Research Article GPS-Assisted Path Loss...

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 912029 10 pageshttpdxdoiorg1011552013912029

Research ArticleGPS-Assisted Path Loss Exponent Estimation forPositioning in IEEE 80211 Networks

Ernesto Navarro-Alvarez1 Mario Siller1 and Kyle OrsquoKeefe2

1 Electrical Engineering and Computer Science Department CINVESTAV-Unidad Guadalajara Av Del Bosque 1145Colonia El Bajio Zapopan JAL 45019 Mexico

2 Geomatics Engineering Department University of Calgary Schulich School of Engineering 2500 University Dr NWCalgary AB Canada T2N 1N4

Correspondence should be addressed to Ernesto Navarro-Alvarez enavarrogdlcinvestavmx

Received 3 November 2012 Revised 2 May 2013 Accepted 8 May 2013

Academic Editor Chenglong Cheng

Copyright copy 2013 Ernesto Navarro-Alvarez et alThis is an open access article distributed under theCreativeCommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

We present a new adaptive method to calculate the path loss exponent (PLE) for microcell outdoor dynamic environments in the24GHz Industrial Scientific and Medical (ISM) frequency band The proposed method calculates the PLE during random walksby recording signal strength measurements from Radio Frequency (RF) transceivers and position data with a consumer-grade GPSreceiver The novelty of this work lies in the formulation of signal propagation conditions as a parametric observation model inorder to estimate first the PLE and then the distance from the received RF signals using nonlinear least squares GPS data is usedto identify long term fading from the received signalrsquos power and helps to refine the power-distance model Ray tracing geometriesfor urban canyon (direct line of sight) and nonurban canyon (obstacles) propagation scenarios are used as the physics of the model(designmatrix) Although themethod was implemented for a lightweight localization algorithm for the 80211bg (Wi-Fi) standardit can also be applied to other ISM band protocols such as 802154 (Zigbee) and 802151 (Bluetooth)

1 Introduction

The emergence of context-aware computing applicationsand location-based services and the proliferation of portableelectronic devices have motivated an extensive research onthe topic of node or device localization for wireless networksoperating under 24GHz ISM band protocols such as Blue-tooth Zigbee and especially Wi-Fi Localization is an im-portant issue for the interaction between portable deviceusers and the surrounding networked devices in intelligentenvironments such as homes offices or other intelligentbuildings [1 2]

The localization problem has been a hot research topic intheWireless Sensor Network (WSN) andMobile Robotics lit-erature According to theWSN terminology a node is a smalldevice with sensing computing storage and communicationcapabilities and the node localization problem is defined asldquodetermining an assignment of coordinates for nodes in awireless ad-hoc or sensor network that is consistent withmeasured pair wise node distancesrdquo [3] The definition states

basically that it is necessary to estimate a distance (range)between the nodes before obtaining coordinates See [4ndash6]for more WSN terminology and applications

A range estimation can be performed using collectedmeasurements from a variety of methods such as acoustic [7ndash9] directional antenna or antenna array [10 11] infrared [12]and Received Signal Strength (RSS) measurements [13 14]Unlike other ranging methods RSS-based methods estimateneither distances nor positions from the angle of arrivalnor traveling time of the signal Additionally no clock syn-chronization is assumed in the nodes Only the incoming RFsignal is used to infer a range to the transmitter The basicpremise is that the received signal power decay is inverselyproportional to the distance This signal power attenuationis called path loss (PL) and can be quantified by a path lossexponent (PLE) Once the ranges to the landmarks (deviceswith known positions) are estimated trilateration methodscan be employed to find the location of an unknown positionnode within a suitable coordinate system

2 International Journal of Distributed Sensor Networks

However RSS levels are highly unpredictable and theformulation of a path loss model (PLM) as function ofdistance is a complex issue This complexity is derived fromthe fact that the received power level is a combination ofdifferent signal propagation mechanisms such as reflectiondiffraction and scattering and absorption losses Due to theseimpairments which depend on the surrounding environ-ment shadowing and multipath fading are produced As aconsequence estimation errors can be introduced for anyRSS-based localization algorithm

In recent years RSS-based localization algorithms havebeen the subject of an increasing interest due to the wideavailability of 80211bg transceivers and the proliferation ofWireless Local Area Networks (WLANs)

This approach exploits existingWLAN infrastructure andprecludes the use of additional hardware such as badges andwearable sensors see [15 16] In fact the IEEE 80211 stand-ard provides the means to obtain the signal strength via theReceived Signal Strength Indicator (RSSI) This indicator isdefined as ldquoa mechanism by which RF energy is to be mea-sured by the circuitry on a wireless NIC This numeric valueis an integer with an allowable range of 0ndash255 (a 1-byte value)rdquo[17] Similar metrics are defined for the IEEE 802154 andIEEE 802151 standards

