenarios BMand B0Msuch that 1) both BMand B0Mresult in

the same Ot_{and 2) B}

M\ CðOtÞ 6¼ B0M\ CðOtÞ, where CðOtÞ

is the candidate set such that CðOt_{Þ ¼ fb}

jjOt½i; j ¼ 1 or

Ot½j; i ¼ 1; 1  i  n; 1  j  ng and CðOt_{Þ 6¼ ;.}

Condition 2 is to ensure that there is a nontrivial difference between BMand B0M. Each beacon in CðOtÞ is detected to be

moved by at least one other beacon.

Theorem 1. Given any movement scenario BM and its

corresponding observation matrix Ot _{obtained in the NB}

scheme, we can always find another movement scenario B0M

such that Ot_{is ambiguous.}

Proof. Given any BM and its corresponding Ot, we can

easily compute BM\ CðOtÞ. To construct another B0M, we

first pick any beacon bk2 BM\ CðOtÞ and move all

beacons in BM fbkg to their new locations, as specified

in the movement scenario BM. Let the corresponding

observation matrix of yet-to-be-constructed movement scenario B0

M be ^O

t_{. We shall show that O}t_{¼ ^O}t_{. For the}

time being, for any beacons biand bj2 B such that bi6¼ bk

and bj6¼ bk, we can derive that ^Ot½i; j ¼ Ot½i; j.

Next, suppose that in the movement scenario BM,

beacon bkis moved from location ‘1to ‘2. Let the moving

vector v*¼ ‘2 ‘1. Then, we move all beacons except bk

(i.e., B  fbkg) by the vector v *

. Such movements will not change the entries Ot_{½i; j and ^O}t_{½i; j for all i 6¼ k and}

j6¼ k. Also, these movements will not change the relative locations of bi and bk for all bi2 B  fbkg, i.e., ^Ot½k; i ¼

Ot½k; i and ^Ot½i; k ¼ Ot_{½i; k for all i. Clearly, the new}

movement scenario will lead to ^Ot_{¼ O}t_{. Furthermore,}

bk2 BM\ CðOtÞ and bk62 B0M, which implies that

bk62 B0M\ Cð ^OtÞ, so this theorem is proved. tu

An example of the proof of Theorem 1 is shown in Fig. 4d. Let BM be the movement scenario in Fig. 4b. To construct

B0_M, b3 is kept unchanged and b4 is moved as scheduled.

Then b1, b2, and b4 are moved in the direction ð0; 1Þ (the

reverse of b3’s moving vector ð0; 1Þ). This shows that the

matrix Ot_{in Fig. 4c is ambiguous.}

Clearly, the above ambiguity property prohibits us from finding the exact BM given any Ot. In the NB scheme, our

derivation will rely on the assumption that unreliable beacons are only a small proportion among all beacons. This assumption is reasonable because, in practice, beacons are usually moved by accident. Hence, we will try to construct a set BD that is as small as possible. First, we transform

matrix Ot_{to a directed observation graph G}

O¼ ðV ; EÞ, where

V ¼ CðOt_{Þ and E ¼ fhb}

i; bjijOt½i; j ¼ 1; bi2 V ; bj2 V g.

Re-call that Ot _{could be asymmetric, so we define G} O as a

directed graph. Second, observe that if hbi; bji exists, then

not only bi but also bj is suspicious. We may consider bi to

be suspicious because the existence of hbi; bji may result

Fig. 4. An example of BMD problem in the NB scheme: (a) the original relation, (b) a movement scenario, (c) observation matrix Ot_{, (d) another}

from the movement of bi and the change of link property

between biand bj. For example, in Fig. 5, the link between bi

and bj is changed from an asymmetric link to a symmetric

one (we are assuming a larger coverage for bi) due to the

movement of bi. Therefore, the problem can be regarded as

a vertex cover problem [8], whose goal is to find the smallest set V0_{ V such that, for each hb}

i; bji 2 E, bi2 V0or bj2 V0

or both. For example, Fig. 4e represents the observation graph of the Ot_{in Fig. 4c.}

The minimum vertex cover problem is known to be NP-complete. Hence, after constructing graph GO, the NB

scheme adopts a heuristic approach as follows. If a beacon bi’s in-degree in GOis higher, it is more suspicious

to be moved. So the engine sorts the vertices in GO

according to their in-degrees of the uncovered edges in a descending order, and then selects the first one. This node is included in BD if any edge incident to it has not been

covered. After selecting the most suspicious one, we will sort the vertices again. This process is repeated until a vertex cover is found (all edges in GOare covered).

