research article alrd: aoa localization with rssi...

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 529489 10 pageshttpdxdoiorg1011552013529489

Research ArticleALRD AoA Localization with RSSI Differences ofDirectional Antennas for Wireless Sensor Networks

Jehn-Ruey Jiang Chih-Ming Lin Feng-Yi Lin and Shing-Tsaan Huang

Department of Computer Science and Information Engineering National Central University Jhongli 32001 Taiwan

Correspondence should be addressed to Jehn-Ruey Jiang jrjiangcsiencuedutw

Received 30 September 2012 Revised 22 January 2013 Accepted 1 February 2013

Academic Editor Chengdong Wu

Copyright copy 2013 Jehn-Ruey Jiang et alThis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper we fit RSSI values into a parabola function of the AoA between 0∘ and 90∘ by applying quadratic regression analysisWe also set up two-directional antennas with perpendicular orientations at the same position and fit the difference of the signalRSSI values of the two antennas into a linear function of the AoA between 0∘ and 90∘ by linear regression analysis Based onthe RSSI-fitting functions we propose a novel localization scheme called AoA Localization with RSSI Differences (ALRD) fora sensor node to quickly estimate its location with the help of two beacon nodes each of which consists of two perpendicularlyorientated directional antennas We apply ALRD to a WSN in a 10 times 10m indoor area with two beacon nodes installed at twocorners of the area Our experiments demonstrate that the average localization error is 124 cm We further propose two methodsnamed maximum-point minimum-diameter and maximum-point minimum-rectangle to reduce localization errors by gatheringmore beacon signals within 1 s for finding the set of estimated locations of maximum density Our results demonstrate that the twomethods can reduce the average localization error by a factor of about 29 to 89 cm

1 Introduction

Awireless sensor network (WSN) consists of tiny sensor nodesequipped with computational communication and sensingcapabilities whereby each sensor node can collect data aboutthe environment such as temperature vibration levels lightelectromagnetic strength and humidity The sensed datais then transmitted to the sink node through a chain ofmultiple intermediate nodes that help forward the data Dueto their capabilities and versatility WSNs have been widelyused in many areas such as military affairs healthcare andenvironmental monitoring In many applications apart fromsensed data the location information of the deployed sensornode is also desirable as it can be used to improve routingefficiency Hence the discovery of the locations or positionsof sensor nodes is one of the most critical issues for WSNs

Localization is the process of determining the absoluteor relative physical location of a specific node or the targetnode Although a global positioning system (GPS) [1] canprovide precise location information the costly hardwareand large size make it unsuitable for WSNs Furthermore aGPS can only be used outdoors since it depends on signals

directly received from satellites for localization Besides theGPS numerous localization methods [2ndash27] have also beenproposed Most of these deploy some beacon (or anchor)nodes which periodically broadcast beacon signals contain-ing their own locations to help other sensor nodes with thelocalization

Localization schemes can be classified as range based orrange-free In range-free schemes the sensor node locationis estimated solely on network connectivity Such schemesneed no extra hardware but their accuracy is too low andthey usually rely on a large deployment of beacon nodesto improve the accuracy Conversely range-based schemesusually have better accuracyTheymeasure the time of arrival(ToA) [2 3] time difference of arrival (TDoA) [4ndash6] angle ofarrival (AoA) [2 4 15 17 18 20 21 27] and received signalstrength indicator (RSSI) [3 7ndash14 16 20 21] to estimate thedistances or angles between pairs of nodes which in turnare used to calculate the locations of nodes Most kinds ofmeasurement are taken with extra auxiliary hardware Forexample ToA and TDoA are very sensitive to timing errorsand hence their measurement relies on highly accuratesynchronized timers The AoA which is defined as the angle

2 International Journal of Distributed Sensor Networks

between the propagation direction of an incident RF waveand a reference direction can be measured by an array ofantennas Unlike the previously mentioned three kinds ofmeasurement RSSI can be outputted bymost commercial off-the-shelf sensor nodes

RSSI-based localizationmethods can be further classifiedinto groups such as propagation model [8 9] proximity[10ndash12] or fingerprinting [13 14 28] Propagation modellocalization methods analyze the relationship between RSSIvalues and distances to learn parameters such as the pathloss exponent of the propagation path-loss model in thecalibration phase The calibrated propagation model is thenapplied to convert the signal strength to the estimateddistance between transmitter and receiver in the localizationphase In proximity localization methods an unknown nodebroadcasts a localization packet to initiate the localizationprocess Nearby location-known reference nodes then reportthe RSSI values measured from the packet to a nominatednode The order of reported RSSI values is then used todetermine the location of the unknown node Fingerprintinglocalization methods measure RSSI values from a set of staticnodes during a calibration phase at several locations Themeasured RSSI values at a particular location are then usedto fingerprint the location In the localization phase a nodemeasures RSSI values from the same static nodes and thenestimates its location by finding the fingerprinting that is theclosest match with the measured RSSI values

In this paper based on the concept of integrating AoALocalization and fingerprinting localization for reducingerrors we propose a novel localization scheme called AoALocalization with RSSI Differences (ALRD) It estimatesthe AoA for localization in 01 s by comparing the RSSIvalues of beacon signals received from two perpendicularlyoriented directional antennas installed at the same placeIn the proposed ALRD we fit RSSI values received froma directional antenna into a parabola function of an AoAbetween 0∘ and 90∘ We also set up a beacon node withtwo perpendicularly oriented directional antennas and fit thedifference of the signal RSSI values of the two antennas intoa linear function of the absolute value of one AoA between0∘ and 90∘ With the parabola and linear functions a sensornode can then self-localize itself quickly (within 01 s) byobserving RSSI values of the beacon signals emitted by thetwo beacon nodes The fitting functions can easily be storedin a WSN node despite their limited storage space and theirinverse functions can be used to speed up the localizationprocess Hence ALRD is suitable for mobile sensing andactuating applications in an open and stable environmentsince it allows a sensor node to fast localize itself with smalllocalization errors Our experiments demonstrate that theaverage localization error is 124 cm when deployed in a 10 times10m indoor area

We further propose two methods namely maximum-point minimum-diameter and maximum-point minimum-rectangle to reduce ALRD localization errors by gatheringmore beacon signals within 1 s for finding the set of estimatedlocations of maximum density Such estimated locationsare then averaged to obtain the final location estimationExperimental results obtained demonstrate that the two

AoA

Sensor node

Propagation direction of the incident RF wave

Directional antenna

Orientation

Figure 1 AoA of a sensor node and a directional antenna

methods can reduce the average localization error by a factorof about 29 to 89 cm Hence ALRD is suitable for mobilesensing and actuating applications as it allows a sensor nodeto quickly localize itself with lower localization errors

The rest of this paper is organized as follows We reviewsome AoA determination schemes in Section 2 In Section 3we describe the proposed localization scheme ALRD indetail Section 4 shows our experimental results Then wedescribe improvements to ALRD and compare it with otherschemes in Section 5 Finally we conclude the paper inSection 6