The node localization algorithms within previous litera-ture are referred to as GPS-free or GPS-less algorithms Thelack ofGPS use can be explained by commondrawbacks attri-buted to several causes such as signal availability costantenna size and energy consumption Nowadays some ofthese arguments are no longer true GPS chips can be ubiquit-ously found in mobile devices such as smart phones handhelds and tablets While GPS chips are available in manydevices there are still many others that do not have it Theexisting GPS positioning capability could be used to estimatethe PLEs of WLAN access points and the derived PLMemployed to enable GPS-free location services

In this paper we propose a PLE estimationmethod whichuses the RSSI provided by a 80211bg transceiver in com-bination with data collected from a commercial grade GPSreceiver The method builds ray tracing models for typicalpropagation scenarios such as urban canyon and non-urbancanyon cases and uses them to formulate the design matrixof an observationmodelThe propagation scenarios take intoaccount the shadowing and multipath effects The observa-tions are composed of RSSI readings and GPS data The sys-tem of equations of the design matrix is linearized usingTaylor series and then solved through least squares Themain contribution of this work is the formulation of a para-metric mathematical model which improves the PLE accu-racy by using the Equivalent Isotropic Radiated Power (EIRP)and Effective Antenna Aperture (EAA) parameters calculatedbefore obtaining the PLE A second contribution is the com-bination of GPS data and RSSI readings in order to identifythe RSSI long term behavior

Depending on the transmitterrsquos power antenna heightand coverage area the RF environments where the devices aredeployed can be classified as macrocell microcell and pico-cell In microcell environments the transmitting power of theradios ranges from 01 to 1 watt the RF coverage area ranges

from 200 to 1000m and the transmitterrsquos height is low (3 to10 meters) [18] Environments within buildings are classifiedas picocells Indoor-to-outdoor configurations are environ-ments with walls blocking the signal and are characterizedby a wall attenuation factor The algorithm proposed in thiswork is tailored to microcell RF environments with indoor-to-outdoor coverage configurations therefore models suchas Okumura-Hata Lee or Walfisch-Bertoni are not treatedhere From this point forward when we refer to a blindnode we mean a device (smart phone hand held tablet orlaptop) whose position needs to be estimated when we referto anchor or beacon or landmark nodes we mean accesspoints (APs) for whose position are already known

The paper is organized as follows Section 2 reviews thelocalization algorithms based on RSSI only and algorithmswith RSSI-GPS collaboration In Section 3 we present theproposed method Section 4 presents the implantation of themethod in real world conditions In Section 5 the accuracy ofthe experimental results is discussed and finally conclusionsand future work are presented in Section 6

2 Related Work

This section is divided in two parts The first part reviewspapers related to either empirical or theoretical RSSI-basedmodels In the second part techniques that rely on both RSSIand GPS to derive power-distance models for node local-ization are examined Note there are other methods for RF-based localization such as fingerprinting [19 20] andBayesianNetworks [21 22]These techniques and some others excludePLE estimation and are not reviewed in this paper

21 PLE from RSSI Measurements The study of RSSI fordifferent purposes is not a new idea Some of these purposesare the optimization of the coverage area of wireless networks[23] assessment of links quality for multihop routing pro-tocols [24] and so forth The use of RSSI as a means fornode localization estimation in a WLAN dates back to 2000For example [25] proposes the use of an Extended KalmanFilter (EKF) to cope with the noise in the measurementsand to maintain a position estimate in harsh conditionsThey conducted an empirical experiment to relate signalstrength to distance between base and mobile stations Theshortcoming of this work is that it is designed to work withinpredefined surroundings in this case an office The accuracyis one room In [26] authors propose a lookup-table methodfor node position triangulation They also conducted datacollection to empirically correlate distance to signal strengthThe shortcoming of this works is that it requires an extensivesurvey at different points in a predefined environment and theconsequent table size In [27] authors proposed an optimalaveraging window length of RSSI samples to cope with fadingof the power and mobility of the nodes By modeling thechannelrsquos fading with a Rayleigh distribution they obtained afactor (1199032)whichmultiplies theRSSI samples (119908)The authorsreported a lower boundmean error of 25mwith119908 = 50Themain drawback is that thismethod is intended for rectangularareas where bacons are placed optimally

International Journal of Distributed Sensor Networks 3

Although these previous works do not calculate a PLEexplicitly they formulate empirical power-distance modelsbased on averaged RSSI measurements surveyed in specificlocationsThey also address some issues affecting the receivedpower levels such as fading due tomultipath nonline of sightnode mobility and sampling

In the following literature review we now focus onlocalization systems for outdoor environments since PLEestimation was first introduced for such environments In[28] the authors propose a methodology for PLE estimationin a WiMAX system Although this methodology is notintended for a WLAN it is carefully examined in thispaper because of the use of common theoretical models toestimate PLE The first part of the methodology pairs RSSImeasurements expressed in dB units with distance (119871[dB]119889[m]) In the second part the authors use the well-knownlog-distance path loss model to formulate a system of equa-tionsThe authors measured propagation losses in two differ-ent points with identical conditions (line of sight condition)and formulated a system of two linear equations