4.3 Signal Strength Binary Scheme

In the previous NB scheme, we only consider the neighborhood relations between beacons. The LB scheme is more accurate because it considers the change of locations of beacons. In the SSB scheme, we assume that beacons can measure the signal strengths of HELLO packets from their neighbors. However, beacons do not report these measure-ments to the BMD engine directly. Instead, each beacon bi

evaluates the amount of signal strength change of each neighboring beacon bj locally and only reports a binary

value to the BMD engine. Let the observed signal strength by bi on bjat time t be sti;j (when t ¼ 0, it means the initial

observed signal strength). The observation ot

i;j of bi on bj is

ot_i;j¼ 1; if sti;j þi;jor sti;j i;j;

0; otherwise; 

where þi;j and i;j are the predefined thresholds of signal

strength variations. Note that if beacon bidoes not hear any

signals from bj, we let sti;j¼ smin, where smin denotes the

minimum signal strength. The thresholds þ_i;jand 

i;jof each pair of beacons bi and

bjcan be determined by the tolerable region Rjof bj. Within

the tolerable region Rj, we pick several sampling points.

For example, in Fig. 6, four sampling points p1, p2, p3, and

p4 are collected on the east, west, south, and north sides of

the boundary of Rj. For each neighboring beacon bi, we

measure the average signal strength at each of these sampling points, assuming that bj is moved to this

sampling point. Note that if beacon bi does not hear any

signals from bjat a sampling point, we let its average signal

strength be smin. Among all sampling points, the average

signal strength at the point with the largest value is selected as the value of max

i;j and the one with the smallest value

is selected as the value of min

i;j . Then, considering the effect

of noise, we further add a tolerable threshold SSB and

set þ

i;j¼ i;jmaxþ SSB and i;j¼ mini;j  SSB.

The major difference between the NB scheme and the SSB scheme is the calculation of local observation. However, the ambiguity property still holds.

Definition 2. An observation matrix Ot _{obtained in the SSB}

scheme is ambiguous if there exist two different movement scenarios BMand B0Msuch that 1) both BMand B0Mresult in

the same Ot_{and 2) B}

M\ CðOtÞ 6¼ B0M\ CðOtÞ, where CðOtÞ

is the candidate set such that CðOt_{Þ ¼ fb}

jjOt½i; j ¼ 1 or

Ot_{½j; i ¼ 1; 1  i  n; 1  j  ng and CðO}t_{Þ 6¼ ;.}

Theorem 2. Given any movement scenario BM and its

corresponding observation matrix Ot _{obtained in the SSB}

scheme, we can always find another movement scenario B0 M

such that Ot_{is ambiguous.}

Proof.The proof is similar to that of Theorem 1. Given BM,

we can construct another movement scenario B0 M in a

similar way. Still, we can prove that 1) for any beacons bi

and bj2 B such that i 6¼ k and j 6¼ k; ^Ot½i; j ¼ Ot½i; j,

and 2) for all i 6¼ k, we can derive that ^Ot½k; i ¼ Ot_{½k; i}

and ^Ot_{½i; k ¼ O}t_{½i; k. To prove 1), we move all beacons}

in BM fbkg to their new locations as specified in the

original movement scenario. To prove 2), we move all beacons except bk by an opposite moving vector of the

original moving vector of bk. After these movements, the

relative positions of beacons are the same as that in the movement scenario BM. Hence, sti;j equals the new

observed signal strength st i;j

0

in B0

M. Besides, the

thresh-old þ

i;j and i;j for each pairs bi and bj only depend on

bj’s tolerable region and the initial deployment, so these

observation matrices will be identical. tu Based on changes of signal strengths, the BMD engine for the SSB scheme can work similarly to that for the NB

Fig. 5. An example of the appearance of edgehbi; bji in GOcaused by

the movement of bi. Note that we assume that the communication range

of biis larger than that of bj.