2 Related Works

In this section we review some research that determinesAoAs for localization Amundson et al developed the RIMAsystem that uses radio interferometry measurements to esti-mate the AoA [15] RIMA estimates the AoA by measuringthe TDoA of an interference signal generated by a antennaarrayThe system consists of a beacon node and a target nodeThe beacon node is formed by grouping three sensor nodes toform an antenna arrayThe three sensor nodes are arranged ina manner such that their antennas are mutually orthogonalTwo of the sensor nodes transmit a pure sinusoidal signalat slightly different frequencies to create a low-frequencyinterference signalThe other sensor node and the target nodeboth measure the phase of the low-frequency signal Thedifference in the phase readingsmeasured by these two nodesis then used to estimate the AoA from the beacon node tothe target node Although RIMA can accurately measure theAoAwithin 1 s it requires very accurate time synchronizationbetween the beacon node and the target node which is verydifficult to achieve

Two methods Estimating Direction-of-Arrival (EDoA)[5] and Rotatable Antenna Localization (RAL) [16] utilizethe property of directional antennas to estimate the AoA ofa signal EDoA estimates the AoA of an incoming signalby using a mechanically actuated parabolic reflector Thereceiver which is fixed to a parabolic reflector rotated bya step motor is used to observe the RSSI values of signalsemitted from a transmitter When the orientation of thereflector is aligned with the direction from the receiver to the

International Journal of Distributed Sensor Networks 3

05

10152025

0 2 4 6 8 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

160

170

180

RSSI

val

ues

AoA

minus180minus170minus160minus150minus140minus130minus120minus110minus100minus90minus80minus70minus60minus50minus40minus30minus20minus10 minus8minus6minus4minus2

minus40

minus45

minus30

minus35

minus20

minus25

minus10

minus15

minus5

1 M5 M10 M

Figure 2 RSSI values of signals received from a directional antenna

90 minus 120579

120579

Figure 3 AoAs relative to directional antennas with perpendicularorientations

transmitter the receiver will observe the highest RSSI valueHence the AoA can be obtained by searching for the reflectororientation in which the highest RSSI value is observedTheirexperimental results show that the error in measuring theAoA has a mean of about 4∘ and a standard deviation ofabout 8∘ in both indoor and outdoor environments HoweverEDoA needs to take a long time to rotate the reflector forsearching the highest RSSI value In RAL a beacon node isequipped with a rotatable directional antenna It regularlyrotates its antenna to emit beacon signals in different direc-tions A sensor node determines the angle from the beaconnode to itself by observing the RSSI values of the receivedbeacon signals which contain the location of the beaconnodeand the current orientation of its antenna Similar to EDoARAL can determine the AoA by determining the strongestsignal By using the estimated AoAs and locations of two

distinct beacon nodes a sensor node can then calculate itsown location with a localization error of 76 cm within a 10 times10-meter indoor area Two enhanced methods were furtherproposed to reduce the localization error by a factor of 10[16] EDoA and RAL both need a long time to rotate theantenna or the reflector for observing the variation of theRSSI values while estimating the AoA Therefore EDoA andRAL are only suitable for localizing static sensor nodes

3 The Proposed Scheme

Existing localization schemes using AoAs may take a longtime to finish the localization or need very accurate timesynchronization In this section we proposeALRD that finishlocalization quickly by learning how theRSSI values varywiththe AoA in advance without the need of time synchronizationbetween the anchor node and the target node

31 Preliminary As shown in Figure 1 we define the AoA asthe angle from the propagation direction of an incident RFwave to the orientation of the directional antenna emittingthe RF wave The AoA is positive if it is counterclockwiseand negative otherwise Figure 2 shows a plot of RSSI valuesover AoA we observe that if the distance between the sensornode and the directional antenna is fixed the RSSI varies likea parabolic function of AoA referenced to the orientationof the directional antenna between minus90∘ and 90∘ with a anaxis of symmetry at AoA = 0∘ Furthermore we set up twoperpendicularly oriented directional antennas installed at thesame location (seen in Figure 3) From the results obtained(as shown in Figure 4) we also observe that the difference ofthe signal RSSI values received by a sensor node localizingbetween the orientations of two-directional antennas varies


1 M5 M10 M

0369

12151821242730

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Diff

eren

ce o

f RSS

I val

ues

AoA

minus30

minus21minus24minus27

minus15minus18

minus12

minus3minus6minus9

Figure 4 Difference of the signal RSSI values received from two-directional antennas with perpendicular orientations

like a linear function of the absolute value of theAoAbetween0∘ and 90∘ It can be noted that absolute values of AoAs areused and that when one absolute AoA value is 120579 the otherabsolute AoA value is 90 minus 120579 We then take only one absoluteAoA value as the representative without ambiguity

32 RSSI Gathering and Analyzing Before deploymentALRD needs to gather and analyze RSSI values of the signalsthat a sensor node receives from a directional antenna atdifferent distances and angles The measured RSSI values arethen analyzed to generate the fitting functions These fittingfunctions are then stored into the storage of each sensor nodefor localization For better accuracy the RSSI gathering andanalyzing tasks are needed to execute at each new systemdeployment location since the environment changes maymake the measured RSSI values have some differences Thetasks are described as follows

(1) Gathering RSSI values as shown in Figure 5 we setup a directional antenna that can be rotated by anangle 120579 from the 119909-axis (or the east direction) (0∘) tothe119910-axis (or the north direction) (90∘) and transmitsbeacon signals containing the rotating angle for everydegree A sensor is placed at the 119909-axis at a distanceof 119889 2119889 119872119889 meters for receiving signals emittedfrom the antenna for several times (eg 100) where119889 and 119872 are specified values (eg 119889 = 1 and 119872 =10) The received signal RSSI values are averagedand stored The gathered RSSI average values aredenoted by 119866

119896119889(120579) where 119896 = 1 2 119872 and 120579 =

0∘

1∘

90∘

(2) Performing quadratic regression for each distance119896119889 the gathered RSSI values are fitted approximatelyinto a quadratic function 119876

119896119889(120579) of the rotating angle

120579 by quadratic regression analysis

(3) Calculating RSSI differences for each distance 119896119889the RSSI difference 119863

119896119889(120579) at angle 120579 is obtained

by calculating 119866119896119889(120579) minus 119866

119896119889(90 minus 120579) In practice

119863119896119889(120579) is approximately the difference of RSSI values

between two signals that a sensor node receives fromtwo perpendicularly oriented directional antennasinstalled at the same location

(4) Performing linear regression for each distance 119896119889the RSSI difference119863

119896119889(120579) at angle 120579 is approximately

fitted into a linear function 119871119896119889(120579) by linear regression

analysis(5) Storing functions the quadratic and linear approxi-

mation functions are loaded into the storage of thesensor nodes before they are deployed

33 ALRD Setup Figure 6 shows the setup for ALRD Weassume that all sensor nodes are randomly deployed in aplanar square area of interest Two beacon nodes 119861

