Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 212806 11 pageshttpdxdoiorg1011552013212806

Research ArticleLocalization with Single Stationary Anchor for Mobile Node inWireless Sensor Networks

Haipeng Qu1 Guojia Hou1 Ying Guo2 Ning Wang1 and Zhongwen Guo1

1 Department of Computer Science Ocean University of China Qingdao 266100 China2 School of Information Science and Technology Qing Dao University of Science and Technology Qingdao 266100 China

Correspondence should be addressed to Haipeng Qu haipengqugmailcom

Received 16 October 2012 Revised 15 January 2013 Accepted 8 February 2013

Academic Editor Long Cheng

Copyright copy 2013 Haipeng Qu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We proposed a localization algorithm named LSARSSI for mobile node based on RSSI (received signal strength indicator) betweenlocating sensor node with inertia module built-in and the single anchor Instead of directly mapping RSSI values into physicaldistance contrasting RSSI values received from anchor in different visited locations LSARSSI utilizes the geometric relationshipof perpendicular intersection to compute node positions Given that the values of RSSI among two visited locations are equal weregard that their distances to anchor node are equal After obtaining several sets of such visited locations the relative location ofmobile node and anchor node can be calculated Because of the limitations of LSARSSI we put forward an improved algorithmnamed ILSARSSI Our scheme uses only one location-known anchor which is useful in low density environment without usingadditional hardware The simulations show that LSARSSI achieves high accuracy and ILSARSSI performs high stability andfeasibility

1 Introduction

Wireless sensor networks (WSNs) are such popular researchfields that are highly interdisciplinary and state-of-the-art[1] It has emerged as one of the key enablers for a varietyof applications such as military environment monitoringemergency response target detection and tracking and somebusiness fields In recent years a number of research achieve-ments aboutWSNs localization have arisen According to thedeployment of beacon nodes (which is also called anchor)the localization approaches that have been proposed can bedivided into two types one of which is based on multiplestationary beacon nodes [2ndash5] and another is based onmobile beacon node(s) [6ndash10]

But these methods are not suitable for all the applicationsof WSNs In some scenarios however there is only a station-ary beacon node [11] or a seed (reference nodewhich positionis known) For example when we observe WSN on the seadata can be transmitted to the shore or on board throughan aggregation node and only the position of aggregationnode is known Another example is regarding mountaininspection the inspectorwould carry sensormodule tomovetransmitting data collected through the aggregation base

station on the peak and only the position of base station isknown In this situation neither methods based on mobilebeacon nor methods based on multiple beacon nodes couldbe used directly

To address the previous issues in this paper we pro-posed a localization algorithm named LSARSSI an RSSI-based localization scheme using single stationary anchor Toincrease the feasibility of our scheme we further put forwardan improved method called ILSARSSI Major contributionsof this paper are as follows

(i) Our schemes can be used to locatemobile node in lowdensity environment which only need single anchor

(ii) In order to avoid errors from directly mappingabsolute RSSI values to distances we obtain thegeometrical relationship of sensors by contrastingthe measured RSSI values We then design a novellocalization scheme LSARSSI which has a betteraccuracy and low overhead

(iii) The simulation results show that our schemes per-form high accuracy and feasibility even in large-scaleenvironment

2 International Journal of Distributed Sensor Networks

119883

119885

119884

119860(1199090 1199100 1199110)

1198750(119909 119910 119911)

119875119894(119909 + Δ119909 119910 + Δ119910 119911 + Δ119911)

Figure 1 A model assumption in 3D

The rest of this paper is organized as follows Section 2introduces the related works about the localization of WSNsSections 3 and 4 respectively present our algorithm ofLSARSSI and ILSARSSI Section 5 presents our implemen-tation and the simulation results We conclude this paper inSection 6

2 Related Works

According to the deployment of beacon nodes localizationtechnology can be classified into two categories multiple sta-tionary beacon nodes based approaches and mobile beaconnode(s) based approaches

21 Multiple Stationary Beacon Nodes Based ApproachesMeasurement techniques inWSNs based onmultiple station-ary beacon nodes can be broadly classified into two cate-gories range-based approaches and range-free approaches

211 Range-Based Approaches Range-based approaches as-sume that sensor nodes can measure the distance andor therelative directions of neighbor nodes Several mechanismshave been proposed to measure the nodersquos physical distanceFor example time of arrival (TOA) obtains range informationthrough signal propagation times [12] and time differenceof arrival (TDOA) estimates the node location by utilizingthe time differences among signals that are received frommultiple senders [13] As an extension of TOA and TDOAangle of arrival (AOA) allows nodes to estimate the relativedirections between neighbors by setting an antenna array foreach node [14]

All the previous approaches require additional hardwareequipment so as to increase the cost of the sensor nodesgreatly Such TDOA needs at least two signal generators [13]AOA needs antenna arrays and multiple ultrasonic receivers[14]

A popular and widely used ranging technique is thereceived signal strength (RSS) or quantified as the received

signal strength indicator (RSSI) RSSI is utilized to estimatethe distance between two nodes with ordinary hardware[12 15] Various theoretical or empirical models of radiosignal propagation have been constructed to map absoluteRSSI values into estimated distances [16] The accuracy andprecision of such models however are far from perfectbecause of factors such as multipath fading and backgroundinterference [15 17]

212 Range-Free Approaches Given that range-based ap-proaches are limited by hardware limitations and energyconstraints researchers have proposed range-free solutionsas cost-effective alternatives

Range-free approaches rely on the connectivity measure-ments between the measurement sensor nodes and a numberof reference nodes called seeds For example in the centroidalgorithm [18] seeds broadcast their position to all neighbornodes that record all received beacons Each node estimatesits location by calculating the center of the locations of allseeds it hears In Approximate Point-in-Triangulation Test(APIT) [19] each node estimates whether it resides inside oroutside several triangular regions bounded by the seeds that ithears and refines the computed location by overlapping suchregions In ring overlapping based on comparison of receivedsignal strength indicator (ROCRSSI) [20] each sensor nodeuses a series of overlapping rings to narrow down the possiblearea in which it resides

22 Mobile Beacons Approaches Localization algorithmsmentioned previously are in static sensor networks whichare not available in some scenarios Recently mobile-assistedlocalization approaches have been proposed to improve theefficiency of range-based approaches [10 21] The location ofa sensor node can be calculated with the rangemeasurementsfrom themobile beacon to itself the localization accuracy canalso be improved bymultiplemeasurements that are obtainedwhen the mobile beacons are in different positions

Several localization schemes are proposed in this fieldFor example Bergamo and Mazzini propose a scheme toperform localization based on the estimation of the powerreceived by only two beacons placed in known positions [22]By starting from the received powers eventually averaged ona given window to counteract interference and fading theactual distance between the sensor and the beacons is derivedand the position is obtained by means of triangulationIn [10] a localization technique based on a single mobilebeacon aware of its position (eg by being equipped with aGPS receiver) was presented Sensor nodes receiving beaconpackets infer proximity constraints to the mobile beacon anduse them to construct and maintain position estimates InPI algorithm [9] instead of using the absolute RSSI valuesby contrasting the measured RSSI values from the mobilebeacon to a sensor node PI utilizes the geometric relationshipof perpendicular intersection to compute the position of thenode

In recent years more researches are focusing on mobilesensor networks which are mainly based on mobile nodes[23ndash25] Unlike other algorithms the scene of the application

International Journal of Distributed Sensor Networks 3

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

(a) (b)

RSSI(1198751) RSSI(1198751)

RSSI(1198750) RSSI(1198750)

RSSI(1198751000)

RSSI(119875999)RSSI(119875999)

RSSI(119875119894)[minmax]

11987201198720

11987211198721

119872119894

119872999 119872999

1198721000

Figure 2 The 1001th message stored by sensor

of ours is locating the mobile node with single stationaryanchor by comparing the measured RSSI values betweenthe locating sensor node with inertia module built-in andthe single anchor In this sense LSARSSI and ILSARSSI areactually range-free approaches

3 LSARSSI Algorithm

In this section we first describe the application model inSection 31 Section 32 presents the design of our localizationscheme in detail Section 33 further presents the localizationalgorithm in 3D space

31 Model Assumptions For better implementing our algo-rithm the hypotheses are as follows (1) an anchor and amobile node with inertial module whose trajectory is notdesignated (2) the environment is an obstacle-free outdoorarea (3) the communication is not continuous and thelocating node receives the RSSI at different time intervals(4) the RSSI values can be measured and the offsets can beobtained and stored by themobile node with inertial module

We can illustrate it by the following model assumptionThe coordinate of anchor 119860 is (119909

0 1199100 1199110) Assume that the

coordinate of initial location of the locating node 119873 is1198750(119909 119910 119911) 119875

119894(119894 isin [1 119899]) is a visited location of the mobile

node 119873 after time 119879 the relative offset of node 119873 among1198750and 119875

119894in the 119883 119884 and 119885 axis is Δ119909 Δ119910 and Δ119911 So the

coordinate of 119875119894is (119909 + Δ119909 119910 + Δ119910 119911 + Δ119911) as shown in

Figure 1Table 1 shows the messages obtained by the locating

node 119873 in different visited locations it contains offsets andRSSI values As the locating node needs to store the relativedistances between locations that it visited as well as the RSSIvalues between those locations to the anchor It may requirelarge memory storage for sensors The issue can be resolvedby the following method assume that sensor can store 1000messages of 119875

0to 119875999

and if the RSSI value of 119875119894is minimum

(or maximum) the message of 1198751000

will replace it as shownin Figure 2

As the communication is not continuous and the visitedlocations for our schemes needed are countable the compu-tation and communication costs are acceptable

Table 1 Messages stored by sensor

Locations Messages (node N)1198750

Δ119909 Δ119910 Δ119911 RSSI(1198750)

1198751

119909 + Δ11990901

119910 + Δ11991001

119911 + Δ11991101

RSSI(1198751)

119875119894

119909 + Δ1199090119894

119910 + Δ1199100119894

119911 + Δ1199110119894

RSSI(119875119894)

119875119899minus1

119909 + Δ1199090119899minus1

119910 + Δ1199100119899minus1

119911 + Δ1199110119899minus1

RSSI(119875119899minus1

)119875119899

119909 + Δ1199090119899

119910 + Δ1199100119899

119911 + Δ1199110119899

RSSI(119875119899)

32 Localization Algorithm Design Typically the ensemblemean received power in a real world obstructed channeldecays proportional to 119889

minus119899119901 where 119899119901

is the path-lossexponent [26] The ensemble mean power at distance 119889 istypically modeled as

[119901119903 (119889)]119889119861119898

= [119901119903(1198890)]119889119861119898

minus 10119899 log 119889

1198890

(1)

where 1198750is the received power (dBm) at short reference

distance 1198890

From (1) we know that ideally the longer the distancebetween sender and receiver the weaker the signal strengthdetected by the receiverThe localization schemewas inspiredby the perpendicular bisector of a chord conjecture [27]Withtwo chords of the same circle the intersection point of twoperpendicular bisectors of the chords will be the center of thecircleThe localization problem can be transformed based onthe conjecture The center of the circle is the position of theanchor the chord is a segment that is a connection of twopositions (the RSSI values of the two positions are equal) ofthe mobile node at a given moment The solution is detailedillustrated in Figure 3