Fig. 6. Determining thresholds þ_i;jand 

i;jby the tolerable region Rjof bj

scheme, except that the observations are computed by each beacon by a different criteria. So we omit the details. However, with more accurate information, this scheme is expected to perform better than the NB scheme. We will verify this through simulations in Section 5.

4.4 Signal Strength Real Scheme

Similarly to the previous SSB scheme, the SSR scheme assumes that beacons can measure the signal strengths from their neighboring beacons. However, in this scheme, the real signal strength variations, instead of binary values, ob-served by a beacon are reported to the BMD engine. Specifically, the observation ot

i;j is ot_i;j¼st i;j s 0 i;j  :

Similarly to the previous schemes, the ambiguity property still remains.

Definition 3. An observation matrix Ot _{obtained in the SSR}

scheme is ambiguous if there exist two different movement scenarios BMand B0Msuch that both BMand B0Mresult in the

same Ot_.

Theorem 3. Given any movement scenario BM and its

corresponding observation matrix Ot _{obtained in the SSR}

scheme, we can always find another movement scenario B0M

such that Ot_{is ambiguous.}

Proof. The proof is similar to that of Theorem 2. The same approach is applied to construct another movement scenario B0M. We can observe that B0M is a shifted

movement scenario of BM. This means that the relative

distance of any beacon bito its neighbor bjin BMis the same

as the relative distance of the corresponding beacon b0 iand

b0

jin B0M. Hence, Ot½i; j ¼ ^Ot½i; j for all i and j. tu

To avoid the effect of slight signal fluctuation and tolerable movement, we apply the following two rules to filter out those small values in the observation matrix: In the first rule, we remove the observations affected by small noises. We define a new n n matrix X such that

X½i; j ¼ 0; Ot½i; j < SSR;

Ot_{½i; j; otherwise;}



where SSR is a tunable threshold value. Hence, we drop

the observations that are insignificant. In the second rule, we intend to avoid selecting those beacons whose move-ments are within their tolerable regions. We filter out all observations on bj if the summations of signal strength

changes observed by other beacons are below a threshold i.

So, we define another n n matrix X0 such that X0½i; j ¼ 0;

Pn

k¼1O½k; j < j;

X½i; j; otherwise; 

where j is related to the tolerable region Rj of bj. To

determine a suitable j, we adopt a similar sampling

strategy as shown in the SSB scheme. The threshold j of

beacon bj is calculated by an approximation as follows.

Within the tolerable region Rj, we pick several sampling

points. For example, four sampling points are selected on the east, west, south, and north sides of the boundary of

Rj in Fig. 6. For each sampling point, we measure the

sum of signal strength changes observed by other beacons assuming that bj is moved to that sampling point. The

sum of the signal strength changes at the point with the smallest value which is selected as the value of j.

Next, we convert the problem to the minimum weight vertex cover problem [10]. We define a directed weighted observation graph GO¼ ðV ; EÞ, where V ¼ fbjjPni¼1X0½i; j 6¼ 0g and

E¼ fhbi; bjijX0½i; j 6¼ 0; bi2 V ; bj2 V g. Similar to the NB

and SSB schemes, we suspect that bior bjhas been moved if

hbi; bji exists. The suspicion degree of beacon bi is defined as

wsðbiÞ ¼Pnj¼1X0½j; i. The maximum suspicion degree is

written as w

s¼ maxi¼1::nfwsðbiÞg. A weight function w :