1198711 [dB] = 119886 + 10 lowast 120574 lowast log

10(1198891)


10(1198892)

(1)

where 119886 is a coefficient that accounts for frequency and otherpropagation factors 120574 is the PLE and 119889 is distance in metersbetween the transmitter and the receiver Solving the systemand using several measurements the authors obtained thefollowing empirical path loss model 119871[dB] = 12302 + 10 lowast

2687 lowast log10(119889)

In [29] the authors used the Okumura-Hata model tocalculate two different PLEs in a WiMAX network althoughthe Okamura-Hata model is usually applied in macrocellenvironments (distances greater than 1 km)They formulatedtwo different map-supported PLMs from RSSI observationsOne PLM corresponds to an ldquourban canyonrdquo area while theother for ldquonon-urban canyonrdquo The developed models con-sidered the type of area based on city map and road networkinformation

Note that an urban canyon area is an area where thereexists an open street between the receiver and the transmitterTherefore the signal reaches longer distances than in areaswith obstacles On the other hand an area with considerableobstacles is classified as noncanyon

Next we shall review works which estimate PLE forWLAN in indoor environments Authors in [30] proposedand implemented a system framework which consists of acentral server a base station and four beacon nodes Thealgorithm dynamically estimates a PLE between the beaconsand the blind node The base station receives the RSS valuescollected by the beacons nodes and sends them to the serverThe authors also employed the log-distance path loss formulabut they add a stochastic component

PL (119889) = PL (1198890) minus 10120572log

10(

119889

1198890

) + 119883120590 (2)

where PL(119889) denotes the path loss in dB as function ofdistance 119889 in meters away from sender PL(119889

0) is a path loss

constant at a reference distance 1198890 120572 is the PLE and 119883

120590is

Gaussian noise in dBm units The 119883120590values account for the

long term variability The 120572 exponent is estimated using thefollowing formula

120572 =

minussum119899

119894=1(PL (119889

119894) minus PL (119889

0))

sum119899

119894=110 (log 119889

119894)

(3)

where 119899 is the number of RSSI measurements at distances119889119894 Basically (3) expresses 120572 in terms of an averaged ratio

between path loss and the logarithm of distance using allmeasurements recorded This averaged PLE is used to obtaindistances between the blind node and the four beaconsFinally a polygonmethod was used to obtain the blind nodersquoscoordinates

Model (2) is commonly used in macrocell scenariosby setting the 119889

0reference distance to 1 km Although the

formula was modified for microcell scenarios (setting 1198890to 1

and 100 meters) we do not think that this is the most suitablePLM because of the particularities of such environments

22 RSSI Measurements and GPS Data Some of the firstapplications of collaborative GPSWi-Fi were geocachingwardriving and the elaboration of signal coverage mapsGeocaching is a recreational outdoor activity in which theusers seek containers with the aid of GPS receiver andmobiledevicesWar driving is the activity of searchingWi-Fi wirelessnetworks in a moving vehicle using a portable computer orother devices connected to a GPS A signal coverage map is amap with geographic information of areas where a wirelessnetworks are deployed It represents signal intensity areas(strong or weak) with contour lines or colors

In [31] the authors presented a solution for manualdeployed networks calledWalking GPS It works by attachingaGPS receiver to a node calledGPSmoteThis node first con-verts its latitude and longitude coordinates into a local coor-dinates system and then it broadcasts its position to the rest ofthe nodes When the carrier (person or vehicle) places a newnode in a certain position and turns it on the node imme-diately receives the broadcast packet from the GPS mote andestimates its own position On the other hand if a node isturning on after being deployed it needs to ask its neighborsfor their positions in order to trilaterate its own positionThemain drawback of this solution is that it was tested in an idealpropagation scenario (open field environment) Moreoverthe blind nodes were deployed within a predefined grid

In [32] the authors proposed a multisensor fusion solu-tion with data from three sources a GPS a radio propagationmap and aWLANpositioning systemTheydivided the radiomap into three areas indoor outdoor and shaded (a shadedarea is an area surrounded by buildings or in closed places)The areas are covered by three fixed APs The algorithmconsists of two phases offline and online In the offline phasethey collect RSSImeasurements at predefined locations in themap At these locations they estimate the expected RSSI val-ues using an equation similar to (3) with a reference distanceof 1 meter Calculating the ratio between the observed andthe expected RSSI they model the corresponding multipathBased on these ratios a polynomial fit function is computed


for all the predefined locations Using this information andtrilateration theWLAN positioning system estimates a blindnode preliminary position Finally in the online phase theGPS is used to identify the area (indoor outdoor or shaded)to improve the estimated positions