Node 119860 is the anchor 119873 is the mobile locating node1198750 1198751 1198752 and 119875

3are the visited locations of locating node

119873 after the time period of 119894119905 119895119905 119896119905 119897119905 119861 119862 are the midpointsof segments 119875

01198751 11987521198753 and RSSI(119875

0) = RSSI(119875

1) RSSI(119875

2) =

RSSI(1198753)

4 International Journal of Distributed Sensor Networks

1198750

1198752

1198753

1198751

119860

119861

119862

Figure 3 An example of LSARSSI algorithm in 2D

The following are the formulas for calculating the locationof locating node

119860 = (1199090 1199100) 119875

0= (119909 119910)

1198751= (119909 + Δ119909

01 119910 + Δ119910

01)

1198752= (119909 + Δ119909

02 119910 + Δ119910

02)

1198753= (119909 + Δ119909

03 119910 + Δ119910

03)

119861 = (119909 + Δ1199090119861 119910 + Δ119910

0119861)

119862 = (119909 + Δ1199090119862 119910 + Δ119910

0119862)

(2)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001) rarr

11987521198753

= (Δ11990923 Δ11991023)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100)

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090)

+ Δ11991001lowast (119910 + Δ119910

0119861minus 1199100) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090)

+ Δ11991023lowast (119910 + Δ119910

0119862minus 1199100) = 0

dArr

(1) Δ11990901lowast 119909 + Δ119910

01lowast 119910

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

(2) Δ11990923lowast 119909 + Δ119910

23lowast 119910

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

(3)

Assume that119886 = Δ119909

01lowast (1199090minus Δ1199090119861)

+ Δ11991001lowast (1199100minus Δ1199100119861)

119887 = Δ11990923lowast (1199090minus Δ1199090119862)

+ Δ11991023lowast (1199100minus Δ1199100119862)

(4)

then (1) (2) can be converted into(3) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 = 119886

(4) Δ11990923lowast 119909 + Δ119910

23lowast 119910 = 119887

dArr

119909 =1198631

119863 119910 =

1198632

119863

(5)

where

119863 =10038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11990923

Δ11991023

10038161003816100381610038161003816100381610038161003816 119863

1=10038161003816100381610038161003816100381610038161003816

119886 Δ11991001

119887 Δ11991023

10038161003816100381610038161003816100381610038161003816

1198632=10038161003816100381610038161003816100381610038161003816

Δ11990901

119886

Δ11990923

119887

10038161003816100381610038161003816100381610038161003816

(6)

33 Algorithm in 3D Here we extend our algorithm tothree-dimensional space As we know if there are threenoncoincident chords on the sphere the intersection of threemidvertical planes is the center of the sphere provided thatthese three planes can intersect

The general idea of this algorithm in 3D utilizes theprevious conjecture This problem can be described as fol-lows the locations of locating node 119873 at different timescompose a collection 119875 = 119875

0 1198751 119875119899 Their RSSI values

are RSSI(1198750)RSSI(119875

1) RSSI(119875

119899) locations can be divided

into a number of subsets 1198731 1198732 119873119898 based on RSSI val-

ues and the RSSI values in each subset are equal respectivelyAfter that given that one of the following conditions occursour LSARSSI algorithm can be achieved (1) |119873

119886| = 2 and

|119873119887| = 2 and |119873

119888| = 2 (as shown in Figure 4(a)) (2) |119873

119886| = 3

and |119873119887| = 2 (as shown in Figure 4(b)) (3) |119873

119886| = 4 (as

shown in Figure 4(c)) (119886 119887 119888 isin [1119898])As (2) and (3) are the special cases of (1) here we take

|119873119886| = 2 |119873

119887| = 2 and |119873

119888| = 2 as an example to indicate

formulas for calculating the location of locating node119860 is theanchor119875

01198751119875211987531198754 and119875

5are the visited locations of the

mobile node 119861 119862 and119863 are the midpoint of 11987501198751 11987521198753 and

11987541198755 And

119860 = (1199090 1199100 1199110)

1198750= (119909 119910 119911)

1198751= (119909 + Δ119909

01 119910 + Δ119910

01 119911 + Δ119911

01)

1198752= (119909 + Δ119909

02 119910 + Δ119910

02 119911 + Δ119911

02)

International Journal of Distributed Sensor Networks 5

119860

119861

119862119863

119884

119883

119885

1198755

1198751 1198752

1198753

1198750 1198754

(a)

119884

119883

119885

119860

1198751

1198752

11987531198754

1198750

(b)

119884

119883

119885

119860

1198752

1198753

1198751

1198750

(c)

Figure 4 Examples of LSARSSI algorithm in 3D

119884

119883

119860

119874

119861

119862

119863

119864

119875998400

1

1198711

11987121198713

1198714

119875998400

3

119875998400

2

119875998400

0

1198751

1198752

1198753

1198750

Figure 5 An example of ILSARSSI algorithm in 2D

1198753= (119909 + Δ119909

03 119910 + Δ119910

03 119911 + Δ119911

03)

1198754= (119909 + Δ119909

04 119910 + Δ119910

04 119911 + Δ119911

04)

1198755= (119909 + Δ119909

05 119910 + Δ119910

05 119911 + Δ119911

05)

RSSI (1198750) = RSSI (119875

1)

RSSI (1198752) = RSSI (119875

3)

RSSI (1198754) = RSSI (119875

5)

(7)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001 Δ11991101) rarr

11987521198753

= (Δ11990923 Δ11991023 Δ11991123)

rarr11987541198755

= (Δ11990945 Δ11991045 Δ11991145)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100 119911 + Δ119911

0119861minus 1199110)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100 119911 + Δ119911

0119862minus 1199110)

dArr

rarr119860119863

= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910

0119863minus 1199100 119911 + Δ119911

0119863minus 1199110)

6 International Journal of Distributed Sensor Networks

Anchor

Locating mobile node

Trajectory

500 lowast 500m2

Figure 6 A trajectory of the locating mobile node

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090) + Δ119910

01lowast (119910 + Δ119910

0119861minus 1199100)

+ Δ11991101lowast (119911 + Δ119911

0119861minus 1199110) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090) + Δ119910

23lowast (119910 + Δ119910

0119862minus 1199100)

+ Δ11991123lowast (119911 + Δ119911

0119862minus 1199110) = 0

dArr

rarr11987541198755

sdot rarr119860119863

= Δ11990945lowast (119909 + Δ119909

0119863minus 1199090) + Δ119910

45lowast (119910 + Δ119910

0119863minus 1199100)

+ Δ11991145lowast (119911 + Δ119911

0119863minus 1199110) = 0

(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

12001000800400 6002000

minus95

minus100

minus105

minus110

minus115

minus120

Time (s)

RSSI

(dBm

)

Figure 7 RSSI values received by locating node after time 119879

(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911

= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(8)

Assume that

119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

International Journal of Distributed Sensor Networks 7

300

250

200

150

100

50

01 2 3 4 5

Transmission period (s)

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

(a) Impact of packet transmission period

250

200

150

100

50

0

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200

Size of sensor field (m2)

(b) Impact of size of sensor field

Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms

119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(9)

then (1) (2) and (3) can be converted into

(4) Δ11990901lowast 119909 + Δ119910

01lowast 119910 + Δ119911

01lowast 119911 = 119886

(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887

(6) Δ11990945lowast 119909 + Δ119910

45lowast 119910 + Δ119911

45lowast 119911 = 119888

dArr

119909 =1198631

119863 119910 =

1198632

119863 119911 =

1198633

119863

(10)

where

119863 =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11991101

Δ11990923

Δ11991023

Δ11991123

Δ11990945

Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198631=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119886 Δ11991001

Δ11991101

119887 Δ11991023

Δ11991123

119888 Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198632=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

119886 Δ11991101

Δ11990923

119887 Δ11991123

Δ11990945

119888 Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198633=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

119886

Δ11990923

Δ11991023

119887

Δ11990945

Δ11991045

119888

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(11)

4 Improved Algorithm ILSARSSI

In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously

cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]

Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875

0) RSSI(1198751015840

0)

RSSI(1198751) RSSI(1198751015840

1) RSSI(119875

2) RSSI(1198751015840

2) RSSI(119875

3) RSSI(1198751015840

3)

and RSSI(1198750) lt RSSI(1198751015840

0) RSSI(119875

1) gt RSSI(1198751015840

1) RSSI(119875

2) gt

RSSI(11987510158402) RSSI(119875

3) gt RSSI(1198751015840

3) The anchor is in the enclosed

region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of

locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained

The following are the formulas for calculating the locationof locating node

119860 (1199090 1199100) 119875

0= (1199091 1199101) 119875

1015840

0= (1199091015840

1 1199101015840

1)

1198751= (1199092 1199102) 119875

1015840

1= (1199091015840

2 1199101015840

2)

1198752= (1199093 1199103) 119875

1015840

2= (1199091015840

3 1199101015840

3)

1198753= (1199094 1199104) 119875

1015840

3= (1199091015840

4 1199101015840

4)

(12)

As 1198711 1198712 1198713 and 119871

4are the perpendicular bisector of

119875011987510158400 119875111987510158401 119875211987510158402 and 119875

311987510158403 according to the geometry of

vector we can obtain that1198711 (1199091minus 1199091015840

1) lowast 119909 + (119910

1minus 1199101015840

1) lowast 119910

= (1199091+ 11990910158401

2) lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1)

8 International Journal of Distributed Sensor Networks

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

Transmission period (s)

(a) Impact of packet transmission period

0

2

4

6

8

10

12

14

16

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

400 lowast 400300 lowast 300 500 lowast 500

Size of sensor field (m2)

100 lowast 100 200 lowast 200

(b) Impact of size of sensor field

Figure 9 Localization error of our LSARSSI algorithm

1198712 (1199092minus 1199091015840

2) lowast 119909 + (119910

2minus 1199101015840

2) lowast 119910

= (1199092+ 11990910158402

2) lowast (119909

2minus 1199091015840

2) + (

1199102+ 11991010158402

2) lowast (119910

2minus 1199101015840

2)

1198713 (1199093minus 1199091015840

3) lowast 119909 + (119910

3minus 1199101015840

3) lowast 119910

= (1199093+ 11990910158403

2) lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2) lowast (119910

3minus 1199101015840

3)

1198714 (1199094minus 1199091015840

4) lowast 119909 + (119910

4minus 1199101015840

4) lowast 119910

= (1199094+ 11990910158404

2) lowast (119909

4minus 1199091015840

4) + (

1199104+ 11991010158404

2) lowast (119910

4minus 1199101015840

4)

As 1198711cap 1198714= 119861 119871

3cap 1198714= 119862

1198712cap 1198713= 119863 119871

1cap 1198712= 119864

dArr

(13)

119909119861=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 1199091015840

1

2)lowast(1199091minus 1199091015840

1) + (

1199101+ 1199101015840

1

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199093+ 1199091015840

3

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 1199101015840

3

2) lowast (119910

3minus 1199101015840

3) 1199103minus 1199101015840

3

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119909119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 11990910158401