V7!Rþ _{is then defined for each b}

i2 V such that wðbiÞ ¼

ws wsðbiÞ. According to the definition of the minimum

weight vertex cover problem, we try to find a vertex cover V0 V such that if hbi; bji 2 E, then bi2 V0or bj2 V0or both,

and the sum Pbi2V0wðbiÞ is minimized. Note that the

minimum weight vertex cover problem is still NP-complete. From the above formulation, we have converted our BMD problem to the minimum weight vertex cover problem. Then, the SSR scheme adopts a heuristic strategy to find a vertex cover with the minimum weight in GO. For

each beacon bi, we define a cost metric ci¼ wðbiÞ=UEðbiÞ,

where UEðbiÞ is the number of uncovered edges of bi. Then,

the beacon with the minimum cost metric is included in our solution. Then we compute the cost metrics of those beacons that are affected due to the selection of the above beacon and pick the next beacon with the minimum cost metric. This is repeated until all edges are covered.

5

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In this section, we present our simulation results to evaluate the proposed schemes. Ideally, we would expect that BM¼ BD. However, for many practical reasons, this may

not be achieved. For ease of discussion, we define two events. A hit event occurs for a beacon biif bi2 BMand the

BMD engine also determines that bi2 BD. A false event

occurs for biif bi62 BMbut bi2 BD. We also use the results

to calibrate the positioning engine and measure the localization error when there are unnoticed beacon move-ment events (i.e., we compare the positioning accuracy when our schemes are applied against the fact that no action is taken with the existence of beacon movement events). Experiments are conducted under different condi-tions, such as the ratio of moved beacons, the maximum movement distance, the degree of radio irregularity, the degree of varied sending power, and the noise level of the environment. Also, we adopt a close-to-reality radio model called RIM [28] to conduct our simulations.

5.1 Simulation Model

The sensing field is a 300 m 300 m area. There are 20 beacons randomly deployed on this field with the restriction that the distance between any two beacons is at least 5 m. This restriction is to avoid some beacons being placed too crowded, thus reducing the detection capability of the network. When a scenario violating the restriction is generated, we will discard it and regenerate another one.

Moved beacons are chosen randomly and a parameter moved ratio (MR) is used to control the number of moved beacons. The moving distance is uniformly distributed between MD  50 and MD, where MD is a parameter called moved degree. The tolerable region of the movement of each beacon is a circle centered at the beacon with a radius of 20 m. Note that constrained by the tolerable regions, only part of the moved beacons will be considered moved.

Based on RIM [28], the received signal strengths at a distance of d is modeled by

PrðdÞ ¼ PtV SP P L

DOI_{ðdÞ þ Nð0; }

fÞ; ð1Þ

where PV SP

t is the transmit power, which may vary among

different hardware, P LDOI_{ðdÞ is the path loss, which has a}

nonisotropic and continuous property, and Nð0; fÞ is a

zero-mean normal random variable with a standard deviation f to stand for dynamically shadowing noise.

RIM introduces the variance of sending power (VSP) to model the impacts of hardware difference and remaining battery of a device on transmit power

P_tV SP ¼ Pt 1 þ Nð0; VSPÞð Þ; ð2Þ

where Ptdenotes the initial transmit power and Nð0; VSPÞ is a

zero-mean normal random variable with a standard devia-tion VSP. The parameter VSP controls the degree of variance of sending power among different beacons. Each beacon randomly selects its PV SP

t when the simulation starts.

In real-world experiments, the irregularity of signal fading is a common phenomenon. However, most path loss models do not take this nonisotropic property of signal coverage into consideration. To capture this effect, RIM imports a degree of irregularity (DOI) to control the amount of path loss in different directions, i.e.,

P LDOIðdÞ ¼ P LðdÞ Ki; ð3Þ

where P LðdÞ is the optimal obstacle-free path loss formulation

P LðdÞ ¼ P Lðd0Þ þ 10log

d d0

; ð4Þ where d0 is the reference distance (here we set d0¼ 1). The

coefficient Kiis to model the level of irregularity at degree i

(i ¼ 0::359) such that Ki ¼ 1; if i¼ 0; Ki1 W ð0; d; Þ DOI; if i¼ 1::359;  ð5Þ where jK0 K359j  DOI and W ð0; d; Þ is a zero-mean

Weibull random variable. The parameter DOI controls the allowable difference of two successive degrees. When Ki¼ 1, it implies an ideal path loss model. When Ki

deviates more from 1, it means a greater deviation from the ideal path loss formulation. Note that (5) is a discrete model with 360 discrete values. To extend to a continuous model, one may adopt an interpolation mechanism.