In [33] the authors presented an outdoor WiFi localiza-tion system assisted by GPSThe system uses a unidirectionalYagi type antenna to triangulate the location of APs usingthe angle of arrival of the received signal The angle of thereceived signal is measured with a GPS compass which isrotated with the antenna and the WiFi receiver at the sametimeAll the equipmentwasmounted on amotorized rotatingbase The proposed algorithm consists of the following steps(i) place the equipment at two different measurements points1198721(1199091 1199101) and 119872

2(1199092 1199102) (ii) find the respective 120579

1and 120579

2

which corresponds to the angles at which themaximumRSSIare observed (iii) find the slopes119898

1= tan 120579

1 and119898

2= tan 120579

2

and calculate 1198881and 1198882using the line equation 119910 = 119898119909 + 119888

and (iv) find the intersection point for 1199101= 11989811199092+ 1198881and

1199102= 11989821199092+ 1198882 This intersection point corresponds to the

estimated location of the AP

3 Proposed Solution

The models described in Section 2 express a power distancerelationship based on the attenuation of the signalrsquos poweras it propagates Such attenuation roughly obeys the inversepower law

119875119903=

1

119889120572 (4)

where 119875119903is the power received in watts 120572 is the PLE (equal to

2 in free space conditions) and 119889 is the distance between thetransmitter and the receiver in meters However the receiverpower attenuates at a much higher rate and exponent 120572 gt

2 A higher 120572 can be explained in terms of losses causedby propagation mechanisms such as diffraction scatteringreflection and refraction For a detailed explanation refer to[34] The combination of these mechanisms is responsiblefor power variations in the RSSI readings These variationsare commonly classified as slow variation or long term fadingand fast variations or short term fading Fast variations arecharacterized by rapid fluctuations in the RSSI levels oververy short distances On the other hand long term fading alsocalled large scale path loss is due the increasing distance asthe receiver moves away from the transmitter

A suitable mathematical tool to model these propagationmechanisms and their effects on RSSI variability is ray-tracing An electromagnetic wave (EM) is composed ofelectric (E) and magnetic (B) fields These fields are perpen-dicular to each other and the direction of the wave is obtainedfrom the cross product of E times B The result is the Poyntingvector (S) that can be modeled as a ray In ray tracing aray is an imaginary straight line depicting the path lighttravels Using geometrically defined propagation scenariosthe trajectory of different S rays can be computed

The proposed method is divided into three phases Inthe first phase the EIRP and PLE parameters are estimatedusing the observation model In the second phase PLMs

RSSI and GPS

data

Fast variations

Slow variations

PLE estimation

[[[[

1199011199031(119889)

119901119903119899(119889)

]]]]

119911 = 120573 +

Figure 1 Schematic diagram for phase 1

for each landmark are formulated in order to translate RSSImeasurements into ranges In the final phase these ranges areused to estimate the locations of one or more blind nodesNext each phase is described in detail

31 Observation Model Formulation The formulation of thesystem to infer the EIRP and PLE is expressed as follows

z = 119867 (x) 120573 + k (5)

where z = [119911111991121199113sdot sdot sdot 119911119899] is a 1times119899 vector of RSSI observations

recorded in dB units at different distances ranging from 1to 200 meters Each 119911

119894represents the measurements at a

particular distance (see Section 4)119867(x) is the design matrixrepresenting the ray tracing models 120573 = [120579

1 1205792] is the vector

of parameters to be estimated and lastly k is a Rayleighdistributed random variable which accounts for fast variationin short distances [35] The block diagram for this phase isshown in Figure 1

Mathematical models expressed in matrix 119867 relate theobservations zwith the parameter vector 120573These models areray tracing equations for an urban canyon and a non urbancanyon Matlab scripts provided by [36] are used to constructthe geometry for the two scenarios See Figure 2

The models perform the addition of direct and reflectedrays and calculate the resulting received power at differentpoints in the scenariosThis is done by calculating the averageof vector S trough an area that is the power flux density(PFD) First average S is expressed in terms ofE-field strengthand then it is related to the Effective Antenna Aperture (EAA)area of the receiving antenna as follows

119875119903= 0119860119903 (6)

The PFD represents the field strength at the receiverrsquosantenna (in Wm2 units) and it is defined as

0 =

1

2

|119890|2

120120587

(7)

where |119890| is the magnitude of the electric field radiated in thefar-field region by the source point 120120587 is the impedance offree space (in Ohms) EAA is defined as

119860119903=

1205822sdot 119892119903

4120587 sdot 119897119903

(8)

where 119892119903is the receiving antenna gain in dBi and 119897r is the

system loss at the receiver PFD is defined as follows


0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100

minus20 minus10minus10119909 (m)

119910(m

)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(a)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(b)

Figure 2 Ray tracing representation of signals traveling distances in (a) urban canyon propagation scenario and (b) nonurban Canyonpropagation scenario