1and

1198612 are deployed in the lower left and lower right corners

of the area respectively Each beacon node is equipped withtwo-directional antennas with perpendicular orientationsThe antennas of the beacon node in the lower left (or right)corner have either an upright or a horizontal to the right (orleft) orientation The antenna with the upright orientationis called the vertical antenna whereas the antenna withthe left or right orientation is called the horizontal antennaEach beacon node is assumed to know its location andorientations of the two antennas The beacon nodes transmitbeacon signals via the two-directional antennas regularly andalternately The beacon signal contains the orientation of theantenna and the location of the beacon node which areexpected to reach the whole area of interest

Note that the setup in Figure 5 can be the basic buildingblock for deploying ALRD in a large indoor localization envi-ronment Figure 7 shows a deployment instance of beacon


RotatableSensor node

Directional antenna

90∘

0∘

119889 2119889 3119889 119872119889

Figure 5 The setup for gathering and analyzing RSSI values

Beacon node Beacon node1198611 at location 1198612 at location

AoA1119907 = 120573

AoA1ℎ = 120572

AoA2119907 = 120575

AoA2ℎ = 120601

(0 119863)(0 0)

Figure 6 Setup for ALRD

nodes in a large area The beacon nodes consist of 1 2 or 4pairs of perpendicularly oriented directional antennas Anytwo adjacent beacon nodes are D units away from each otherin the horizontal direction and 2D units away from each otherin the vertical direction Based on the setup of Figure 6 wecan see that any two adjacent beacon nodes in the horizontaldirection can properly localize target nodes within an area ofD by D units For example in Figure 7 the beacon nodes Xand Y can properly localize target nodes within the shadedarea Hence ALRD can help localize sensor nodes in a largearea by installing a lot of beacon nodes

34 Localization Procedure In ALRD a sensor node executesthe following steps to estimate its location

(1) Receiving beacon signals in order to localize itselfthe sensor node needs to collect the signal RSSI values1198771ℎ

and 1198771V of the horizontal and vertical antennas

of beacon node 1198611 It also needs to collect the signal

RSSI values 1198772ℎand 119877

2V of the horizontal and verticalantennas of beacon node 119861

2

(2) Estimating distance for each distance 119896119889 for 119896 =1 2 119872 two absolute values of AoAs 120572

119896119889and 120573

119896119889

corresponding to the horizontal and vertical antennasof the beacon node 119861

1are obtained by calculating

120572119896119889= 119876minus1

119896119889

(1198771ℎ) and 120573

119896119889= 119876minus1

119896119889

(1198771V) for 0

∘

le 120572119896119889

and120573119896119889le 90∘ Here 119876minus1

119896119889

(sdot) is an inverse function of thequadratic function 119876

119896119889(sdot) obtained in RSSI gathering

and analysis As shown in Figure 6 120572119896119889+ 120573119896119889

shouldideally be 90∘ Therefore the sensor node can obtain

119863

119863

119883 119884

Figure 7 Deployment instance of beacon nodes in a large area

a rough estimate of the distance from itself to thebeacon node 119861

1 by finding 119896119889 for 119896 = 1 2 119872

such that 120572119896119889+120573119896119889is closest to 90∘ Let the discovered

119896119889 be denoted by 1198961198891 Similarly by 119877

2ℎand 119877

2V thesensor node can find 119896119889 such that 120601

119896119889+ 120575119896119889

is closestto 90∘ where 120601

119896119889and 120575

119896119889are two absolute values of

AoAs (where 0∘ le 120601119896119889

and 120575119896119889le 90∘) corresponding

to the horizontal and vertical antennas of the beaconnode 119861

2and 120601

119896119889= 119876minus1

119896119889

(1198772ℎ) and 120575

119896119889= 119876minus1

119896119889

(1198772V) Let

the discovered 119896119889 be denoted by 1198961198892

(3) Estimating AoA the distance estimate 1198961198891obtained

in Step 2 is used to choose a proper linear approxi-mation function 119871

1198961198891

for estimating the AoA of thesensor node corresponding to the beacon node 119861

1

The AoA corresponding to the horizontal antennaof 1198611is calculated as 120572

1198961198891

= 119871minus1

1198961198891

(1198771ℎminus 1198771V)

where 119871minus11198961198891

(sdot) is the inverse function of the linearfunction 119871

1198961198891

(sdot) obtained in the RSSI gathering andanalysis stage Similarly by 119896119889

2and (119877

2ℎminus 1198772V) the

AoA corresponding to the horizontal antenna of thebeacon node119861

2can be calculated as 120601

1198961198892

= 119871minus1

1198961198892

(1198772ℎminus

1198772V)

(4) Calculating location after obtaining theAoAs1205721198961198891

(or120572 for short) and 120601

1198961198892

(or 120601 for short) correspondingto the horizontal antennas of the two beacon nodes


(a)

(b)

Figure 8 (a)The beacon nodes used in RSSI gathering and analysis(b) The beacon node used in localization

1198611and 119861

2 the sensor node can determine its location

(119909 119910) by calculating

(119909 119910) = (119863 times tan120601

tan120572 + tan120601119863 times tan120572 times tan120601tan120572 + tan120601

)

0 le 119909 119910 le 119863

(1)

where 119863 is the known distance of 1198611and 119861

2 Note

that we can also calculate this by using only 1198961198891and

1198961198892 However our experiments show that using 120572

1198961198891

and 1206011198961198892

results in locations that are more accurateThis explains why ALRD uses 119877

1ℎ 1198771V 1198772ℎ and 1198772V

to calculate 1198961198891and 119896119889

2 uses 119896119889

1and 119896119889

2to calculate

1205721198961198891

and 1206011198961198892

and then uses 1205721198961198891

and 1206011198961198892

to calculatethe location

Figure 9 The ALRD experimental setup

4 Experiment Results

In this section we describe the implementation of ALRD andthe results of the experiments using the implementation

41 Implementation The sensor nodes and the beacon nodesof the proposed ALRD scheme are implemented in nesCwith TinyOS support on the Moteiv BAT mote sensor TheBAT mote sensor has a Texas Instruments MSP430 F1611microcontroller running at 8MHzwith 10 kBRAMand48 kBflash memory It is equipped with the Chipcon CC2420 IEEE802154 compliant wireless transceiver using the 24GHzband with a 250 kbps data rate With an integrated onboardomnidirectional antenna the BAT mote sensor has a max-imum transmission range of 50m (indoor) or 125m (out-door)

The beacon node used for RSSI gathering and analysisis also attached with a Maxim AP-12 panel antenna whichis rotated by a Fastech Ezi-Servo 28 L step motor as shownin Figure 8(a) The beacon node used in localization isattached with two AP-12 panel antennas with perpendicularantennas as shown in Figure 8(b) Its horizontal and verticalbeamwidths are 65∘ and 28∘ respectively