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

119910119861=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

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Submit your manuscripts athttpwwwhindawicom

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 International Journal of Distributed Sensor Networks

119883

119885

119884

119860(1199090 1199100 1199110)

1198750(119909 119910 119911)

119875119894(119909 + Δ119909 119910 + Δ119910 119911 + Δ119911)

Figure 1 A model assumption in 3D

The rest of this paper is organized as follows Section 2introduces the related works about the localization of WSNsSections 3 and 4 respectively present our algorithm ofLSARSSI and ILSARSSI Section 5 presents our implemen-tation and the simulation results We conclude this paper inSection 6

2 Related Works

According to the deployment of beacon nodes localizationtechnology can be classified into two categories multiple sta-tionary beacon nodes based approaches and mobile beaconnode(s) based approaches

21 Multiple Stationary Beacon Nodes Based ApproachesMeasurement techniques inWSNs based onmultiple station-ary beacon nodes can be broadly classified into two cate-gories range-based approaches and range-free approaches

211 Range-Based Approaches Range-based approaches as-sume that sensor nodes can measure the distance andor therelative directions of neighbor nodes Several mechanismshave been proposed to measure the nodersquos physical distanceFor example time of arrival (TOA) obtains range informationthrough signal propagation times [12] and time differenceof arrival (TDOA) estimates the node location by utilizingthe time differences among signals that are received frommultiple senders [13] As an extension of TOA and TDOAangle of arrival (AOA) allows nodes to estimate the relativedirections between neighbors by setting an antenna array foreach node [14]

All the previous approaches require additional hardwareequipment so as to increase the cost of the sensor nodesgreatly Such TDOA needs at least two signal generators [13]AOA needs antenna arrays and multiple ultrasonic receivers[14]

A popular and widely used ranging technique is thereceived signal strength (RSS) or quantified as the received

signal strength indicator (RSSI) RSSI is utilized to estimatethe distance between two nodes with ordinary hardware[12 15] Various theoretical or empirical models of radiosignal propagation have been constructed to map absoluteRSSI values into estimated distances [16] The accuracy andprecision of such models however are far from perfectbecause of factors such as multipath fading and backgroundinterference [15 17]

212 Range-Free Approaches Given that range-based ap-proaches are limited by hardware limitations and energyconstraints researchers have proposed range-free solutionsas cost-effective alternatives

Range-free approaches rely on the connectivity measure-ments between the measurement sensor nodes and a numberof reference nodes called seeds For example in the centroidalgorithm [18] seeds broadcast their position to all neighbornodes that record all received beacons Each node estimatesits location by calculating the center of the locations of allseeds it hears In Approximate Point-in-Triangulation Test(APIT) [19] each node estimates whether it resides inside oroutside several triangular regions bounded by the seeds that ithears and refines the computed location by overlapping suchregions In ring overlapping based on comparison of receivedsignal strength indicator (ROCRSSI) [20] each sensor nodeuses a series of overlapping rings to narrow down the possiblearea in which it resides

22 Mobile Beacons Approaches Localization algorithmsmentioned previously are in static sensor networks whichare not available in some scenarios Recently mobile-assistedlocalization approaches have been proposed to improve theefficiency of range-based approaches [10 21] The location ofa sensor node can be calculated with the rangemeasurementsfrom themobile beacon to itself the localization accuracy canalso be improved bymultiplemeasurements that are obtainedwhen the mobile beacons are in different positions

Several localization schemes are proposed in this fieldFor example Bergamo and Mazzini propose a scheme toperform localization based on the estimation of the powerreceived by only two beacons placed in known positions [22]By starting from the received powers eventually averaged ona given window to counteract interference and fading theactual distance between the sensor and the beacons is derivedand the position is obtained by means of triangulationIn [10] a localization technique based on a single mobilebeacon aware of its position (eg by being equipped with aGPS receiver) was presented Sensor nodes receiving beaconpackets infer proximity constraints to the mobile beacon anduse them to construct and maintain position estimates InPI algorithm [9] instead of using the absolute RSSI valuesby contrasting the measured RSSI values from the mobilebeacon to a sensor node PI utilizes the geometric relationshipof perpendicular intersection to compute the position of thenode

In recent years more researches are focusing on mobilesensor networks which are mainly based on mobile nodes[23ndash25] Unlike other algorithms the scene of the application

International Journal of Distributed Sensor Networks 3

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

(a) (b)

RSSI(1198751) RSSI(1198751)

RSSI(1198750) RSSI(1198750)

RSSI(1198751000)

RSSI(119875999)RSSI(119875999)

RSSI(119875119894)[minmax]

11987201198720

11987211198721

119872119894

119872999 119872999

1198721000

Figure 2 The 1001th message stored by sensor

of ours is locating the mobile node with single stationaryanchor by comparing the measured RSSI values betweenthe locating sensor node with inertia module built-in andthe single anchor In this sense LSARSSI and ILSARSSI areactually range-free approaches

3 LSARSSI Algorithm

In this section we first describe the application model inSection 31 Section 32 presents the design of our localizationscheme in detail Section 33 further presents the localizationalgorithm in 3D space

31 Model Assumptions For better implementing our algo-rithm the hypotheses are as follows (1) an anchor and amobile node with inertial module whose trajectory is notdesignated (2) the environment is an obstacle-free outdoorarea (3) the communication is not continuous and thelocating node receives the RSSI at different time intervals(4) the RSSI values can be measured and the offsets can beobtained and stored by themobile node with inertial module

We can illustrate it by the following model assumptionThe coordinate of anchor 119860 is (119909

0 1199100 1199110) Assume that the

coordinate of initial location of the locating node 119873 is1198750(119909 119910 119911) 119875

119894(119894 isin [1 119899]) is a visited location of the mobile

node 119873 after time 119879 the relative offset of node 119873 among1198750and 119875

119894in the 119883 119884 and 119885 axis is Δ119909 Δ119910 and Δ119911 So the

coordinate of 119875119894is (119909 + Δ119909 119910 + Δ119910 119911 + Δ119911) as shown in

Figure 1Table 1 shows the messages obtained by the locating

node 119873 in different visited locations it contains offsets andRSSI values As the locating node needs to store the relativedistances between locations that it visited as well as the RSSIvalues between those locations to the anchor It may requirelarge memory storage for sensors The issue can be resolvedby the following method assume that sensor can store 1000messages of 119875

0to 119875999

and if the RSSI value of 119875119894is minimum

(or maximum) the message of 1198751000

will replace it as shownin Figure 2

As the communication is not continuous and the visitedlocations for our schemes needed are countable the compu-tation and communication costs are acceptable

Table 1 Messages stored by sensor

Locations Messages (node N)1198750

Δ119909 Δ119910 Δ119911 RSSI(1198750)

1198751

119909 + Δ11990901

119910 + Δ11991001

119911 + Δ11991101

RSSI(1198751)

119875119894

119909 + Δ1199090119894

119910 + Δ1199100119894

119911 + Δ1199110119894

RSSI(119875119894)

119875119899minus1

119909 + Δ1199090119899minus1

119910 + Δ1199100119899minus1

119911 + Δ1199110119899minus1

RSSI(119875119899minus1

)119875119899

119909 + Δ1199090119899

119910 + Δ1199100119899

119911 + Δ1199110119899

RSSI(119875119899)

32 Localization Algorithm Design Typically the ensemblemean received power in a real world obstructed channeldecays proportional to 119889

minus119899119901 where 119899119901

is the path-lossexponent [26] The ensemble mean power at distance 119889 istypically modeled as

[119901119903 (119889)]119889119861119898

= [119901119903(1198890)]119889119861119898

minus 10119899 log 119889

1198890

(1)

where 1198750is the received power (dBm) at short reference

distance 1198890

From (1) we know that ideally the longer the distancebetween sender and receiver the weaker the signal strengthdetected by the receiverThe localization schemewas inspiredby the perpendicular bisector of a chord conjecture [27]Withtwo chords of the same circle the intersection point of twoperpendicular bisectors of the chords will be the center of thecircleThe localization problem can be transformed based onthe conjecture The center of the circle is the position of theanchor the chord is a segment that is a connection of twopositions (the RSSI values of the two positions are equal) ofthe mobile node at a given moment The solution is detailedillustrated in Figure 3

Node 119860 is the anchor 119873 is the mobile locating node1198750 1198751 1198752 and 119875

3are the visited locations of locating node

119873 after the time period of 119894119905 119895119905 119896119905 119897119905 119861 119862 are the midpointsof segments 119875

01198751 11987521198753 and RSSI(119875

0) = RSSI(119875

1) RSSI(119875

2) =

RSSI(1198753)

4 International Journal of Distributed Sensor Networks

1198750

1198752

1198753

1198751

119860

119861

119862

Figure 3 An example of LSARSSI algorithm in 2D

The following are the formulas for calculating the locationof locating node

119860 = (1199090 1199100) 119875

0= (119909 119910)

1198751= (119909 + Δ119909

01 119910 + Δ119910

01)

1198752= (119909 + Δ119909

02 119910 + Δ119910

02)

1198753= (119909 + Δ119909

03 119910 + Δ119910

03)

119861 = (119909 + Δ1199090119861 119910 + Δ119910

0119861)

119862 = (119909 + Δ1199090119862 119910 + Δ119910

0119862)

(2)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001) rarr

11987521198753

= (Δ11990923 Δ11991023)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100)

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090)

+ Δ11991001lowast (119910 + Δ119910

0119861minus 1199100) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090)

+ Δ11991023lowast (119910 + Δ119910

0119862minus 1199100) = 0

dArr

(1) Δ11990901lowast 119909 + Δ119910

01lowast 119910

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

(2) Δ11990923lowast 119909 + Δ119910

23lowast 119910

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

(3)

Assume that119886 = Δ119909

01lowast (1199090minus Δ1199090119861)

+ Δ11991001lowast (1199100minus Δ1199100119861)

119887 = Δ11990923lowast (1199090minus Δ1199090119862)

+ Δ11991023lowast (1199100minus Δ1199100119862)

(4)

then (1) (2) can be converted into(3) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 = 119886

(4) Δ11990923lowast 119909 + Δ119910

23lowast 119910 = 119887

dArr

119909 =1198631

119863 119910 =

1198632

119863

(5)

where

119863 =10038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11990923

Δ11991023

10038161003816100381610038161003816100381610038161003816 119863

1=10038161003816100381610038161003816100381610038161003816

119886 Δ11991001

119887 Δ11991023

10038161003816100381610038161003816100381610038161003816

1198632=10038161003816100381610038161003816100381610038161003816

Δ11990901

119886

Δ11990923

119887

10038161003816100381610038161003816100381610038161003816

(6)

33 Algorithm in 3D Here we extend our algorithm tothree-dimensional space As we know if there are threenoncoincident chords on the sphere the intersection of threemidvertical planes is the center of the sphere provided thatthese three planes can intersect

The general idea of this algorithm in 3D utilizes theprevious conjecture This problem can be described as fol-lows the locations of locating node 119873 at different timescompose a collection 119875 = 119875