Expressing (6) as a function of distance

119875119903(1198890) = 119860

119903

1003816100381610038161003816119890119879(1198890)1003816100381610038161003816

2

2120578

(9)

where 119890119879is the modulus of complex number 119890

119879and rep-

resents the total field strength of the rays combining at thereceiver (119890

119879= 1198900+ 1198901+ 1198902+ 1198903) The term 119890

0represents the

direct ray field strength 1198901represents the ray reflected in the

ground and 1198902 1198903represent the rays reflected on walls The

formulas for each term are

1198900= radic

60119901119892

119897

119890(minus1198951198961198890)

1198890

1198901= radic

60119901119892

119897

GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

1198902= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

1198903= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198893)

1198890+ 1198893

(10)

where 1198890is the direct ray distance between the transmitter

and the receiver 1198891is the additional distance the ray travels

due to reflection on the ground 1198892and 119889

3are the additional

distances due to wall reflections These additional distances(1198891 1198892 1198893) are fixed according to the specified geometry

Constants WG and WR are ground and wall reflectionscoefficients respectively Substituting (10) in (9) we obtain

119860119903

100381610038161003816100381610038161003816100381610038161003816

radic60119901119892

119897

(

119890(minus1198951198961198890)

1198890

+ GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

+WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

+119882119877

119890minus119895119896(1198890+1198893)

1198890+ 1198893

)

100381610038161003816100381610038161003816100381610038161003816

2

(2120578)minus1

(11)

The term 119901119905119892119905119897119905is the EIRP and one of the parameters to

estimate Substituting (11) in matrix 119867119860in (5) the resulting

system is

z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + k (12)

32 Range Estimation After linearizing (12) using Taylorseries we apply least squares to estimate EIRP and EAAIn order to obtain a more accurate PLE we use transmittedpower 119901

119905received power 119901

119903transmitter antenna gain 119892

119905

receiver antenna gain 119892119903 transmitter system loss 119897

119905and

receiver system loss 119897119903 to formulate a new system

z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + n (13)

In this formulation the RSSI observation vector z con-tains the short term or slow variations which were filtered


Table 1

AP ssid Actual coordinates Estimated PLE (120574)

ENA 131 N 566263617E 70093253

242

ENE 136 N 566266942E 70084148

235

NM 110 N 566254219E 70093153

231

KNB 125u N 566244524E 70080563

240

KNB 132 N 566242101E 70079860

241

MC 184 N 566245213E 70087963

252

MC 197 N 566247447E 70092779

255

out of the raw readings This extraction was carried out by arunningmean A runningmean calculates the signal strengthaverages within a certain length distance interval Commonlyused length interval ranges from 20 to 40 times 120582 [37] Theseaverages are indexed and the vector z is formed where 119899 =

1 sdot sdot sdotmax distance The variable n is a normal distributedrandom variable which accounts for slow variations in longterm fading The model for this systemrsquos design matrix is thelogarithm of the Friis formula

119901119903(119889) = (119901

119905+ 119892119905+ 119892119903minus 119897119905minus 119897119903) + (10 sdot 2 sdot log

10(

120582

4120587

))

+ 120574 sdot 10 sdot log10(119889)

(14)

The terms between parentheses are constant and werecalculated in the previous step therefore the parameter 120573 =

[120579] to be estimated is the PLE 120574 and remains in the last termSeven APs located in the University of Calgary campus

were selected as landmarks during the data collection pro-cess (Refer to Section 5 for more information) having thefollowing service set identification (ssid) ENA 131 ENE 136and NM 110 KNB 125u KNB 132 MC 184 and MC 197After the method was applied to the signal strength receivedfrom them and to the GPS data collected a PLE and a pathloss model for each one were estimated Table 1 lists ssidestimated PLE values and the actualUTMcoordinates for thelandmarks In this work the UTM system is employed due toits use of meters instead of degrees of latitude and longitude

Figure 3 shows short term received power and the cor-responding long term path loss model for APs ENA 131ENE 136 and NM 110 Figures 3(c) and 3(d) correspondto non-urban canyon and reflect more harsh propagationconditions

33 Node Localization In order to determine the blind nodeposition in 2D space 119899 landmarks are employed Althoughtwo landmarks would be enough there would be two

possible solutions A third landmark reduces the estimationto a unique solution With the ranges estimated from a blindnode to 119899 landmark APs and the coordinates of the latterthe method can formulate the following system of nonlinearsimultaneous equations

1205881= radic(119909

1minus 119909119906)2

+ (1199101minus 119910119906)2

+ (1199111minus 119911119906)2

1205882= radic(119909

2minus 119909119906)2

+ (1199102minus 119910119906)2

+ (1199112minus 119911119906)2

120588119899= radic(119909

119899minus 119909119906)2

+ (119910119899minus 119910119906)2

+ (119911119899minus 119911119906)2

(15)

where (1199091 1199101) (1199092 1199102) and (119909

3 1199103) are the APs known coor-

dinates (119909119906 119910119906) is the position to find and 120588

1 1205882 120588

119899are

the estimated rangesUTMNorthing andEasting coordinatesare identified with 119910 and 119909 respectively Because the blindnode and the APs are placed at ground level the 119911 coordinateis constant with an altitude of 11124meters Because the num-ber of equations is larger than the number of unknowns thesystem has no analytical solution However it can be solvedthrough linearization and iteration First we decompose theunknowns into approximate and incremental components119909119906= 119909119906+Δ119909119906 119910119906= 119910119906+Δ119910119906 119911119906= 119906+Δ119911119906 whereΔ119909