All results are from the average of 20 experiments. To reduce the influence of noise, signal strength is calculated from the average of 50 HELLO packets. The default simula-tion parameters are set to Pt¼ 15 dBm, d0¼ 1 m, P Lðd0Þ ¼

41:5dBm,  ¼ 3:3, f¼ 2, VSP ¼ 0:2, DOI ¼ 0:005, d¼ 0:1,

and  ¼ 1.

5.2 Parameters of the SSB and SSR Schemes Before conducting thorough simulation studies, we first tune the parameters of the SSB and SSR schemes. In these schemes, we have two thresholds SSB and SSR to

eliminate the effect of signal fluctuation and irregularity, respectively. Generally speaking, larger thresholds incur higher hit probabilities and lower false probabilities. Fig. 7 illustrates the hit and false probabilities of SSB and SSR under different values of thresholds. Hence, based on these results, we let SSB¼ 3 and SSR¼ 6.

5.3 Probabilities of Hit and False Events

In this simulation study, we evaluate the hit and false probabilities of the proposed schemes under different environmental conditions. Here, we define the hit prob-ability as the frequency of occurrence of hit events, e.g.,

jBD\BMj

jBMj , and the false probability as the frequency of

occurrence of false events, e.g.,jBDBMj

jBBMj. First, in Fig. 8a, we

vary the noise level by adjusting the standard deviation fof

RIM from 0 and 4. As expected, the NB scheme performs the worst because it is too insensitive to beacon movement events. Hence, only a few beacon movement events are correctly detected and many unmoved beacons are falsely alarmed. Under our simulation parameters, the LB scheme can detect all beacon movement events under different noise levels, but it has higher false probability than SSB and SSR.

In Fig. 8b, we study the influence of the radio irregularity on each scheme. We can observe that the false probabilities of SSB, SSR, and LB increase as the radio propagation is more irregular. For SSB and SSR, their false probabilities are high due to their static thresholds SSB

and SSR, which prohibit them from dynamically

adjust-ing themselves to fit to the environment. For LB, it initially outperforms NB when the degree of irregularity is low, but is outperformed by NB as the degree of irregularity becomes higher than 0.006.

Fig. 8c illustrates the influence of beacons’ variable sending power. Larger values of VSP mean that beacons’ sending power is of higher degree of differences, which in turn imply that we may see more asymmetric links between

beacons. Since our modeling has considered asymmetric links, all schemes except the NB scheme can handle such situations well. For the NB scheme, we see a significant increase in its false probability.

5.4 Movement Degrees and Movement Ratios In Fig. 9a, we vary the values of MR between 0.1 and 0.5 to make the comparison. In terms of the hit probability, the LB scheme performs the best, followed by SSB, SSR, and then NB. However, the LB scheme also induces the highest false probability. As a result, SSB and SSR are considered the best, which provide a hit probability over 0.85 and a false probability under 0.17 even when the MR is 0.4. The NB scheme always has the worst hit and false probabilities due

Fig. 8. Comparison of hit and false probabilities by varying (a) the standard deviation f, (b) the degree of irregularity DOI, and (c) the varied sending

to its oversimplified detection model. The high false probability of the LB scheme can be explained by its high sensitivity to signal change. Since beacons will all report their observations, the movement of a beacon can easily propagate errors to its neighboring beacons. Thus, a lot of reliable beacons will be reported as unreliable. The same phenomenon can also be seen for the SSR scheme when the MR gets higher. However, its false probability is much less than that of the LB scheme.