42 Experimental Setup We installed the ALRD setup in a10times10m region of an indoor basketball court for conductingexperiments as shown in Figures 9 and 10 Two beacon nodeswere set up at two ends of the edge of the experiment areaand the localization accuracy was tested at 81 grid points (asarranged in Figure 10) Since the largest distance between ameasurement point and a beacon node is about 1273m wegathered and analyze the RSSI values of signals emitted atdistances of 1 2 13m for every degree from 0∘ to 90∘TheRSSI value for each distance and each degree was obtained byaveraging 100 measurements

The gathered RSSI values are shown in Figure 11 Theinterval for gathering the RSSI values is set as 1m becausethe RSSI values will be indistinguishable if the interval istoo small To reduce the gathering time and space used forstoring the approximation functions we only measured RSSIvalues for one of the four antennas of the same type ofthe two beacon nodes in our experiments The coefficientsof determination 1198772 of all the approximation functionsare shown in Figure 12 We note that the coefficients ofdetermination are high and all exceed 096 Therefore theapproximation functions are very suitable for expressing themeasured RSSI values and RSSI differences


987654321

181716151413121110

272625242322212019

363534333231302928

454443424139 403837

545352515049484746

636261605958575655

727170696867666564

818079787776757473

1198611 = (0 0) 1198612 = (0 10)

Figure 10 The ALRD experimental setup and 81 grid points fortesting

147

10

0 10 20 30 40 50 60 70 80 90(deg)

RSSI

val

ues

minus47

minus44

minus41

minus38

minus35

minus32

minus29

minus26

minus23

minus20

minus17

minus14

minus11

minus8

minus5

minus2

1 M2 M3 M4 M5 M6 M7 M

8 M9 M

13 M

10 M11 M12 M

Figure 11 The gathered RSSI values

43 Localization Errors The localization accuracy is testedat the 81 grid points shown in Figure 10 The beacon nodestransmit beacon signals via each of their antennas 10 times persecond Therefore a sensor node can localize itself 10 timesper second We take the average of 10 localization resultsand plot the cumulative distribution in Figure 13The average

09

091

092

093

094

095

096

097

098

099

1

1 2 3 4 5 6 7 8 9 10 11 12 13

Distance (M)

Coe

ffici

ents

of d

eter

min

atio

n1198772

119876()119871()

Figure 12 The coefficients of determination 1198772 of the quadratic(119876) and linear (119871) approximation functions for different distances

0

10

20

30

40

50

60

70

80

90

100

0 05 1 15 2 25 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()

Localization error (m)

Figure 13 Cumulative distribution function of the localizationerror

localization error of the localization experiment is 124 cm InFigure 14 we use different colors to represent the localizationerrors of the test points The brighter color indicates thesmaller localization error As Figure 13 shows the test pointsthat lie in the middle of the region have smaller localizationerrorsThis can be explained by Figure 4 in which the curvesalmost look like straight lines in the middle

5 Improvement

As the results showALRDcan let sensor nodes localize them-selves by measuring RSSI values of signals from two beacon


9

8

7

6

5

4

3

2

1987654321

2-31-20-1

Figure 14 The localization error distribution

025 05 075 1 125 15 175 2 225 25 275 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()


ALRD + MPMDALRD + MPMAALRD

0

10

20

30

40

50

60

70

80

90

100

Figure 15 Cumulative distributions of localization errors

nodes in a short time (01 s) However the measured RSSIvalues may be influenced by environmental interferences sothe estimated locationmay deviate from the real location andhas a localization error Thus if a node spends more timemeasuring more RSSI values then more location estimationscan be made which in turn can reduce the deviations Basedon the concepts introduced in [28] we propose twomethodsnamely maximum-point minimum-diameter (MPMD) andmaximum-point minimum-rectangle (MPMR) to removesome estimated location from a set of estimated locations forthe purposes of reducing the localization error

Assuming that 119875 is the set of estimated locations MPMDandMPMR remove some locations by finding a subset1198751015840 sube 119875

Table 1 Comparisons of localization errors

ALRD ALRD +MPMD ALRD +MPMRLocalization errors (cm) 124 90 89Improvement mdash 28 288

with the largest density The density 120588 of a set of estimatedlocations is defined as follows

120588 =119873

Dia(MPMD) or 120588 = 119873

Area(MPMR) (2)

where 119873 is the cardinality of the set Dia is the diameter ofthe locations in the set and Area is the area of the smallestaxis-parallel rectangle containing all locations in the set Thediameter Dia of a set of locations can be obtained by finding apair of locations with the longest distance between themTheArea of a set of locations can be obtained by finding the fourextremes (ie the leftmost rightmost highest and lowestextremes) and calculating the area of the rectangle boundedby them

The following steps are executed by a sensor node to applyMPMD orMPMR to obtain a subset 1198751015840 of a set 119875 of locationssuch that 1198751015840 has the largest density

Step 1 If |119875| lt 3 then return 119875

Step 2 Derive subset 1198751015840 of 119875 by removing the location withthemaximum summation of the distances from itself to otherlocations in 119875 and calculate the density 1205881015840 of 1198751015840

Step 3 If 120588 gt 1205881015840 then return 119875 otherwise set 119875 = 1198751015840 and goto Step 1

By using the set of estimated locations with the max-imum density returned by MPMD and MPMR we canthen calculate the average of all locations to derive a newestimated location with a small localization error Table 1shows the average of the localization errors after applyingMPMD and MPMR to 10 localization results collected by asensor node within 1 second Figure 15 shows the cumulativedistributions of the ALRD localization errors and thoseimproved byMPMD andMPMR As shown MPMD is moresuitable than MPMR for sensor nodes because it makessimilar improvements as MPMR but has less computationaloverheads

Table 2 compares ALRD with other three localizationschemes namely EDoA [4] RAL [13] and RIMA [15] Aswe have mentioned previously EDoA and RAL take a longtime to localize sensor nodes because they have to rotatethe antennas or the reflector RIMA is able to accuratelylocalize a target node in a short time but it requires timesynchronization between the beacon node and the targetnode By contrast ALRD can localize sensor nodes in a shorttime and provides relatively low localization errors withoutthe need for time synchronization


Table 2 Comparison of localization schemes

Method BN Antenna SYN Time AE LE

ALRD 2 2BN N lt1 s 6∘ndash8∘ 89 cmRIMA 1 3BN Y 16 s 3∘ mdashEDoA mdash 1SN N 200 s 4∘ndash8∘ mdashRAL 2 2BN N 180 s 4∘ndash8∘ 76 cmBN the number of beacon nodes

Antenna the number of antennas per beacon node (BN) or per sensor node(SN)AE angle errorLE localization errorSYN time synchronization requirement