119906Δ119910119906

Δ119911119906are the unknowns and 119909

119906 119910119906 119906are considered known

by assigning theman initial value By substituting these valuesin (15) and differentiationing we obtain

119901 (119909119906+ Δ119909119906 119910119906+ Δ119910119906 119906+ Δ119911119906)

= 119901 (119909119906 119910119906 119906) +

120597119901 (119909119906 119910119906 119906)

120597119909119906

Δ119909119906

+

120597119901 (119909119906 119910119906 119906)

120597119910119906

Δ119910119906+

120597119901 (119909119906 119910119906 119906)

120597119909119906

Δ119911119906+ sdot sdot sdot

(16)

The series is truncated after the first-order partial deriva-tives eliminating nonlinear terms With initial values for119909119906 119910119906 119906 new values for Δ119909

119906 Δ119910119906 Δ119911119906can be calculated

and used to modify original 119909119906 119910119906 119906values The modified

values are used again to find new deltas This iteration con-tinues until the absolute values of deltas are within a certainpredetermined limit For a detailed explanation of this pro-cess see [38]

For instance with Wi-Fi only data collected at test point566262236N 70089486E and the PLEs and coordinates ofAPs ENA 131 ENE 136 and NM 110 (listed in Table 1) thefollowing mean ranges were obtained 120588

1= 439158 meters

1205882= 605400 meters and 120588

3= 655568 meters Real ranges

are 3858 6842 and 9143 meters After solving the systemthe resulting estimated coordinates for the blind node were119909119906= 5662600 119910

119906= 700900 and 119911

119906= 11124 (red color

balloon in Figure 4) In this particular case the position errorwas 229432m


0 50 100 150 200Traveled distance (m)

(dB)

minus120minus110minus100minus90minus80minus70minus60minus50minus40

(a)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

Traveled distance (km)

(dB)

(b)

0 50 100 150 200 250minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Traveled distance (m)

(dB)

(c)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(d)


(dB)


(e)

0 005 01 015 02minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(f)

Figure 3 (a) AP ENA 131 short term received signal power for an urban canyon model (b) Corresponding long term distance model withPLE = 242 (c) AP ENE 136 short term received signal power for non-urban canyon (d) Corresponding long term distance model withPLE = 235 (e) AP NM 110 short term received signal power for urban canyon model (f) Corresponding long term model with PLE = 231

4 Implementation of the Method

In order to test our proposal several experiments wereperformed at a university campusThe data collection process

consists in recording the signal strength from nearby Wi-FiAPs The geographic location of the points where data wascollected was also logged and paired with the Wi-Fi data atrate of 3HzThe data collection was carried out with a laptop


Figure 4 One example result and visualization on Google Earth

and a GPS Garmin model GPSmap 60CSx In the laptop theinSSIDer program was installed and the GPS receiver wasconnected via USB port The campus infrastructure consistsof 1280APs with transmission rate of 54Mbps maximumTx sensitivity of +170 dBm and minimum Rx sensitivity ofminus730 dBm 87 out of 1280APs were identified along withtheir geographic positions but only seven were used in theexperiments (see Table 1) The data was collected duringseveral random walks each 15 minutes long and was carriedout on August 7 11 15 and 29 and June 15 and 23 2011 Alltests took place within the area located between the threebuildings See Figure 4 The data was logged in the GPSeXchange format

lttimegt2011-08-16T00 26 460Zlttimegtltwpt lat=ldquo51079936rdquo lon=ldquominus114133793rdquogtltMACgt00 0B 86 D6 CB 43ltMACgtltRSSIgt minus78ltRSSIgt

The lttimegt tag stores the UTC time when the mea-surement was taken The ltwptgt tag stores the latitude andlongitude where the measurement was taken The ltMACgt tagstores the physical address of the AP that sent the signal Thetag ltRSSIgt stores the power level of that signal To obtainthe distance between the point where the data was collectedand the point where the transmitting AP is located we usethe Spherical Law of Cosines This law gives accurate resultsdown to distances as small as 1 meter Finally the data wasclassified according to theMAC address of the identified APsand sorted from closest to farthest distance in order to obtainthe observations vector z = [119911

111991121199113sdot sdot sdot 119911119899]

5 Experimental Results

After data collection and model formulation phases threeblind node positions within the campus were selected to testour method The coordinates of these positions are listed inthe second column of Table 2 In order to evaluate accuracyof the results Wi-Fi only readings and GPS only waypointswere collected at these positions Note that this number ofpositions represents the best readings for both Wi-Fi andGPS signals in our experimental scenario The overall PLEestimation can be improved as the number of blind node