0 1198751 119875119899 Their RSSI values

are RSSI(1198750)RSSI(119875

1) RSSI(119875

119899) locations can be divided

into a number of subsets 1198731 1198732 119873119898 based on RSSI val-

ues and the RSSI values in each subset are equal respectivelyAfter that given that one of the following conditions occursour LSARSSI algorithm can be achieved (1) |119873

119886| = 2 and

|119873119887| = 2 and |119873

119888| = 2 (as shown in Figure 4(a)) (2) |119873

119886| = 3

and |119873119887| = 2 (as shown in Figure 4(b)) (3) |119873

119886| = 4 (as

shown in Figure 4(c)) (119886 119887 119888 isin [1119898])As (2) and (3) are the special cases of (1) here we take

|119873119886| = 2 |119873

119887| = 2 and |119873

119888| = 2 as an example to indicate

formulas for calculating the location of locating node119860 is theanchor119875

01198751119875211987531198754 and119875

5are the visited locations of the

mobile node 119861 119862 and119863 are the midpoint of 11987501198751 11987521198753 and

11987541198755 And

119860 = (1199090 1199100 1199110)

1198750= (119909 119910 119911)

1198751= (119909 + Δ119909

01 119910 + Δ119910

01 119911 + Δ119911

01)

1198752= (119909 + Δ119909

02 119910 + Δ119910

02 119911 + Δ119911

02)

International Journal of Distributed Sensor Networks 5

119860

119861

119862119863

119884

119883

119885

1198755

1198751 1198752

1198753

1198750 1198754

(a)

119884

119883

119885

119860

1198751

1198752

11987531198754

1198750

(b)

119884

119883

119885

119860

1198752

1198753

1198751

1198750

(c)

Figure 4 Examples of LSARSSI algorithm in 3D

119884

119883

119860

119874

119861

119862

119863

119864

119875998400

1

1198711

11987121198713

1198714

119875998400

3

119875998400

2

119875998400

0

1198751

1198752

1198753

1198750

Figure 5 An example of ILSARSSI algorithm in 2D

1198753= (119909 + Δ119909

03 119910 + Δ119910

03 119911 + Δ119911

03)

1198754= (119909 + Δ119909

04 119910 + Δ119910

04 119911 + Δ119911

04)

1198755= (119909 + Δ119909

05 119910 + Δ119910

05 119911 + Δ119911

05)

RSSI (1198750) = RSSI (119875

1)

RSSI (1198752) = RSSI (119875

3)

RSSI (1198754) = RSSI (119875

5)

(7)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001 Δ11991101) rarr

11987521198753

= (Δ11990923 Δ11991023 Δ11991123)

rarr11987541198755

= (Δ11990945 Δ11991045 Δ11991145)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100 119911 + Δ119911

0119861minus 1199110)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100 119911 + Δ119911

0119862minus 1199110)

dArr

rarr119860119863

= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910

0119863minus 1199100 119911 + Δ119911

0119863minus 1199110)

6 International Journal of Distributed Sensor Networks

Anchor

Locating mobile node

Trajectory

500 lowast 500m2

Figure 6 A trajectory of the locating mobile node

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090) + Δ119910

01lowast (119910 + Δ119910

0119861minus 1199100)

+ Δ11991101lowast (119911 + Δ119911

0119861minus 1199110) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090) + Δ119910

23lowast (119910 + Δ119910

0119862minus 1199100)

+ Δ11991123lowast (119911 + Δ119911

0119862minus 1199110) = 0

dArr

rarr11987541198755

sdot rarr119860119863

= Δ11990945lowast (119909 + Δ119909

0119863minus 1199090) + Δ119910

45lowast (119910 + Δ119910

0119863minus 1199100)

+ Δ11991145lowast (119911 + Δ119911

0119863minus 1199110) = 0

(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

12001000800400 6002000

minus95

minus100

minus105

minus110

minus115

minus120

Time (s)

RSSI

(dBm

)

Figure 7 RSSI values received by locating node after time 119879

(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911

= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(8)

Assume that

119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

International Journal of Distributed Sensor Networks 7

300

250

200

150

100

50

01 2 3 4 5

Transmission period (s)

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

(a) Impact of packet transmission period

250

200

150

100

50

0

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200

Size of sensor field (m2)

(b) Impact of size of sensor field

Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms

119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(9)

then (1) (2) and (3) can be converted into

(4) Δ11990901lowast 119909 + Δ119910

01lowast 119910 + Δ119911

01lowast 119911 = 119886

(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887

(6) Δ11990945lowast 119909 + Δ119910

45lowast 119910 + Δ119911

45lowast 119911 = 119888

dArr

119909 =1198631

119863 119910 =

1198632

119863 119911 =

1198633

119863

(10)

where

119863 =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11991101

Δ11990923

Δ11991023

Δ11991123

Δ11990945

Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198631=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119886 Δ11991001

Δ11991101

119887 Δ11991023

Δ11991123

119888 Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198632=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

119886 Δ11991101

Δ11990923

119887 Δ11991123

Δ11990945

119888 Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198633=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

119886

Δ11990923

Δ11991023

119887

Δ11990945

Δ11991045

119888

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(11)

4 Improved Algorithm ILSARSSI

In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously

cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]

Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875

0) RSSI(1198751015840

0)

RSSI(1198751) RSSI(1198751015840

1) RSSI(119875

2) RSSI(1198751015840

2) RSSI(119875

3) RSSI(1198751015840

3)

and RSSI(1198750) lt RSSI(1198751015840

0) RSSI(119875

1) gt RSSI(1198751015840

1) RSSI(119875

2) gt

RSSI(11987510158402) RSSI(119875

3) gt RSSI(1198751015840

3) The anchor is in the enclosed

region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of

locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained

The following are the formulas for calculating the locationof locating node

119860 (1199090 1199100) 119875

0= (1199091 1199101) 119875

1015840

0= (1199091015840

1 1199101015840

1)

1198751= (1199092 1199102) 119875

1015840

1= (1199091015840

2 1199101015840

2)

1198752= (1199093 1199103) 119875

1015840

2= (1199091015840

3 1199101015840

3)

1198753= (1199094 1199104) 119875

1015840

3= (1199091015840

4 1199101015840

4)

(12)

As 1198711 1198712 1198713 and 119871

4are the perpendicular bisector of

119875011987510158400 119875111987510158401 119875211987510158402 and 119875

311987510158403 according to the geometry of

vector we can obtain that1198711 (1199091minus 1199091015840

1) lowast 119909 + (119910

1minus 1199101015840

1) lowast 119910

= (1199091+ 11990910158401

2) lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1)

8 International Journal of Distributed Sensor Networks

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

Transmission period (s)

(a) Impact of packet transmission period

0

2

4

6

8

10

12

14

16

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

400 lowast 400300 lowast 300 500 lowast 500

Size of sensor field (m2)

100 lowast 100 200 lowast 200

(b) Impact of size of sensor field

Figure 9 Localization error of our LSARSSI algorithm

1198712 (1199092minus 1199091015840

2) lowast 119909 + (119910

2minus 1199101015840

2) lowast 119910

= (1199092+ 11990910158402

2) lowast (119909

2minus 1199091015840

2) + (

1199102+ 11991010158402

2) lowast (119910

2minus 1199101015840

2)

1198713 (1199093minus 1199091015840

3) lowast 119909 + (119910

3minus 1199101015840

3) lowast 119910

= (1199093+ 11990910158403

2) lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2) lowast (119910

3minus 1199101015840

3)

1198714 (1199094minus 1199091015840

4) lowast 119909 + (119910

4minus 1199101015840

4) lowast 119910

= (1199094+ 11990910158404

2) lowast (119909

4minus 1199091015840

4) + (

1199104+ 11991010158404

2) lowast (119910

4minus 1199101015840

4)

As 1198711cap 1198714= 119861 119871

3cap 1198714= 119862

1198712cap 1198713= 119863 119871

1cap 1198712= 119864

dArr

(13)

119909119861=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 1199091015840

1

2)lowast(1199091minus 1199091015840

1) + (

1199101+ 1199101015840

1

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199093+ 1199091015840

3

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 1199101015840

3

2) lowast (119910

3minus 1199101015840

3) 1199103minus 1199101015840

3

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119909119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 11990910158401

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

119910119861=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 3

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

middot middot middot

(a) (b)

RSSI(1198751) RSSI(1198751)

RSSI(1198750) RSSI(1198750)

RSSI(1198751000)

RSSI(119875999)RSSI(119875999)

RSSI(119875119894)[minmax]

11987201198720

11987211198721

119872119894

119872999 119872999

1198721000

Figure 2 The 1001th message stored by sensor

of ours is locating the mobile node with single stationaryanchor by comparing the measured RSSI values betweenthe locating sensor node with inertia module built-in andthe single anchor In this sense LSARSSI and ILSARSSI areactually range-free approaches

3 LSARSSI Algorithm

In this section we first describe the application model inSection 31 Section 32 presents the design of our localizationscheme in detail Section 33 further presents the localizationalgorithm in 3D space

31 Model Assumptions For better implementing our algo-rithm the hypotheses are as follows (1) an anchor and amobile node with inertial module whose trajectory is notdesignated (2) the environment is an obstacle-free outdoorarea (3) the communication is not continuous and thelocating node receives the RSSI at different time intervals(4) the RSSI values can be measured and the offsets can beobtained and stored by themobile node with inertial module

We can illustrate it by the following model assumptionThe coordinate of anchor 119860 is (119909

0 1199100 1199110) Assume that the

coordinate of initial location of the locating node 119873 is1198750(119909 119910 119911) 119875

119894(119894 isin [1 119899]) is a visited location of the mobile

node 119873 after time 119879 the relative offset of node 119873 among1198750and 119875

119894in the 119883 119884 and 119885 axis is Δ119909 Δ119910 and Δ119911 So the

coordinate of 119875119894is (119909 + Δ119909 119910 + Δ119910 119911 + Δ119911) as shown in

Figure 1Table 1 shows the messages obtained by the locating

node 119873 in different visited locations it contains offsets andRSSI values As the locating node needs to store the relativedistances between locations that it visited as well as the RSSIvalues between those locations to the anchor It may requirelarge memory storage for sensors The issue can be resolvedby the following method assume that sensor can store 1000messages of 119875

0to 119875999

and if the RSSI value of 119875119894is minimum

(or maximum) the message of 1198751000

will replace it as shownin Figure 2

As the communication is not continuous and the visitedlocations for our schemes needed are countable the compu-tation and communication costs are acceptable

Table 1 Messages stored by sensor

Locations Messages (node N)1198750

Δ119909 Δ119910 Δ119911 RSSI(1198750)

1198751

119909 + Δ11990901

119910 + Δ11991001

119911 + Δ11991101

RSSI(1198751)

119875119894

119909 + Δ1199090119894

119910 + Δ1199100119894

119911 + Δ1199110119894

RSSI(119875119894)

119875119899minus1

119909 + Δ1199090119899minus1

119910 + Δ1199100119899minus1

119911 + Δ1199110119899minus1

RSSI(119875119899minus1

)119875119899

119909 + Δ1199090119899

119910 + Δ1199100119899

119911 + Δ1199110119899

RSSI(119875119899)