In Fig. 9b, we vary the MD. Generally, because a larger MD means that each movement is more dramatic, this is beneficial for our detection work. Therefore, we see increases of hit probabilities and decreases of false prob-abilities as MD increases in all schemes except the NB and LB schemes. Again, this demonstrates that the NB scheme is oversimplified and the LB scheme is too sensitive.

Furthermore, we are interested in the evaluation of MD and MR under the ideal log-distance path loss model. Recall that when V SP ¼ 0 and DOI ¼ 0, RIM actually reduces to the log-distance model. The results are shown in Fig. 10. Comparing Figs. 9 and 10, we can observe that they have similar trends. Beside, both the hit and false probabilities are improved under the log-distance model, because its radio propagation is more predictable.

5.5 Effect of Beacons’ Density

Intuitively, more beacons are beneficial to the BMD problem. More beacons imply that each beacon has a

chance to be monitored by more neighboring beacons, so the hit and false probabilities may be improved. We can verify this claim in Fig. 11. As the number of beacons increases, the hit probabilities of all schemes are improved. As for the false probability, only minor improvement can be seen for the SSB and SSR schemes. However, we see noticeable improvement for LB. When the number of beacons is more than 25, the false probability of LB will be comparable with SSB and SSR. The reason is that the positioning accuracy also improves as the number of beacons increases. This proves that the performance of LB is highly dependent on the positioning accuracy. Hence, we can conclude that in a denser scenario with many beacons, the LB scheme is an ideal choice because it gives a comparable hit probability and a lower false probability. However, in a sparser environment, the SSB and SSR schemes are better choices because of not only their performance but also their lower complexity.

5.6 Impact of BMD on Localization Accuracy After determining the moved set BD, the positioning engine

should be recalibrated to improve its positioning capability. We adopt the pattern-matching localization algorithm [3] in our simulation, where the location database contains the signal vector i¼ ½i;1; i;2; . . . ; i;n of each training

location ‘i in the sensing field, where i;j is the average

signal strength of beacon bjobserved at location ‘i; i¼ 1::m.

For the calibration purpose, we will ignore the element i;j

corresponding to each bj2 BD during the localization

procedure. Clearly, this will reduce the number of beacons to be referenced (including hit and false ones). However, if contributions from those moved beacons are not deleted, the errors may be high. In the following, we will evaluate how our schemes can improve localization errors if there exist beacon movement events.

In our experiment, we collect 961 training locations at locations ð10 i; 10 jÞ, for i ¼ 0::30 and j ¼ 0::30. Then, in the positioning phase, we simulate a moving object in the field following the random waypoint model. It will switch between a moving state and a pausing state. In the moving state, it will randomly select a destination in the sensing field and move to it at a constant speed of 1 m/sec.

After reaching the destination, it will switch to the pausing state and stay there for 3 seconds. The tracked object also measures the signal strengths of all beacons every 1 second. The total simulation time is 1,000 seconds. We compare our results against the Optimal case, where the hit probability is always 1 and the false probability is always 0, and the no_BMD case, where the hit probability is always 0 and the false probability is always 0 (i.e., no special action is taken). Figs. 12a and 12b illustrate the average positioning errors under different MR and MD, respectively. The results in Fig. 12a demonstrate that SSB and SSR incur positioning errors closest to the Optimal case. One interesting simulation result is that NB’s errors are quite unacceptable, sometimes even worse than the no_BMD

Fig. 11. Comparison of hit and false probabilities by varying the density of beacons.

case. This is because of its low hit probability and high false probability. LB is slightly worse than SSR when MR 0:3. However, referring to Fig. 9a, we see that LB also has high false probabilities as MR increases. Hence, when MR ¼ 0:5, LB’s positioning errors are higher than those of the other schemes.