6 Conclusion

In this paper we proposed AoA Localization with RSSIDifferences (ALRD) to estimate angle of arrival (AoA) bycomparing the received signal strength indicator (RSSI)values of beacon signals received from two perpendicularlyoriented directional antennas installed at the same placeWe have implemented and installed ALRD in a 10 times 10mindoor environment Our experimental results showed thata sensor node can estimate its location by using only fourbeacon signals within 01 s with an average localization errorof 124 cm Hence ALRD conserves the time and energy spenton localization Furthermore we proposed two methodsnamely maximum-point minimum-diameter (MPMD) andmaximum-point minimum-rectangle (MPMR) to reduceALRD localization errors by gathering more beacon signalswithin 1 s to find the set of estimated locations of maximumdensity The results demonstrated that MPMD and MPMRcan reduce the localization error by a factor of about 29 to89 cmThus as ALRD allows a sensor node to quickly localizeitself with lower errors it is suitable for mobile sensing andactuating applications

As our experiments show it is sufficient to gather RSSIvalues for only one of four antennas of the same type toachieve sufficient localization accuracy By equipping anten-nas of the same type to all beacon nodes the sensor nodesmerely need to store the quadratic and linear approximationfunctions of one antenna In the future we will focus onapplying ALRD to realize a large-area localization systemMoreover we will also try to apply different types of direc-tional antennas and their combinations to ALRD in the hopeof further reducing localization error

References

[1] B Hofmann-Wellenhof H Lichtenegger and J Collins GlobalPositioning System Theory and Practice Springer Berlin Ger-many 1997

[2] T Y Chen C C Chiu and T C Tu ldquoMixing and Combiningwith AOA and TOA for Enhanced accuracy of mobile locationrdquoin Proceedings of the 5th European PersonalMobile Communica-tions Conference pp 276ndash280 2003

[3] N Patwari and A O Hero III ldquoLocation estimation accuracy inwireless sensor networksrdquo in Proceedings of the 36th Asilomar

Conference on Signals Systems and Computers pp 1523ndash1527November 2002

[4] C Li and ZWeihua ldquoHybrid TDOAAOAmobile user locationfor wideband CDMA cellular systemsrdquo IEEE Transactions onWireless Communications vol 1 no 3 pp 439ndash447 2002

[5] F Gustafsson and F Gunnarsson ldquoPositioning using time-difference of arrival measurementsrdquo in Proceedings of theIEEE International Conference on Accoustics Speech and SignalProcessing pp 553ndash556 April 2003

[6] W Xiao Y Weng and L Xie ldquoTotal least squares methodfor robust source localization in sensor networks using TDOAmeasurementsrdquo International Journal of Distributed SensorNetworks vol 2011 Article ID 172902 8 pages 2011

[7] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in Proceedings of the19th IEEE International Conference on Computer Commmunica-tions (IFOCOM rsquo00) pp 775ndash784 2000

[8] P K Sahoo and I Hwang ldquoCollaborative localization algo-rithms forwireless sensor networks with reduced localizationerrorrdquo Sensors vol 11 no 10 pp 9989ndash10009 2011

[9] J Shirahama and T Ohtsuki ldquoRSS-based localization in envi-ronments with different path loss exponent for each linkrdquo inProceedings of the IEEEVehicular Technology Conference-SpringVTC pp 1509ndash1513 May 2008

[10] J Lee W Chung and E Kim ldquoA new range-free localizationmethod using quadratic programmingrdquo Computer Communi-cations vol 34 no 8 pp 998ndash1010 2011

[11] Z Liu and J Chen ldquoA new sequence-based iterative localizationin wireless sensor networksrdquo in Proceedings of the InternationalConference on Information Engineering and Computer Science(ICIECS rsquo09) December 2009

[12] K Yedavalli and B Krishnamachari ldquoSequence-based localiza-tion in wireless sensor networksrdquo IEEE Transactions on MobileComputing vol 7 no 1 pp 81ndash94 2008

[13] S Fang and T Lin ldquoA dynamic system approach for radiolocation fingerprinting in wireless local area networksrdquo IEEETransactions on Communications vol 58 no 4 pp 1020ndash10252010

[14] P M Scholl S Kohlbrecher V Sachidananda and K VanLaerhoven ldquoFast Indoor Radio-Map Building for RSSI-basedLocalization Systemsrdquo in Proceedings of the 9th InternationalConference on Networked Sensing System pp 1ndash2 2012

[15] I Amundson J Sallai X Koutsoukos and A Ledeczi ldquoRadiointerferometric angle of arrival estimationrdquo Lecture Notes inComputer Science vol 5970 pp 1ndash16 2010

[16] S J Halder andW Kim ldquoA fusion approach of RSSI and LQI forindoor localization systemusing adaptive smoothersrdquo Journal ofComputer Networks and Communications Article ID 790374 10pages 2012

[17] I Amundson J Sallai X Koutsoukos and A Ledeczi ldquoMobilesensor navigation via RF-based angle of arrival localizationrdquoInternational Journal of Distributed Sensor Networks vol 2012Article ID 842107 15 pages 2012

[18] I Amundson J Sallai X Koutsoukos and A Ledeczi ldquoMobilesensor navigation using rapidRF-based angle of arrival localiza-tionrdquo in Proceedings of the 17th IEEE Real-Time and EmbeddedTechnology and Applications Symposium pp 316ndash325 ChicagoIll USA 2011

[19] A Cenedese G Ortolan and M Bertinato ldquoLow-densitywireless sensor networks for localization and tracking in criticalenvironmentsrdquo IEEE Transactions on Vehicular Technology vol59 no 6 pp 2951ndash2962 2010


[20] B N Hood and P Barooah ldquoEstimating DoA from radio-frequency rssi measurements using an actuated reflectorrdquo IEEESensors Journal vol 11 no 2 pp 413ndash417 2011

[21] J R Jiang C H Lin and Y J Hsu ldquoLocalization withRotatable directional antennas for wireless sensor networksrdquoin Proceedings of the 39th International Conference on ParallelProcessing Workshops (ICPPW rsquo10) pp 542ndash548 September2010

[22] T Kim M Shon M Kim D S Kim and H Choo1 ldquoAnchor-node-based distributed localization with error correction inwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2012 Article ID 975147 14 pages 2012

[23] Y Liu X Yi and Y He ldquoA novel centroid localization forwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2012 Article ID 829253 8 pages 2012

[24] A Nasipuri and K Li ldquoExperimental evaluation of an anglebased indoor localization systemrdquo in Proceedings of the 5thInternational Symposium on Modeling and Optimization inMobile Ad Hoc and Wireless Networks pp 1ndash9 2006

[25] D Niculescu and B Nath ldquoDV based positioning in ad hocnetworksrdquo Telecommunication Systems vol 22 no 1 pp 267ndash280 2003

[26] C H Ou ldquoA localization scheme for wireless sensor networksusing mobile anchors with directional antennasrdquo IEEE SensorsJournal vol 11 no 7 pp 1607ndash1616 2011

[27] R Peng and M L Sichitiu ldquoAngle of arrival localization forwireless sensor networksrdquo in Proceedings of the 3rd Annual IEEECommunications Society on Sensor and Ad hoc Communicationsand Networks (Secon rsquo06) pp 374ndash382 September 2006