32 Localization Algorithm Design Typically the ensemblemean received power in a real world obstructed channeldecays proportional to 119889

minus119899119901 where 119899119901

is the path-lossexponent [26] The ensemble mean power at distance 119889 istypically modeled as

[119901119903 (119889)]119889119861119898

= [119901119903(1198890)]119889119861119898

minus 10119899 log 119889

1198890

(1)

where 1198750is the received power (dBm) at short reference

distance 1198890

From (1) we know that ideally the longer the distancebetween sender and receiver the weaker the signal strengthdetected by the receiverThe localization schemewas inspiredby the perpendicular bisector of a chord conjecture [27]Withtwo chords of the same circle the intersection point of twoperpendicular bisectors of the chords will be the center of thecircleThe localization problem can be transformed based onthe conjecture The center of the circle is the position of theanchor the chord is a segment that is a connection of twopositions (the RSSI values of the two positions are equal) ofthe mobile node at a given moment The solution is detailedillustrated in Figure 3

Node 119860 is the anchor 119873 is the mobile locating node1198750 1198751 1198752 and 119875

3are the visited locations of locating node

119873 after the time period of 119894119905 119895119905 119896119905 119897119905 119861 119862 are the midpointsof segments 119875

01198751 11987521198753 and RSSI(119875

0) = RSSI(119875

1) RSSI(119875

2) =

RSSI(1198753)

4 International Journal of Distributed Sensor Networks

1198750

1198752

1198753

1198751

119860

119861

119862

Figure 3 An example of LSARSSI algorithm in 2D

The following are the formulas for calculating the locationof locating node

119860 = (1199090 1199100) 119875

0= (119909 119910)

1198751= (119909 + Δ119909

01 119910 + Δ119910

01)

1198752= (119909 + Δ119909

02 119910 + Δ119910

02)

1198753= (119909 + Δ119909

03 119910 + Δ119910

03)

119861 = (119909 + Δ1199090119861 119910 + Δ119910

0119861)

119862 = (119909 + Δ1199090119862 119910 + Δ119910

0119862)

(2)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001) rarr

11987521198753

= (Δ11990923 Δ11991023)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100)

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090)

+ Δ11991001lowast (119910 + Δ119910

0119861minus 1199100) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090)

+ Δ11991023lowast (119910 + Δ119910

0119862minus 1199100) = 0

dArr

(1) Δ11990901lowast 119909 + Δ119910

01lowast 119910

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

(2) Δ11990923lowast 119909 + Δ119910

23lowast 119910

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

(3)

Assume that119886 = Δ119909

01lowast (1199090minus Δ1199090119861)

+ Δ11991001lowast (1199100minus Δ1199100119861)

119887 = Δ11990923lowast (1199090minus Δ1199090119862)

+ Δ11991023lowast (1199100minus Δ1199100119862)

(4)

then (1) (2) can be converted into(3) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 = 119886

(4) Δ11990923lowast 119909 + Δ119910

23lowast 119910 = 119887

dArr

119909 =1198631

119863 119910 =

1198632

119863

(5)

where

119863 =10038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11990923

Δ11991023

10038161003816100381610038161003816100381610038161003816 119863

1=10038161003816100381610038161003816100381610038161003816

119886 Δ11991001

119887 Δ11991023

10038161003816100381610038161003816100381610038161003816

1198632=10038161003816100381610038161003816100381610038161003816

Δ11990901

119886

Δ11990923

119887

10038161003816100381610038161003816100381610038161003816

(6)

33 Algorithm in 3D Here we extend our algorithm tothree-dimensional space As we know if there are threenoncoincident chords on the sphere the intersection of threemidvertical planes is the center of the sphere provided thatthese three planes can intersect

The general idea of this algorithm in 3D utilizes theprevious conjecture This problem can be described as fol-lows the locations of locating node 119873 at different timescompose a collection 119875 = 119875

0 1198751 119875119899 Their RSSI values

are RSSI(1198750)RSSI(119875

1) RSSI(119875

119899) locations can be divided

into a number of subsets 1198731 1198732 119873119898 based on RSSI val-

ues and the RSSI values in each subset are equal respectivelyAfter that given that one of the following conditions occursour LSARSSI algorithm can be achieved (1) |119873

119886| = 2 and

|119873119887| = 2 and |119873

119888| = 2 (as shown in Figure 4(a)) (2) |119873

119886| = 3

and |119873119887| = 2 (as shown in Figure 4(b)) (3) |119873

119886| = 4 (as

shown in Figure 4(c)) (119886 119887 119888 isin [1119898])As (2) and (3) are the special cases of (1) here we take

|119873119886| = 2 |119873

119887| = 2 and |119873

119888| = 2 as an example to indicate

formulas for calculating the location of locating node119860 is theanchor119875

01198751119875211987531198754 and119875

5are the visited locations of the

mobile node 119861 119862 and119863 are the midpoint of 11987501198751 11987521198753 and

11987541198755 And

119860 = (1199090 1199100 1199110)

1198750= (119909 119910 119911)

1198751= (119909 + Δ119909

01 119910 + Δ119910

01 119911 + Δ119911

01)

1198752= (119909 + Δ119909

02 119910 + Δ119910

02 119911 + Δ119911

02)

International Journal of Distributed Sensor Networks 5

119860

119861

119862119863

119884

119883

119885

1198755

1198751 1198752

1198753

1198750 1198754

(a)

119884

119883

119885

119860

1198751

1198752

11987531198754

1198750

(b)

119884

119883

119885

119860

1198752

1198753

1198751

1198750

(c)

Figure 4 Examples of LSARSSI algorithm in 3D

119884

119883

119860

119874

119861

119862

119863

119864

119875998400

1

1198711

11987121198713

1198714

119875998400

3

119875998400

2

119875998400

0

1198751

1198752

1198753

1198750

Figure 5 An example of ILSARSSI algorithm in 2D

1198753= (119909 + Δ119909

03 119910 + Δ119910

03 119911 + Δ119911

03)

1198754= (119909 + Δ119909

04 119910 + Δ119910

04 119911 + Δ119911

04)

1198755= (119909 + Δ119909

05 119910 + Δ119910

05 119911 + Δ119911

05)

RSSI (1198750) = RSSI (119875

1)

RSSI (1198752) = RSSI (119875

3)

RSSI (1198754) = RSSI (119875

5)

(7)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001 Δ11991101) rarr

11987521198753

= (Δ11990923 Δ11991023 Δ11991123)

rarr11987541198755

= (Δ11990945 Δ11991045 Δ11991145)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100 119911 + Δ119911

0119861minus 1199110)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100 119911 + Δ119911

0119862minus 1199110)

dArr

rarr119860119863

= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910

0119863minus 1199100 119911 + Δ119911

0119863minus 1199110)

6 International Journal of Distributed Sensor Networks

Anchor

Locating mobile node

Trajectory

500 lowast 500m2

Figure 6 A trajectory of the locating mobile node

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090) + Δ119910

01lowast (119910 + Δ119910

0119861minus 1199100)

+ Δ11991101lowast (119911 + Δ119911

0119861minus 1199110) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090) + Δ119910

23lowast (119910 + Δ119910

0119862minus 1199100)

+ Δ11991123lowast (119911 + Δ119911

0119862minus 1199110) = 0

dArr

rarr11987541198755

sdot rarr119860119863

= Δ11990945lowast (119909 + Δ119909

0119863minus 1199090) + Δ119910

45lowast (119910 + Δ119910

0119863minus 1199100)

+ Δ11991145lowast (119911 + Δ119911

0119863minus 1199110) = 0

(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

12001000800400 6002000

minus95

minus100

minus105

minus110

minus115

minus120

Time (s)

RSSI

(dBm

)

Figure 7 RSSI values received by locating node after time 119879

(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911

= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(8)

Assume that

119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

International Journal of Distributed Sensor Networks 7

300

250

200

150

100

50

01 2 3 4 5

Transmission period (s)

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

(a) Impact of packet transmission period

250

200

150

100

50

0

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200

Size of sensor field (m2)

(b) Impact of size of sensor field

Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms

119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(9)

then (1) (2) and (3) can be converted into

(4) Δ11990901lowast 119909 + Δ119910

01lowast 119910 + Δ119911

01lowast 119911 = 119886

(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887

(6) Δ11990945lowast 119909 + Δ119910

45lowast 119910 + Δ119911

45lowast 119911 = 119888

dArr

119909 =1198631

119863 119910 =

1198632

119863 119911 =

1198633

119863

(10)

where

119863 =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11991101

Δ11990923

Δ11991023

Δ11991123

Δ11990945

Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198631=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119886 Δ11991001

Δ11991101

119887 Δ11991023

Δ11991123

119888 Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198632=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

119886 Δ11991101

Δ11990923

119887 Δ11991123

Δ11990945

119888 Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198633=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

119886

Δ11990923

Δ11991023

119887

Δ11990945

Δ11991045

119888

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(11)

4 Improved Algorithm ILSARSSI

In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously

cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]

Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875

0) RSSI(1198751015840

0)

RSSI(1198751) RSSI(1198751015840

1) RSSI(119875

2) RSSI(1198751015840

2) RSSI(119875

3) RSSI(1198751015840

3)

and RSSI(1198750) lt RSSI(1198751015840

0) RSSI(119875

1) gt RSSI(1198751015840

1) RSSI(119875

2) gt

RSSI(11987510158402) RSSI(119875

3) gt RSSI(1198751015840

3) The anchor is in the enclosed

region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of

locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained

The following are the formulas for calculating the locationof locating node

119860 (1199090 1199100) 119875

0= (1199091 1199101) 119875

1015840

0= (1199091015840

1 1199101015840

1)

1198751= (1199092 1199102) 119875

1015840

1= (1199091015840

2 1199101015840

2)

1198752= (1199093 1199103) 119875

1015840

2= (1199091015840

3 1199101015840

3)

1198753= (1199094 1199104) 119875

1015840

3= (1199091015840

4 1199101015840

4)

(12)

As 1198711 1198712 1198713 and 119871

4are the perpendicular bisector of

119875011987510158400 119875111987510158401 119875211987510158402 and 119875

311987510158403 according to the geometry of

vector we can obtain that1198711 (1199091minus 1199091015840

1) lowast 119909 + (119910

1minus 1199101015840

1) lowast 119910

= (1199091+ 11990910158401

2) lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1)

8 International Journal of Distributed Sensor Networks

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

Transmission period (s)

(a) Impact of packet transmission period

0

2

4

6

8

10

12

14

16

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

400 lowast 400300 lowast 300 500 lowast 500

Size of sensor field (m2)

100 lowast 100 200 lowast 200

(b) Impact of size of sensor field

Figure 9 Localization error of our LSARSSI algorithm

1198712 (1199092minus 1199091015840

2) lowast 119909 + (119910

2minus 1199101015840

2) lowast 119910

= (1199092+ 11990910158402

2) lowast (119909

2minus 1199091015840

2) + (

1199102+ 11991010158402

2) lowast (119910

2minus 1199101015840

2)

1198713 (1199093minus 1199091015840

3) lowast 119909 + (119910

3minus 1199101015840

3) lowast 119910

= (1199093+ 11990910158403

2) lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2) lowast (119910

3minus 1199101015840

3)