The comparisons of the positioning errors under differ-ent values of MD are shown in Fig. 12b. The trends are similar. Under all simulated MR, SSB and SSR perform very close to the Optimal case. NB incurs the worst performance. To model the error recovery capability using the Optimal case as the baseline, we propose the following Error Improvement Ratio metric:

EIRðBMD SchemeÞ

¼errorno BMD errorBMD Scheme errorno BMD errorOptimal

100%:

The ideal value of EIR is 100 percent. However, this is hard to achieve because our current results cannot achieve 100 percent hit and 0 percent false probabilities. For example, under the default settings, the EIR values are 47.77, -58.85, 72.99, and 70.66 percent for LB, NB, SSB, and SSR, respectively.

6

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In this paper, we have identified a new BMD problem in wireless sensor networks for localization applications. This problem describes a situation where some beacon sensors which participate in the localization procedure are moved unexpectedly, called beacon movement events. The nega-tive impact is a reduced localization accuracy if we disregard such events. We propose to allow beacons to monitor each other to identify such events. Four schemes are presented for the BMD problem. Moreover, we have proven some ambiguity theorems which may prohibit the BMD problem from being solved correctly under some situations. Some heuristics are proposed by mapping the BMD problem to the vertex-cover problem. Hit and false probabilities of these heuristics are obtained through simulations under a realistic radio irregularity model [28]. It is shown that the best heuristics, SSB and SSR, have an error improvement ratio of more than 70 percent in most cases. As to future work, it deserves to further investigate

the BMD problem if there is some trust model among beacons. Based on the observations contributed from the trust model, the BMD problem should be solved more effectively. Besides, in this paper, we omit the observations from the moved beacons to avoid more serious positioning errors in the localization process. It could be more beneficial to the localization system if we can relocate those moved beacons. Finally, a variant of the beacon movement detection problem, when there are some mobile beacons which may move away from their original moving trajectories, also deserves further investigation.

A

A preliminary version of this paper appeared in [11]. Y.-C. Tseng’s research was cosponsored by MoE ATU Plan, by NSC grants 96-2218-E-009-004, 3114-E-009-001, 97-2221-E-009-142-MY3, and 2219-E-009-005, by MOEA 98-EC-17-A-02-S2-0048, and by ITRI, Taiwan.

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Sheng-Po Kuo received the BS and MS degrees in computer science and information engineering and the PhD degree in computer science from the National Chiao Tung Univer-sity, Hsinchu, Taiwan, in 2001, 2003, and 2008, respectively. He is currently a senior scientist at Telcordia Technologies. His current research interests are primarily in applying machine learning techniques to indoor localization, in-cluding large-scale pattern-matching localization algorithms, location tracking algorithms, and hybrid localization systems. He is a member of the IEEE Computer Society.

Hsiao-Ju Kuo received the BS and MS degrees in computer science and information engineering in 2004 and 2006, respectively, from the National Chiao Tung University, Hsinchu, Tai-wan. She is currently an engineer at MediaTek Incorporation. Her current research interest is in communication protocol enhancement for GSM/ GPRS systems. She especially focuses on GSM radio access stratum-related technologies, in-cluding network searching mechanism, call establishment, and AGPS.

Yu-Chee Tseng received the PhD degree in computer and information science from the Ohio State University in January 1994. He is a professor (2000-present), chairman (2005-pre-sent), and associate dean (2007-present) at the Department of Computer Science, National Chiao-Tung University, Taiwan. He is also an adjunct chair professor at Chung Yuan Christian University (2006-present). He received the Out-standing Research Award by the National Science Council, ROC, in both 2001-2002 and 2003-2005, the Best Paper Award at the International Conference on Parallel Processing in 2003, the Elite IT Award in 2004, and the Distinguished Alumnus Award by the Ohio State University in 2005. His research interests include mobile computing, wireless communication, and parallel and distributed computing. He serves on the editorial boards for Telecommunication Systems (2005-present), the IEEE Transactions on Vehicular Technol-ogy (2005-present), the IEEE Transactions on Mobile Computing (2006-present), and the IEEE Transactions on Parallel and Distributed Systems (2008-present). He is a senior member of the IEEE Computer Society.

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