Table 2

Positions Coordinates RMS2 Mean HDOP

ONE N 566262236E 70089486

62863 37488

TWO N 56624691E 70084036

73534 15291

THREE N 566250343E 70091576

36885 14245

Average 57760 22341

position readings is increased However this is subject togood quality readings

Before evaluating results it is necessary to select theappropriate accuracy metrics Since this work uses a GPSreceiver to infer a power-distance model it is necessaryto employ common metrics used by GPS manufacturerssuch as Circular Error Probable (CEP) one-dimensionalroot mean square (rms

1) and two-dimensional root mean

square (rms2) See [39] for the definitions of these and other

metricsSince the proposed localization algorithm is intended for

portable electronic devices such as tablets laptops or hand-helds the localization takes place in a 2D map Thereforehorizontal accuracy metric rms

2is selected The metric rms

2

is the square root of the average of the squared horizontalerror and is calculated as follows

rms2= radic120590

2

119909+ 1205902

119910 (17)

where1205902119909and1205902119910are the rootmean square errors of the119909 and119910

components of the estimated positions if measurements andmodel errors are assumed uncorrelated and the same for allobservations If this assumption is not fulfilled the 1205902

119909and 1205902119910

are the variance of the 119909 and 119910 components A related metricis Horizontal Dilution of Precision (HDOP) It is defined asthe ratio of rms

2to the root mean square of the range errors

The closer the HDOP value is to 1 the higher the accuracyobtained These two metrics are employed to quantify errorswithin this section

51 GPS Only Data 7963 GPS waypoints were collected atpositions ONE 6792 at positions TWO and lastly 8340 atposition THREEThese waypoints were processed in order toextract Northing and Easting coordinates and HDOP Withthis information the horizontal error position with respect tothe actual coordinates of position ONE TWO and THREEwas calculated The results for metrics rms

2and HDOP are

shown in Table 2

52 Wi-Fi Only Measurements Now the same metrics arecalculated for the WiFi only readings In this case 5116readings were collected at the test positions Three landmarkAPs were selected for positions ONE and TWO and only twofor position THREE Using the PLEs obtained in Section 4for each AP ranges to them were estimated With the APsactual coordinates the real ranges were calculated (listed in


Table 3

Estimated mean ranges to APs (meters) Real ranges to APSs(meters)

RMS2 Mean HDOP

Position ONEENA 131 439158ENE 136 605400NM 110 655568

385868419143

157322 07866

Position TWOKNB 125u 486630KNB 132 515463MC 184 419375

517475704132

322975 17112

Position THREE MC 197 232717NM 110 342559

30094391

60423 05857

Average 18024 10278

Table 3) Using this information the method derived esti-mated positions for the three test points The resulting rms

2

and HDOP are summarized in Table 3Comparing Tables 2 and 3 it can be seen that the rms

2

measure of our results is almost 3 times the GPS rms2mea-

sure It should be noted that a comparison of GPS and WiFiderived HDOP values is not appropriate as each method hasits own unrelated ranging error

6 Conclusions and Future Work

In this paper an adaptive method to formulate a power-distance model and infer distances to AP landmarks wasproposed The method is formulated as state space systemThe method uses GPS and RSSI data to identify the shortterm and long term behavior on of the received signal powerThe systemrsquos design matrix includes the ray tracing models(canyon and non-canyon) needed to estimate the PLE Basedon this the distance to each RSSI measurement source isestimated and consequently its respective position Once theGPS-Assisted PLEmodel is derived at any time a user withoutGPS (for instance equipped with a WiFi-only device) iscapable of estimating herhis position

A case study was implemented employing an 80211 basednetwork and data from a consumer-grade GPS receiver Theresults were encouraging The rms

2error using only RSSI

and the derived GPS-Assisted PLE model was on average1802 meters On the other hand the average error usingonly a consumer grade GPS was 577 meters This means thatthe proposed method is capable of formulating propagationmodels that overcome signal impairments and deliver resultswhich are approximately 3 times the GPS error The proposalresults are promising and its accuracy is higher than disableGPS Selective Availability service which consisted of 100mhorizontal

Although there are different works in the literature reviewthat combine GPS and RSSI none of them explicitly producea PLE model However there are related works with realimplementations which obtain a higher accuracy but theyrequire additional GPS hardware or manual deployments inpredefined grids

Future work includes additional case studies for protocolssuch as 802154 and 802151 Also since least squares arethe basis of the proposed methodology this can be extendedto other applications such as blind node tracking based onKalman Filters

References

[1] A Ward A Jones and A Hopper ldquoA new location techniquefor the active officerdquo IEEE Personal Communications vol 4 no5 pp 42ndash47 1997

[2] Y C Tseng S Wu C Chao et al ldquoLocation awareness in adhoc wireless mobile networksrdquo IEEE Computer vol 34 no 6pp 46ndash52 2001