[28] R Atanassov P BoseM Couture et al ldquoAlgorithms for optimaloutlier removalrdquo Journal of Discrete Algorithms vol 7 no 2 pp239ndash248 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



between the propagation direction of an incident RF waveand a reference direction can be measured by an array ofantennas Unlike the previously mentioned three kinds ofmeasurement RSSI can be outputted bymost commercial off-the-shelf sensor nodes

RSSI-based localizationmethods can be further classifiedinto groups such as propagation model [8 9] proximity[10ndash12] or fingerprinting [13 14 28] Propagation modellocalization methods analyze the relationship between RSSIvalues and distances to learn parameters such as the pathloss exponent of the propagation path-loss model in thecalibration phase The calibrated propagation model is thenapplied to convert the signal strength to the estimateddistance between transmitter and receiver in the localizationphase In proximity localization methods an unknown nodebroadcasts a localization packet to initiate the localizationprocess Nearby location-known reference nodes then reportthe RSSI values measured from the packet to a nominatednode The order of reported RSSI values is then used todetermine the location of the unknown node Fingerprintinglocalization methods measure RSSI values from a set of staticnodes during a calibration phase at several locations Themeasured RSSI values at a particular location are then usedto fingerprint the location In the localization phase a nodemeasures RSSI values from the same static nodes and thenestimates its location by finding the fingerprinting that is theclosest match with the measured RSSI values

In this paper based on the concept of integrating AoALocalization and fingerprinting localization for reducingerrors we propose a novel localization scheme called AoALocalization with RSSI Differences (ALRD) It estimatesthe AoA for localization in 01 s by comparing the RSSIvalues of beacon signals received from two perpendicularlyoriented directional antennas installed at the same placeIn the proposed ALRD we fit RSSI values received froma directional antenna into a parabola function of an AoAbetween 0∘ and 90∘ We also set up a beacon node withtwo perpendicularly oriented directional antennas and fit thedifference of the signal RSSI values of the two antennas intoa linear function of the absolute value of one AoA between0∘ and 90∘ With the parabola and linear functions a sensornode can then self-localize itself quickly (within 01 s) byobserving RSSI values of the beacon signals emitted by thetwo beacon nodes The fitting functions can easily be storedin a WSN node despite their limited storage space and theirinverse functions can be used to speed up the localizationprocess Hence ALRD is suitable for mobile sensing andactuating applications in an open and stable environmentsince it allows a sensor node to fast localize itself with smalllocalization errors Our experiments demonstrate that theaverage localization error is 124 cm when deployed in a 10 times10m indoor area

We further propose two methods namely maximum-point minimum-diameter and maximum-point minimum-rectangle to reduce ALRD localization errors by gatheringmore beacon signals within 1 s for finding the set of estimatedlocations of maximum density Such estimated locationsare then averaged to obtain the final location estimationExperimental results obtained demonstrate that the two

AoA

Sensor node

Propagation direction of the incident RF wave

Directional antenna

Orientation

Figure 1 AoA of a sensor node and a directional antenna

methods can reduce the average localization error by a factorof about 29 to 89 cm Hence ALRD is suitable for mobilesensing and actuating applications as it allows a sensor nodeto quickly localize itself with lower localization errors

The rest of this paper is organized as follows We reviewsome AoA determination schemes in Section 2 In Section 3we describe the proposed localization scheme ALRD indetail Section 4 shows our experimental results Then wedescribe improvements to ALRD and compare it with otherschemes in Section 5 Finally we conclude the paper inSection 6

2 Related Works

In this section we review some research that determinesAoAs for localization Amundson et al developed the RIMAsystem that uses radio interferometry measurements to esti-mate the AoA [15] RIMA estimates the AoA by measuringthe TDoA of an interference signal generated by a antennaarrayThe system consists of a beacon node and a target nodeThe beacon node is formed by grouping three sensor nodes toform an antenna arrayThe three sensor nodes are arranged ina manner such that their antennas are mutually orthogonalTwo of the sensor nodes transmit a pure sinusoidal signalat slightly different frequencies to create a low-frequencyinterference signalThe other sensor node and the target nodeboth measure the phase of the low-frequency signal Thedifference in the phase readingsmeasured by these two nodesis then used to estimate the AoA from the beacon node tothe target node Although RIMA can accurately measure theAoAwithin 1 s it requires very accurate time synchronizationbetween the beacon node and the target node which is verydifficult to achieve

Two methods Estimating Direction-of-Arrival (EDoA)[5] and Rotatable Antenna Localization (RAL) [16] utilizethe property of directional antennas to estimate the AoA ofa signal EDoA estimates the AoA of an incoming signalby using a mechanically actuated parabolic reflector Thereceiver which is fixed to a parabolic reflector rotated bya step motor is used to observe the RSSI values of signalsemitted from a transmitter When the orientation of thereflector is aligned with the direction from the receiver to the


05

10152025

0 2 4 6 8 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

160

170

180

RSSI

val

ues

AoA


minus40

minus45

minus30

minus35

minus20

minus25

minus10

minus15

minus5

1 M5 M10 M


90 minus 120579

120579








1 M5 M10 M

0369

12151821242730

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Diff

eren

ce o

f RSS

I val

ues

AoA

minus30


minus15minus18

minus12

minus3minus6minus9





119896119889(120579) where 119896 = 1 2 119872 and 120579 =

0∘

1∘

90∘
















1and






Directional antenna

90∘

0∘

119889 2119889 3119889 119872119889



AoA1119907 = 120573

AoA1ℎ = 120572

AoA2119907 = 120575

AoA2ℎ = 120601

(0 119863)(0 0)









2


119896119889and 120573

119896119889



120572119896119889= 119876minus1

119896119889

(1198771ℎ) and 120573

119896119889= 119876minus1

119896119889

(1198771V) for 0

∘

le 120572119896119889

and120573119896119889le 90∘ Here 119876minus1

119896119889





119863

119863

119883 119884



1 by finding 119896119889 for 119896 = 1 2 119872



2ℎand 119877


119896119889+ 120575119896119889


119896119889and 120575


AoAs (where 0∘ le 120601119896119889



2and 120601

119896119889= 119876minus1

119896119889

(1198772ℎ) and 120575

119896119889= 119876minus1

119896119889

(1198772V) Let




1198961198891


1


1198961198891

= 119871minus1

1198961198891

(1198771ℎminus 1198771V)

where 119871minus11198961198891


1198961198891


2and (119877




1198961198892

= 119871minus1

1198961198892

(1198772ℎminus

1198772V)



1198961198892



(a)

(b)


1198611and 119861



(119909 119910) = (119863 times tan120601


)

0 le 119909 119910 le 119863

(1)