1198714 (1199094minus 1199091015840

4) lowast 119909 + (119910

4minus 1199101015840

4) lowast 119910

= (1199094+ 11990910158404

2) lowast (119909

4minus 1199091015840

4) + (

1199104+ 11991010158404

2) lowast (119910

4minus 1199101015840

4)

As 1198711cap 1198714= 119861 119871

3cap 1198714= 119862

1198712cap 1198713= 119863 119871

1cap 1198712= 119864

dArr

(13)

119909119861=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 1199091015840

1

2)lowast(1199091minus 1199091015840

1) + (

1199101+ 1199101015840

1

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199093+ 1199091015840

3

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 1199101015840

3

2) lowast (119910

3minus 1199101015840

3) 1199103minus 1199101015840

3

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119909119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 11990910158401

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

119910119861=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 International Journal of Distributed Sensor Networks

1198750

1198752

1198753

1198751

119860

119861

119862

Figure 3 An example of LSARSSI algorithm in 2D

The following are the formulas for calculating the locationof locating node

119860 = (1199090 1199100) 119875

0= (119909 119910)

1198751= (119909 + Δ119909

01 119910 + Δ119910

01)

1198752= (119909 + Δ119909

02 119910 + Δ119910

02)

1198753= (119909 + Δ119909

03 119910 + Δ119910

03)

119861 = (119909 + Δ1199090119861 119910 + Δ119910

0119861)

119862 = (119909 + Δ1199090119862 119910 + Δ119910

0119862)

(2)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001) rarr

11987521198753

= (Δ11990923 Δ11991023)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100)

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090)

+ Δ11991001lowast (119910 + Δ119910

0119861minus 1199100) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090)

+ Δ11991023lowast (119910 + Δ119910

0119862minus 1199100) = 0

dArr

(1) Δ11990901lowast 119909 + Δ119910

01lowast 119910

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

(2) Δ11990923lowast 119909 + Δ119910

23lowast 119910

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

(3)

Assume that119886 = Δ119909

01lowast (1199090minus Δ1199090119861)

+ Δ11991001lowast (1199100minus Δ1199100119861)

119887 = Δ11990923lowast (1199090minus Δ1199090119862)

+ Δ11991023lowast (1199100minus Δ1199100119862)

(4)

then (1) (2) can be converted into(3) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 = 119886

(4) Δ11990923lowast 119909 + Δ119910

23lowast 119910 = 119887

dArr

119909 =1198631

119863 119910 =

1198632

119863

(5)

where

119863 =10038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11990923

Δ11991023

10038161003816100381610038161003816100381610038161003816 119863

1=10038161003816100381610038161003816100381610038161003816

119886 Δ11991001

119887 Δ11991023

10038161003816100381610038161003816100381610038161003816

1198632=10038161003816100381610038161003816100381610038161003816

Δ11990901

119886

Δ11990923

119887

10038161003816100381610038161003816100381610038161003816

(6)

33 Algorithm in 3D Here we extend our algorithm tothree-dimensional space As we know if there are threenoncoincident chords on the sphere the intersection of threemidvertical planes is the center of the sphere provided thatthese three planes can intersect

The general idea of this algorithm in 3D utilizes theprevious conjecture This problem can be described as fol-lows the locations of locating node 119873 at different timescompose a collection 119875 = 119875

0 1198751 119875119899 Their RSSI values

are RSSI(1198750)RSSI(119875

1) RSSI(119875

119899) locations can be divided

into a number of subsets 1198731 1198732 119873119898 based on RSSI val-

ues and the RSSI values in each subset are equal respectivelyAfter that given that one of the following conditions occursour LSARSSI algorithm can be achieved (1) |119873

119886| = 2 and

|119873119887| = 2 and |119873

119888| = 2 (as shown in Figure 4(a)) (2) |119873

119886| = 3

and |119873119887| = 2 (as shown in Figure 4(b)) (3) |119873

119886| = 4 (as

shown in Figure 4(c)) (119886 119887 119888 isin [1119898])As (2) and (3) are the special cases of (1) here we take

|119873119886| = 2 |119873

119887| = 2 and |119873

119888| = 2 as an example to indicate

formulas for calculating the location of locating node119860 is theanchor119875

01198751119875211987531198754 and119875

5are the visited locations of the

mobile node 119861 119862 and119863 are the midpoint of 11987501198751 11987521198753 and

11987541198755 And

119860 = (1199090 1199100 1199110)

1198750= (119909 119910 119911)

1198751= (119909 + Δ119909

01 119910 + Δ119910

01 119911 + Δ119911

01)

1198752= (119909 + Δ119909

02 119910 + Δ119910

02 119911 + Δ119911

02)

International Journal of Distributed Sensor Networks 5

119860

119861

119862119863

119884

119883

119885

1198755

1198751 1198752

1198753

1198750 1198754

(a)

119884

119883

119885

119860

1198751

1198752

11987531198754

1198750

(b)

119884

119883

119885

119860

1198752

1198753

1198751

1198750

(c)

Figure 4 Examples of LSARSSI algorithm in 3D

119884

119883

119860

119874

119861

119862

119863

119864

119875998400

1

1198711

11987121198713

1198714

119875998400

3

119875998400

2

119875998400

0

1198751

1198752

1198753

1198750

Figure 5 An example of ILSARSSI algorithm in 2D

1198753= (119909 + Δ119909

03 119910 + Δ119910

03 119911 + Δ119911

03)

1198754= (119909 + Δ119909

04 119910 + Δ119910

04 119911 + Δ119911

04)

1198755= (119909 + Δ119909

05 119910 + Δ119910

05 119911 + Δ119911

05)

RSSI (1198750) = RSSI (119875

1)

RSSI (1198752) = RSSI (119875

3)

RSSI (1198754) = RSSI (119875

5)

(7)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001 Δ11991101) rarr

11987521198753

= (Δ11990923 Δ11991023 Δ11991123)

rarr11987541198755

= (Δ11990945 Δ11991045 Δ11991145)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100 119911 + Δ119911

0119861minus 1199110)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100 119911 + Δ119911

0119862minus 1199110)

dArr

rarr119860119863

= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910

0119863minus 1199100 119911 + Δ119911

0119863minus 1199110)

6 International Journal of Distributed Sensor Networks

Anchor

Locating mobile node

Trajectory

500 lowast 500m2

Figure 6 A trajectory of the locating mobile node

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090) + Δ119910

01lowast (119910 + Δ119910

0119861minus 1199100)

+ Δ11991101lowast (119911 + Δ119911

0119861minus 1199110) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090) + Δ119910

23lowast (119910 + Δ119910

0119862minus 1199100)

+ Δ11991123lowast (119911 + Δ119911

0119862minus 1199110) = 0

dArr

rarr11987541198755

sdot rarr119860119863

= Δ11990945lowast (119909 + Δ119909

0119863minus 1199090) + Δ119910

45lowast (119910 + Δ119910

0119863minus 1199100)

+ Δ11991145lowast (119911 + Δ119911

0119863minus 1199110) = 0

(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

12001000800400 6002000

minus95

minus100

minus105

minus110

minus115

minus120

Time (s)

RSSI

(dBm

)

Figure 7 RSSI values received by locating node after time 119879

(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911

= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(8)

Assume that

119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

International Journal of Distributed Sensor Networks 7

300

250

200

150

100

50

01 2 3 4 5

Transmission period (s)

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

(a) Impact of packet transmission period

250

200

150

100

50

0

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200

Size of sensor field (m2)

(b) Impact of size of sensor field

Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms

119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(9)

then (1) (2) and (3) can be converted into

(4) Δ11990901lowast 119909 + Δ119910

01lowast 119910 + Δ119911

01lowast 119911 = 119886

(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887

(6) Δ11990945lowast 119909 + Δ119910

45lowast 119910 + Δ119911

45lowast 119911 = 119888

dArr

119909 =1198631

119863 119910 =

1198632

119863 119911 =

1198633

119863

(10)

where

119863 =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11991101

Δ11990923

Δ11991023

Δ11991123

Δ11990945

Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198631=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119886 Δ11991001

Δ11991101

119887 Δ11991023

Δ11991123

119888 Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198632=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

119886 Δ11991101

Δ11990923

119887 Δ11991123

Δ11990945

119888 Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198633=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

119886

Δ11990923

Δ11991023

119887

Δ11990945

Δ11991045

119888

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(11)

4 Improved Algorithm ILSARSSI

In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously

cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]

Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875

0) RSSI(1198751015840

0)

RSSI(1198751) RSSI(1198751015840

1) RSSI(119875

2) RSSI(1198751015840

2) RSSI(119875

3) RSSI(1198751015840

3)

and RSSI(1198750) lt RSSI(1198751015840

0) RSSI(119875

1) gt RSSI(1198751015840

1) RSSI(119875

2) gt

RSSI(11987510158402) RSSI(119875

3) gt RSSI(1198751015840

3) The anchor is in the enclosed

region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of

locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained

The following are the formulas for calculating the locationof locating node

119860 (1199090 1199100) 119875

0= (1199091 1199101) 119875

1015840

0= (1199091015840

1 1199101015840

1)

1198751= (1199092 1199102) 119875

1015840

1= (1199091015840

2 1199101015840

2)

1198752= (1199093 1199103) 119875

1015840

2= (1199091015840

3 1199101015840

3)

1198753= (1199094 1199104) 119875

1015840

3= (1199091015840

4 1199101015840

4)

(12)

As 1198711 1198712 1198713 and 119871

4are the perpendicular bisector of

119875011987510158400 119875111987510158401 119875211987510158402 and 119875

311987510158403 according to the geometry of

vector we can obtain that1198711 (1199091minus 1199091015840

1) lowast 119909 + (119910

1minus 1199101015840

1) lowast 119910

= (1199091+ 11990910158401

2) lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1)

8 International Journal of Distributed Sensor Networks

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

Transmission period (s)

(a) Impact of packet transmission period

0

2

4

6

8

10

12

14

16

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

400 lowast 400300 lowast 300 500 lowast 500

Size of sensor field (m2)

100 lowast 100 200 lowast 200

(b) Impact of size of sensor field

Figure 9 Localization error of our LSARSSI algorithm

1198712 (1199092minus 1199091015840

2) lowast 119909 + (119910

2minus 1199101015840

2) lowast 119910

= (1199092+ 11990910158402

2) lowast (119909

2minus 1199091015840

2) + (

1199102+ 11991010158402

2) lowast (119910

2minus 1199101015840

2)

1198713 (1199093minus 1199091015840

3) lowast 119909 + (119910

3minus 1199101015840

3) lowast 119910

= (1199093+ 11990910158403

2) lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2) lowast (119910

3minus 1199101015840

3)

1198714 (1199094minus 1199091015840

4) lowast 119909 + (119910

4minus 1199101015840

4) lowast 119910

= (1199094+ 11990910158404

2) lowast (119909

4minus 1199091015840

4) + (

1199104+ 11991010158404

2) lowast (119910

4minus 1199101015840

4)

As 1198711cap 1198714= 119861 119871

3cap 1198714= 119862

1198712cap 1198713= 119863 119871

1cap 1198712= 119864

dArr

(13)