2 Note



1198961198891

and 1206011198961198892


1ℎ 1198771V 1198772ℎ and 1198772V

to calculate 1198961198891and 119896119889

2 uses 119896119889

1and 119896119889

2to calculate

1205721198961198891

and 1206011198961198892

and then uses 1205721198961198891

and 1206011198961198892










987654321

181716151413121110

272625242322212019

363534333231302928

454443424139 403837

545352515049484746

636261605958575655

727170696867666564

818079787776757473

1198611 = (0 0) 1198612 = (0 10)


147

10

0 10 20 30 40 50 60 70 80 90(deg)

RSSI

val

ues

minus47

minus44

minus41

minus38

minus35

minus32

minus29

minus26

minus23

minus20

minus17

minus14

minus11

minus8

minus5

minus2

1 M2 M3 M4 M5 M6 M7 M

8 M9 M

13 M

10 M11 M12 M



09

091

092

093

094

095

096

097

098

099

1

1 2 3 4 5 6 7 8 9 10 11 12 13

Distance (M)

Coe

ffici

ents

of d

eter

min

atio

n1198772

119876()119871()


0

10

20

30

40

50

60

70

80

90

100

0 05 1 15 2 25 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()




5 Improvement



9

8

7

6

5

4

3

2

1987654321

2-31-20-1


025 05 075 1 125 15 175 2 225 25 275 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()



0

10

20

30

40

50

60

70

80

90

100







120588 =119873

Dia(MPMD) or 120588 = 119873

Area(MPMR) (2)













6 Conclusion



References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










05

10152025

0 2 4 6 8 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

160

170

180

RSSI

val

ues

AoA


minus40

minus45

minus30

minus35

minus20

minus25

minus10

minus15

minus5

1 M5 M10 M


90 minus 120579

120579








1 M5 M10 M

0369

12151821242730

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Diff

eren

ce o

f RSS

I val

ues

AoA

minus30


minus15minus18

minus12

minus3minus6minus9





119896119889(120579) where 119896 = 1 2 119872 and 120579 =

0∘

1∘

90∘
















1and






Directional antenna

90∘

0∘

119889 2119889 3119889 119872119889



AoA1119907 = 120573

AoA1ℎ = 120572

AoA2119907 = 120575

AoA2ℎ = 120601

(0 119863)(0 0)









2


119896119889and 120573

119896119889



120572119896119889= 119876minus1

119896119889

(1198771ℎ) and 120573

119896119889= 119876minus1

119896119889

(1198771V) for 0

∘

le 120572119896119889

and120573119896119889le 90∘ Here 119876minus1

119896119889





119863

119863

119883 119884



1 by finding 119896119889 for 119896 = 1 2 119872



2ℎand 119877


119896119889+ 120575119896119889


119896119889and 120575


AoAs (where 0∘ le 120601119896119889



2and 120601

119896119889= 119876minus1

119896119889

(1198772ℎ) and 120575

119896119889= 119876minus1

119896119889

(1198772V) Let




1198961198891


1


1198961198891

= 119871minus1

1198961198891

(1198771ℎminus 1198771V)

where 119871minus11198961198891


1198961198891


2and (119877




1198961198892

= 119871minus1

1198961198892

(1198772ℎminus

1198772V)



1198961198892



(a)

(b)


1198611and 119861



(119909 119910) = (119863 times tan120601


)

0 le 119909 119910 le 119863

(1)


2 Note



1198961198891

and 1206011198961198892


1ℎ 1198771V 1198772ℎ and 1198772V

to calculate 1198961198891and 119896119889

2 uses 119896119889

1and 119896119889

2to calculate

1205721198961198891

and 1206011198961198892

and then uses 1205721198961198891

and 1206011198961198892










987654321

181716151413121110

272625242322212019

363534333231302928

454443424139 403837

545352515049484746

636261605958575655

727170696867666564

818079787776757473

1198611 = (0 0) 1198612 = (0 10)


147

10

0 10 20 30 40 50 60 70 80 90(deg)

RSSI

val

ues

minus47

minus44

minus41

minus38

minus35

minus32

minus29

minus26

minus23

minus20

minus17

minus14

minus11

minus8

minus5

minus2

1 M2 M3 M4 M5 M6 M7 M

8 M9 M

13 M

10 M11 M12 M



09

091

092

093

094

095

096

097

098

099

1

1 2 3 4 5 6 7 8 9 10 11 12 13

Distance (M)

Coe

ffici

ents

of d

eter

min

atio

n1198772

119876()119871()


0

10

20

30

40

50

60

70

80

90

100

0 05 1 15 2 25 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()




5 Improvement



9

8

7

6

5

4

3

2

1987654321

2-31-20-1


025 05 075 1 125 15 175 2 225 25 275 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()



0

10

20

30

40

50

60

70

80

90

100







120588 =119873

Dia(MPMD) or 120588 = 119873

Area(MPMR) (2)













6 Conclusion



References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 M5 M10 M

0369

12151821242730

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Diff

eren

ce o

f RSS

I val

ues

AoA

minus30


minus15minus18

minus12

minus3minus6minus9





119896119889(120579) where 119896 = 1 2 119872 and 120579 =

0∘

1∘

90∘
















1and






Directional antenna

90∘

0∘

119889 2119889 3119889 119872119889



AoA1119907 = 120573

AoA1ℎ = 120572

AoA2119907 = 120575

AoA2ℎ = 120601

(0 119863)(0 0)









2


119896119889and 120573

119896119889



120572119896119889= 119876minus1

119896119889

(1198771ℎ) and 120573

119896119889= 119876minus1

119896119889

(1198771V) for 0

∘

le 120572119896119889

and120573119896119889le 90∘ Here 119876minus1

119896119889





119863

119863

119883 119884



1 by finding 119896119889 for 119896 = 1 2 119872



2ℎand 119877


119896119889+ 120575119896119889


119896119889and 120575


AoAs (where 0∘ le 120601119896119889



2and 120601

119896119889= 119876minus1

119896119889

(1198772ℎ) and 120575

119896119889= 119876minus1

119896119889

(1198772V) Let




1198961198891


1


1198961198891

= 119871minus1

1198961198891

(1198771ℎminus 1198771V)

where 119871minus11198961198891


1198961198891


2and (119877




1198961198892

= 119871minus1

1198961198892

(1198772ℎminus

1198772V)



1198961198892



(a)

(b)


1198611and 119861



(119909 119910) = (119863 times tan120601


)

0 le 119909 119910 le 119863

(1)


2 Note



1198961198891

and 1206011198961198892


1ℎ 1198771V 1198772ℎ and 1198772V

to calculate 1198961198891and 119896119889

2 uses 119896119889

1and 119896119889

2to calculate

1205721198961198891

and 1206011198961198892

and then uses 1205721198961198891

and 1206011198961198892










987654321

181716151413121110

272625242322212019

363534333231302928

454443424139 403837

545352515049484746

636261605958575655

727170696867666564

818079787776757473

1198611 = (0 0) 1198612 = (0 10)


147

10

0 10 20 30 40 50 60 70 80 90(deg)