119909119861=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 1199091015840

1

2)lowast(1199091minus 1199091015840

1) + (

1199101+ 1199101015840

1

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199093+ 1199091015840

3

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 1199101015840

3

2) lowast (119910

3minus 1199101015840

3) 1199103minus 1199101015840

3

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119909119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 11990910158401

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

119910119861=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

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Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 5

119860

119861

119862119863

119884

119883

119885

1198755

1198751 1198752

1198753

1198750 1198754

(a)

119884

119883

119885

119860

1198751

1198752

11987531198754

1198750

(b)

119884

119883

119885

119860

1198752

1198753

1198751

1198750

(c)

Figure 4 Examples of LSARSSI algorithm in 3D

119884

119883

119860

119874

119861

119862

119863

119864

119875998400

1

1198711

11987121198713

1198714

119875998400

3

119875998400

2

119875998400

0

1198751

1198752

1198753

1198750

Figure 5 An example of ILSARSSI algorithm in 2D

1198753= (119909 + Δ119909

03 119910 + Δ119910

03 119911 + Δ119911

03)

1198754= (119909 + Δ119909

04 119910 + Δ119910

04 119911 + Δ119911

04)

1198755= (119909 + Δ119909

05 119910 + Δ119910

05 119911 + Δ119911

05)

RSSI (1198750) = RSSI (119875

1)

RSSI (1198752) = RSSI (119875

3)

RSSI (1198754) = RSSI (119875

5)

(7)

According to the geometry of vector we can obtain that

rarr11987501198751

= (Δ11990901 Δ11991001 Δ11991101) rarr

11987521198753

= (Δ11990923 Δ11991023 Δ11991123)

rarr11987541198755

= (Δ11990945 Δ11991045 Δ11991145)

rarr119860119861

= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910

0119861minus 1199100 119911 + Δ119911

0119861minus 1199110)

rarr119860119862

= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910

0119862minus 1199100 119911 + Δ119911

0119862minus 1199110)

dArr

rarr119860119863

= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910

0119863minus 1199100 119911 + Δ119911

0119863minus 1199110)

6 International Journal of Distributed Sensor Networks

Anchor

Locating mobile node

Trajectory

500 lowast 500m2

Figure 6 A trajectory of the locating mobile node

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090) + Δ119910

01lowast (119910 + Δ119910

0119861minus 1199100)

+ Δ11991101lowast (119911 + Δ119911

0119861minus 1199110) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090) + Δ119910

23lowast (119910 + Δ119910

0119862minus 1199100)

+ Δ11991123lowast (119911 + Δ119911

0119862minus 1199110) = 0

dArr

rarr11987541198755

sdot rarr119860119863

= Δ11990945lowast (119909 + Δ119909

0119863minus 1199090) + Δ119910

45lowast (119910 + Δ119910

0119863minus 1199100)

+ Δ11991145lowast (119911 + Δ119911

0119863minus 1199110) = 0

(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

12001000800400 6002000

minus95

minus100

minus105

minus110

minus115

minus120

Time (s)

RSSI

(dBm

)

Figure 7 RSSI values received by locating node after time 119879

(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911

= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(8)

Assume that

119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

International Journal of Distributed Sensor Networks 7

300

250

200

150

100

50

01 2 3 4 5

Transmission period (s)

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

(a) Impact of packet transmission period

250

200

150

100

50

0

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200

Size of sensor field (m2)

(b) Impact of size of sensor field

Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms

119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(9)

then (1) (2) and (3) can be converted into

(4) Δ11990901lowast 119909 + Δ119910

01lowast 119910 + Δ119911

01lowast 119911 = 119886

(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887

(6) Δ11990945lowast 119909 + Δ119910

45lowast 119910 + Δ119911

45lowast 119911 = 119888

dArr

119909 =1198631

119863 119910 =

1198632

119863 119911 =

1198633

119863

(10)

where

119863 =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11991101

Δ11990923

Δ11991023

Δ11991123

Δ11990945

Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198631=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119886 Δ11991001

Δ11991101

119887 Δ11991023

Δ11991123

119888 Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198632=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

119886 Δ11991101

Δ11990923

119887 Δ11991123

Δ11990945

119888 Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198633=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

119886

Δ11990923

Δ11991023

119887

Δ11990945

Δ11991045

119888

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(11)

4 Improved Algorithm ILSARSSI

In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously

cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]

Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875

0) RSSI(1198751015840

0)

RSSI(1198751) RSSI(1198751015840

1) RSSI(119875

2) RSSI(1198751015840

2) RSSI(119875

3) RSSI(1198751015840

3)

and RSSI(1198750) lt RSSI(1198751015840

0) RSSI(119875

1) gt RSSI(1198751015840

1) RSSI(119875

2) gt

RSSI(11987510158402) RSSI(119875

3) gt RSSI(1198751015840

3) The anchor is in the enclosed

region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of

locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained

The following are the formulas for calculating the locationof locating node

119860 (1199090 1199100) 119875

0= (1199091 1199101) 119875

1015840

0= (1199091015840

1 1199101015840

1)

1198751= (1199092 1199102) 119875

1015840

1= (1199091015840

2 1199101015840

2)

1198752= (1199093 1199103) 119875

1015840

2= (1199091015840

3 1199101015840

3)

1198753= (1199094 1199104) 119875

1015840

3= (1199091015840

4 1199101015840

4)

(12)

As 1198711 1198712 1198713 and 119871

4are the perpendicular bisector of

119875011987510158400 119875111987510158401 119875211987510158402 and 119875

311987510158403 according to the geometry of

vector we can obtain that1198711 (1199091minus 1199091015840

1) lowast 119909 + (119910

1minus 1199101015840

1) lowast 119910

= (1199091+ 11990910158401

2) lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1)

8 International Journal of Distributed Sensor Networks

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

Transmission period (s)

(a) Impact of packet transmission period

0

2

4

6

8

10

12

14

16

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

400 lowast 400300 lowast 300 500 lowast 500

Size of sensor field (m2)

100 lowast 100 200 lowast 200

(b) Impact of size of sensor field

Figure 9 Localization error of our LSARSSI algorithm

1198712 (1199092minus 1199091015840

2) lowast 119909 + (119910

2minus 1199101015840

2) lowast 119910

= (1199092+ 11990910158402

2) lowast (119909

2minus 1199091015840

2) + (

1199102+ 11991010158402

2) lowast (119910

2minus 1199101015840

2)

1198713 (1199093minus 1199091015840

3) lowast 119909 + (119910

3minus 1199101015840

3) lowast 119910

= (1199093+ 11990910158403

2) lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2) lowast (119910

3minus 1199101015840

3)

1198714 (1199094minus 1199091015840

4) lowast 119909 + (119910

4minus 1199101015840

4) lowast 119910

= (1199094+ 11990910158404

2) lowast (119909

4minus 1199091015840

4) + (

1199104+ 11991010158404

2) lowast (119910

4minus 1199101015840

4)

As 1198711cap 1198714= 119861 119871

3cap 1198714= 119862

1198712cap 1198713= 119863 119871

1cap 1198712= 119864

dArr

(13)

119909119861=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 1199091015840

1

2)lowast(1199091minus 1199091015840

1) + (

1199101+ 1199101015840

1

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199093+ 1199091015840

3

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 1199101015840

3

2) lowast (119910

3minus 1199101015840

3) 1199103minus 1199101015840

3

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119909119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 11990910158401

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

119910119861=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 International Journal of Distributed Sensor Networks

Anchor

Locating mobile node

Trajectory

500 lowast 500m2

Figure 6 A trajectory of the locating mobile node

rarr11987501198751

sdot rarr119860119861

= Δ11990901lowast (119909 + Δ119909

0119861minus 1199090) + Δ119910

01lowast (119910 + Δ119910

0119861minus 1199100)

+ Δ11991101lowast (119911 + Δ119911

0119861minus 1199110) = 0

rarr11987521198753

sdot rarr119860119862

= Δ11990923lowast (119909 + Δ119909

0119862minus 1199090) + Δ119910

23lowast (119910 + Δ119910

0119862minus 1199100)

+ Δ11991123lowast (119911 + Δ119911

0119862minus 1199110) = 0

dArr

rarr11987541198755

sdot rarr119860119863

= Δ11990945lowast (119909 + Δ119909

0119863minus 1199090) + Δ119910

45lowast (119910 + Δ119910

0119863minus 1199100)

+ Δ11991145lowast (119911 + Δ119911

0119863minus 1199110) = 0

(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911

= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911

= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

12001000800400 6002000

minus95

minus100

minus105

minus110

minus115

minus120

Time (s)

RSSI

(dBm

)

Figure 7 RSSI values received by locating node after time 119879

(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911

= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(8)

Assume that

119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910

01lowast (1199100minus Δ1199100119861)

+ Δ11991101lowast (1199110minus Δ1199110119861)

International Journal of Distributed Sensor Networks 7

300

250

200

150

100

50

01 2 3 4 5

Transmission period (s)

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

(a) Impact of packet transmission period

250

200

150

100

50

0

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200

Size of sensor field (m2)

(b) Impact of size of sensor field

Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms

119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(9)

then (1) (2) and (3) can be converted into

(4) Δ11990901lowast 119909 + Δ119910

01lowast 119910 + Δ119911

01lowast 119911 = 119886

(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887

(6) Δ11990945lowast 119909 + Δ119910

45lowast 119910 + Δ119911

45lowast 119911 = 119888

dArr

119909 =1198631

119863 119910 =

1198632

119863 119911 =

1198633

119863

(10)

where

119863 =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11991101

Δ11990923

Δ11991023

Δ11991123

Δ11990945

Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198631=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119886 Δ11991001

Δ11991101

119887 Δ11991023

Δ11991123

119888 Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198632=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

119886 Δ11991101

Δ11990923

119887 Δ11991123

Δ11990945

119888 Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198633=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

119886

Δ11990923

Δ11991023

119887

Δ11990945

Δ11991045

119888

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(11)

4 Improved Algorithm ILSARSSI

In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously

cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]

Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875

0) RSSI(1198751015840

0)

RSSI(1198751) RSSI(1198751015840

1) RSSI(119875

2) RSSI(1198751015840

2) RSSI(119875

3) RSSI(1198751015840

3)

and RSSI(1198750) lt RSSI(1198751015840

0) RSSI(119875

1) gt RSSI(1198751015840

1) RSSI(119875

2) gt

RSSI(11987510158402) RSSI(119875

3) gt RSSI(1198751015840

3) The anchor is in the enclosed

region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of

locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained

The following are the formulas for calculating the locationof locating node

119860 (1199090 1199100) 119875

0= (1199091 1199101) 119875

1015840

0= (1199091015840

1 1199101015840

1)

1198751= (1199092 1199102) 119875

1015840

1= (1199091015840

2 1199101015840

2)

1198752= (1199093 1199103) 119875

1015840

2= (1199091015840

3 1199101015840

3)

1198753= (1199094 1199104) 119875

1015840

3= (1199091015840

4 1199101015840

4)

(12)