RSSI

val

ues

minus47

minus44

minus41

minus38

minus35

minus32

minus29

minus26

minus23

minus20

minus17

minus14

minus11

minus8

minus5

minus2

1 M2 M3 M4 M5 M6 M7 M

8 M9 M

13 M

10 M11 M12 M



09

091

092

093

094

095

096

097

098

099

1

1 2 3 4 5 6 7 8 9 10 11 12 13

Distance (M)

Coe

ffici

ents

of d

eter

min

atio

n1198772

119876()119871()


0

10

20

30

40

50

60

70

80

90

100

0 05 1 15 2 25 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()




5 Improvement



9

8

7

6

5

4

3

2

1987654321

2-31-20-1


025 05 075 1 125 15 175 2 225 25 275 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()



0

10

20

30

40

50

60

70

80

90

100







120588 =119873

Dia(MPMD) or 120588 = 119873

Area(MPMR) (2)













6 Conclusion



References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Directional antenna

90∘

0∘

119889 2119889 3119889 119872119889



AoA1119907 = 120573

AoA1ℎ = 120572

AoA2119907 = 120575

AoA2ℎ = 120601

(0 119863)(0 0)









2


119896119889and 120573

119896119889



120572119896119889= 119876minus1

119896119889

(1198771ℎ) and 120573

119896119889= 119876minus1

119896119889

(1198771V) for 0

∘

le 120572119896119889

and120573119896119889le 90∘ Here 119876minus1

119896119889





119863

119863

119883 119884



1 by finding 119896119889 for 119896 = 1 2 119872



2ℎand 119877


119896119889+ 120575119896119889


119896119889and 120575


AoAs (where 0∘ le 120601119896119889



2and 120601

119896119889= 119876minus1

119896119889

(1198772ℎ) and 120575

119896119889= 119876minus1

119896119889

(1198772V) Let




1198961198891


1


1198961198891

= 119871minus1

1198961198891

(1198771ℎminus 1198771V)

where 119871minus11198961198891


1198961198891


2and (119877




1198961198892

= 119871minus1

1198961198892

(1198772ℎminus

1198772V)



1198961198892



(a)

(b)


1198611and 119861



(119909 119910) = (119863 times tan120601


)

0 le 119909 119910 le 119863

(1)


2 Note



1198961198891

and 1206011198961198892


1ℎ 1198771V 1198772ℎ and 1198772V

to calculate 1198961198891and 119896119889

2 uses 119896119889

1and 119896119889

2to calculate

1205721198961198891

and 1206011198961198892

and then uses 1205721198961198891

and 1206011198961198892










987654321

181716151413121110

272625242322212019

363534333231302928

454443424139 403837

545352515049484746

636261605958575655

727170696867666564

818079787776757473

1198611 = (0 0) 1198612 = (0 10)


147

10

0 10 20 30 40 50 60 70 80 90(deg)

RSSI

val

ues

minus47

minus44

minus41

minus38

minus35

minus32

minus29

minus26

minus23

minus20

minus17

minus14

minus11

minus8

minus5

minus2

1 M2 M3 M4 M5 M6 M7 M

8 M9 M

13 M

10 M11 M12 M



09

091

092

093

094

095

096

097

098

099

1

1 2 3 4 5 6 7 8 9 10 11 12 13

Distance (M)

Coe

ffici

ents

of d

eter

min

atio

n1198772

119876()119871()


0

10

20

30

40

50

60

70

80

90

100

0 05 1 15 2 25 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()




5 Improvement



9

8

7

6

5

4

3

2

1987654321

2-31-20-1


025 05 075 1 125 15 175 2 225 25 275 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()



0

10

20

30

40

50

60

70

80

90

100







120588 =119873

Dia(MPMD) or 120588 = 119873

Area(MPMR) (2)













6 Conclusion



References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

(b)


1198611and 119861



(119909 119910) = (119863 times tan120601


)

0 le 119909 119910 le 119863

(1)


2 Note



1198961198891

and 1206011198961198892


1ℎ 1198771V 1198772ℎ and 1198772V

to calculate 1198961198891and 119896119889

2 uses 119896119889

1and 119896119889

2to calculate

1205721198961198891

and 1206011198961198892

and then uses 1205721198961198891

and 1206011198961198892










987654321

181716151413121110

272625242322212019

363534333231302928

454443424139 403837

545352515049484746

636261605958575655

727170696867666564

818079787776757473

1198611 = (0 0) 1198612 = (0 10)


147

10

0 10 20 30 40 50 60 70 80 90(deg)

RSSI

val

ues

minus47

minus44

minus41

minus38

minus35

minus32

minus29

minus26

minus23

minus20

minus17

minus14

minus11

minus8

minus5

minus2

1 M2 M3 M4 M5 M6 M7 M

8 M9 M

13 M

10 M11 M12 M



09

091

092

093

094

095

096

097

098

099

1

1 2 3 4 5 6 7 8 9 10 11 12 13

Distance (M)

Coe

ffici

ents

of d

eter

min

atio

n1198772

119876()119871()


0

10

20

30

40

50

60

70

80

90

100

0 05 1 15 2 25 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()




5 Improvement



9

8

7

6

5

4

3

2

1987654321

2-31-20-1


025 05 075 1 125 15 175 2 225 25 275 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()



0

10

20

30

40

50

60

70

80

90

100







120588 =119873

Dia(MPMD) or 120588 = 119873

Area(MPMR) (2)













6 Conclusion



References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










987654321

181716151413121110

272625242322212019

363534333231302928

454443424139 403837

545352515049484746

636261605958575655

727170696867666564

818079787776757473

1198611 = (0 0) 1198612 = (0 10)


147

10

0 10 20 30 40 50 60 70 80 90(deg)

RSSI

val

ues

minus47

minus44

minus41

minus38

minus35

minus32

minus29

minus26

minus23

minus20

minus17

minus14

minus11

minus8

minus5

minus2

1 M2 M3 M4 M5 M6 M7 M

8 M9 M

13 M

10 M11 M12 M



09

091

092

093

094

095

096

097

098

099

1

1 2 3 4 5 6 7 8 9 10 11 12 13

Distance (M)

Coe

ffici

ents

of d

eter

min

atio

n1198772

119876()119871()


0

10

20

30

40

50

60

70

80

90

100

0 05 1 15 2 25 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()




5 Improvement



9

8

7

6

5

4

3

2

1987654321

2-31-20-1


025 05 075 1 125 15 175 2 225 25 275 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()



0

10

20

30

40

50

60

70

80

90

100







120588 =119873

Dia(MPMD) or 120588 = 119873

Area(MPMR) (2)













6 Conclusion



References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










9

8

7

6

5

4

3

2

1987654321

2-31-20-1


025 05 075 1 125 15 175 2 225 25 275 3

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

()



0

10

20

30

40

50

60

70

80

90

100







120588 =119873

Dia(MPMD) or 120588 = 119873

Area(MPMR) (2)













6 Conclusion



References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














6 Conclusion



References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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