As 1198711 1198712 1198713 and 119871

4are the perpendicular bisector of

119875011987510158400 119875111987510158401 119875211987510158402 and 119875

311987510158403 according to the geometry of

vector we can obtain that1198711 (1199091minus 1199091015840

1) lowast 119909 + (119910

1minus 1199101015840

1) lowast 119910

= (1199091+ 11990910158401

2) lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1)

8 International Journal of Distributed Sensor Networks

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

Transmission period (s)

(a) Impact of packet transmission period

0

2

4

6

8

10

12

14

16

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

400 lowast 400300 lowast 300 500 lowast 500

Size of sensor field (m2)

100 lowast 100 200 lowast 200

(b) Impact of size of sensor field

Figure 9 Localization error of our LSARSSI algorithm

1198712 (1199092minus 1199091015840

2) lowast 119909 + (119910

2minus 1199101015840

2) lowast 119910

= (1199092+ 11990910158402

2) lowast (119909

2minus 1199091015840

2) + (

1199102+ 11991010158402

2) lowast (119910

2minus 1199101015840

2)

1198713 (1199093minus 1199091015840

3) lowast 119909 + (119910

3minus 1199101015840

3) lowast 119910

= (1199093+ 11990910158403

2) lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2) lowast (119910

3minus 1199101015840

3)

1198714 (1199094minus 1199091015840

4) lowast 119909 + (119910

4minus 1199101015840

4) lowast 119910

= (1199094+ 11990910158404

2) lowast (119909

4minus 1199091015840

4) + (

1199104+ 11991010158404

2) lowast (119910

4minus 1199101015840

4)

As 1198711cap 1198714= 119861 119871

3cap 1198714= 119862

1198712cap 1198713= 119863 119871

1cap 1198712= 119864

dArr

(13)

119909119861=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 1199091015840

1

2)lowast(1199091minus 1199091015840

1) + (

1199101+ 1199101015840

1

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199093+ 1199091015840

3

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 1199101015840

3

2) lowast (119910

3minus 1199101015840

3) 1199103minus 1199101015840

3

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119909119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 11990910158401

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

119910119861=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 7

300

250

200

150

100

50

01 2 3 4 5

Transmission period (s)

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

(a) Impact of packet transmission period

250

200

150

100

50

0

Num

ber o

f loc

atio

ns

LSARSSIILSARSSI

Average LSARSSI numbersAverage ILSARSSI numbers

100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200

Size of sensor field (m2)

(b) Impact of size of sensor field

Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms

119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910

23lowast (1199100minus Δ1199100119862)

+ Δ11991123lowast (1199110minus Δ1199110119862)

119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910

45lowast (1199100minus Δ1199100119863)

+ Δ11991145lowast (1199110minus Δ1199110119863)

(9)

then (1) (2) and (3) can be converted into

(4) Δ11990901lowast 119909 + Δ119910

01lowast 119910 + Δ119911

01lowast 119911 = 119886

(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887

(6) Δ11990945lowast 119909 + Δ119910

45lowast 119910 + Δ119911

45lowast 119911 = 119888

dArr

119909 =1198631

119863 119910 =

1198632

119863 119911 =

1198633

119863

(10)

where

119863 =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

Δ11991101

Δ11990923

Δ11991023

Δ11991123

Δ11990945

Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198631=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119886 Δ11991001

Δ11991101

119887 Δ11991023

Δ11991123

119888 Δ11991045

Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198632=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

119886 Δ11991101

Δ11990923

119887 Δ11991123

Δ11990945

119888 Δ11991145

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198633=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

Δ11990901

Δ11991001

119886

Δ11990923

Δ11991023

119887

Δ11990945

Δ11991045

119888

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(11)

4 Improved Algorithm ILSARSSI

In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously

cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]

Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875

0) RSSI(1198751015840

0)

RSSI(1198751) RSSI(1198751015840

1) RSSI(119875

2) RSSI(1198751015840

2) RSSI(119875

3) RSSI(1198751015840

3)

and RSSI(1198750) lt RSSI(1198751015840

0) RSSI(119875

1) gt RSSI(1198751015840

1) RSSI(119875

2) gt

RSSI(11987510158402) RSSI(119875

3) gt RSSI(1198751015840

3) The anchor is in the enclosed

region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of

locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained

The following are the formulas for calculating the locationof locating node

119860 (1199090 1199100) 119875

0= (1199091 1199101) 119875

1015840

0= (1199091015840

1 1199101015840

1)

1198751= (1199092 1199102) 119875

1015840

1= (1199091015840

2 1199101015840

2)

1198752= (1199093 1199103) 119875

1015840

2= (1199091015840

3 1199101015840

3)

1198753= (1199094 1199104) 119875

1015840

3= (1199091015840

4 1199101015840

4)

(12)

As 1198711 1198712 1198713 and 119871

4are the perpendicular bisector of

119875011987510158400 119875111987510158401 119875211987510158402 and 119875

311987510158403 according to the geometry of

vector we can obtain that1198711 (1199091minus 1199091015840

1) lowast 119909 + (119910

1minus 1199101015840

1) lowast 119910

= (1199091+ 11990910158401

2) lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1)

8 International Journal of Distributed Sensor Networks

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

Transmission period (s)

(a) Impact of packet transmission period

0

2

4

6

8

10

12

14

16

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

400 lowast 400300 lowast 300 500 lowast 500

Size of sensor field (m2)

100 lowast 100 200 lowast 200

(b) Impact of size of sensor field

Figure 9 Localization error of our LSARSSI algorithm

1198712 (1199092minus 1199091015840

2) lowast 119909 + (119910

2minus 1199101015840

2) lowast 119910

= (1199092+ 11990910158402

2) lowast (119909

2minus 1199091015840

2) + (

1199102+ 11991010158402

2) lowast (119910

2minus 1199101015840

2)

1198713 (1199093minus 1199091015840

3) lowast 119909 + (119910

3minus 1199101015840

3) lowast 119910

= (1199093+ 11990910158403

2) lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2) lowast (119910

3minus 1199101015840

3)

1198714 (1199094minus 1199091015840

4) lowast 119909 + (119910

4minus 1199101015840

4) lowast 119910

= (1199094+ 11990910158404

2) lowast (119909

4minus 1199091015840

4) + (

1199104+ 11991010158404

2) lowast (119910

4minus 1199101015840

4)

As 1198711cap 1198714= 119861 119871

3cap 1198714= 119862

1198712cap 1198713= 119863 119871

1cap 1198712= 119864

dArr

(13)

119909119861=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 1199091015840

1

2)lowast(1199091minus 1199091015840

1) + (

1199101+ 1199101015840

1

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199093+ 1199091015840

3

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 1199101015840

3

2) lowast (119910

3minus 1199101015840

3) 1199103minus 1199101015840

3

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119909119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 11990910158401

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

119910119861=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Distributed Sensor Networks

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

Transmission period (s)

(a) Impact of packet transmission period

0

2

4

6

8

10

12

14

16

LSARSSI algorithmSsursquos algorithmBT algorithm

Aver

age l

ocal

izat

ion

erro

r (m

)

400 lowast 400300 lowast 300 500 lowast 500

Size of sensor field (m2)

100 lowast 100 200 lowast 200

(b) Impact of size of sensor field

Figure 9 Localization error of our LSARSSI algorithm

1198712 (1199092minus 1199091015840

2) lowast 119909 + (119910

2minus 1199101015840

2) lowast 119910

= (1199092+ 11990910158402

2) lowast (119909

2minus 1199091015840

2) + (

1199102+ 11991010158402

2) lowast (119910

2minus 1199101015840

2)

1198713 (1199093minus 1199091015840

3) lowast 119909 + (119910

3minus 1199101015840

3) lowast 119910

= (1199093+ 11990910158403

2) lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2) lowast (119910

3minus 1199101015840

3)

1198714 (1199094minus 1199091015840

4) lowast 119909 + (119910

4minus 1199101015840

4) lowast 119910

= (1199094+ 11990910158404

2) lowast (119909

4minus 1199091015840

4) + (

1199104+ 11991010158404

2) lowast (119910

4minus 1199101015840

4)

As 1198711cap 1198714= 119861 119871

3cap 1198714= 119862

1198712cap 1198713= 119863 119871

1cap 1198712= 119864

dArr

(13)

119909119861=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 1199091015840

1

2)lowast(1199091minus 1199091015840

1) + (

1199101+ 1199101015840

1

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2) lowast (119910

4minus 1199101015840

4) 1199104minus 1199101015840

4

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119909119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

(

1199093+ 1199091015840

3

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 1199101015840

3

2) lowast (119910

3minus 1199101015840

3) 1199103minus 1199101015840

3

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119909119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(

1199091+ 11990910158401

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 11991010158401

2) lowast (119910

1minus 1199101015840

1) 1199101minus 1199101015840

1

(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2) lowast (119910

2minus 1199101015840

2) 1199102minus 1199101015840

2

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

119910119861=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 9

119910119862=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199094minus 1199091015840

4(

1199094+ 1199091015840

4

2)lowast (119909

4minus 1199091015840

4) + (

1199104+ 1199101015840

4

2)lowast (119910

4minus 1199101015840

4)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199094minus 1199091015840

41199104minus 1199101015840

4

10038161003816100381610038161003816100381610038161003816

119910119863=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1199093minus 1199091015840

3(

1199093+ 11990910158403

2)lowast (119909

3minus 1199091015840

3) + (

1199103+ 11991010158403

2)lowast (119910

3minus 1199101015840

3)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199092minus 1199091015840

21199102minus 1199101015840

2

1199093minus 1199091015840

31199103minus 1199101015840

3

10038161003816100381610038161003816100381610038161003816

119910119864=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

1(

1199091+ 1199091015840

1

2)lowast (119909

1minus 1199091015840

1) + (

1199101+ 1199101015840

1

2)lowast (119910

1minus 1199101015840

1)

1199092minus 1199091015840

2(

1199092+ 1199091015840

2

2)lowast (119909

2minus 1199091015840

2) + (

1199102+ 1199101015840

2

2)lowast (119910

2minus 1199101015840

2)

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1199091minus 1199091015840

11199101minus 1199101015840

1

1199092minus 1199091015840

21199102minus 1199101015840

2

10038161003816100381610038161003816100381610038161003816

dArr

1199090=119909119861+ 119909119888+ 119909119863+ 119909119864

4

1199100=119910119861+ 119910119888+ 119910119863+ 119910119864

4

(14)

The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality

5 Simulation Results

To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6

In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms

Table 2 Simulation parameters

Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2

Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500

51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility

(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively

(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field

52 Average Localization Error Simulations

(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m

(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast

100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m

(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Distributed Sensor Networks

60

50

40

30

20

10

0200 300 400 500 600 700 800 900 1000

Aver

age l

ocal

izat

ion

erro

r (m

)

LSARSSI algorithmILSARSSI algorithm

Time (s)

Figure 10 Average localization error of LSARSSI and ILSARSSI

6 Conclusions

In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment

Acknowledgment

This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002

[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005

[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999

[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001

[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004

[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009

[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006

[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007

[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008

[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004

[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004

[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000

[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001

[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003

[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000

[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999

[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006

[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 11

[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003

[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004

[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005

[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002

[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011

[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007

[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046

[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005

[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987

[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008

[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of