[3] DNiculescu and BNath ldquoAd hoc positioning system (APS)rdquo inIEEE Global Telecommunicatins Conference (GLOBECOM rsquo01)pp 2926ndash2931 San Antonio Tex usa November 2001

[4] A Bharathidasan and V A S Ponduru Sensor Networks AnOverview Department of Computer Science University ofCalifornia Los Angeles Calif USA

[5] D Culler D Estrin andM Srivastava ldquoGuest editorsrsquo introduc-tion overview of sensor networksrdquo Computer vol 37 no 8 pp41ndash49 2004

[6] I F AkyildizW Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash105 2002

[7] N B Priyantha A Chakraborty and H Balakrishnan ldquoCricketlocation-support systemrdquo in 6th ACM Annual InternationalConference on Mobile Computing and Networking (MOBICOMrsquo00) pp 32ndash43 Boston Mass USA August 2000

[8] M Kushwaha K Molnar J Sallai P Volgyesi M Maroti andA Ledeczi ldquoSensor node localization using mobile acoustic be-aconsrdquo in 2nd IEEE International Conference on Mobile Ad-hocand Sensor Systems (MASS rsquo05) pp 483ndash491 November 2005

[9] A Savvides H Park and M B Srivastava ldquoThe bits and flopsof the n-hop multilateration primitive for node localizationproblemsrdquo inProceedings of the 1st ACM InternationalWorkshopon Wireless Sensor Networks and Applications (WSNA rsquo02) pp112ndash121 September 2002

[10] D Niculescu and B Nath ldquoPosition and orientation in ad hocnetworksrdquo Ad Hoc Networks vol 2 no 2 pp 133ndash151 2004

[11] P Kulakowski J Vales-Alonso E Egea-Lopez W Ludwin andJ Garcıa-Haro ldquoAngle-of-arrival localization based on antenna


arrays for wireless sensor networksrdquo Computers amp ElectricalEngineering vol 36 no 6 pp 1181ndash1186 2010

[12] R Want A Hopper V Falcao and J Gibbons ldquoActive badgelocation systemrdquo ACM Transactions on Information Systemsvol 10 no 1 pp 91ndash102 1992

[13] J Hightower G Borriello and R Want ldquoSpotOn an indoor 3dlocation sensing technology based on RF signal strengthrdquo TechRep IEEE Transactions on Consumer Electronics 2000

[14] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in Proceedings of the19th IEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo00) vol 2 pp 775ndash784Tel Aviv Israel March 2000

[15] S Sen R R Choudhury and S Nelakuditi ldquoSpinLoc spinonce to know your locationrdquo in Proceedings of the Workshopon Mobile Computing Systems and Applications (HotMobile rsquo12)San Diego Calif USA February 2010

[16] S Mazuelas A Bahillo R M Lorenzo et al ldquoRobust indoorpositioning provided by real-time RSSI values in unmodifiedWLAN networksrdquo IEEE Journal of Selected Topics in Signal Pro-cessing vol 3 no 5 pp 821ndash831 2009

[17] The Institute of Electrical and Electronics Engineers IEEE80211 Wireless LAN Medium Access Control (MAC) and Phys-ical Layer (PHY) Specifications IEEE-SA Piscataway NJ USA2007

[18] A Neskovic N Neskovic and G Paunovic ldquoModern Ap-proaches in Modeling of Mobile Radio Systems PropagationEnvironmentrdquo in IEEECommunications SurveysThirdQuarterIEEE Press Piscataway NJ USA 2000

[19] E C L Chan G Baciu and S C Mak ldquoUsing wi-fi signalstrength to localize in wireless sensor networksrdquo in Proceedingsof the WRI International Conference on Communications andMobile Computing (CMC rsquo09) pp 538ndash542 January 2009

[20] P Prasithsangaree P Krishnamurthy and P K ChrysanthisldquoOn indoor position location with wireless lansrdquo in Proceedingsof the 13th IEEE International Symposium on Personal IndoorandMobile Radio Communications (PIMRC rsquo02) vol 2 pp 720ndash724 September 2002

[21] P Castro P -Chiu T Kremeneck and R Muntz ldquoA proba-bilistic location service for wireless networks environmentsrdquoin Proceeding of the 3rd International Conference on UbiquitousComputing (Ubicomp rsquo01) pp 18ndash24 Springer September 2001

[22] A M Ladd K E Bekris A P Rudys D S Wallach and L EKavraki ldquoOn the feasibility of using wireless ethernet for indoorlocalizationrdquo IEEE Transactions on Robotics and Automationvol 20 no 3 pp 555ndash559 2004

[23] S Yang Y Lee R Y Yen et al ldquoA wireless LAN measurementmethod based on RSSI and FERrdquo in Proceedings of the 5th Asia-Pacific Conference on Communications and 4th Optoelectronicsand Communications Conference (APCCOECC rsquo99) vol 1 pp821ndash824 October 1999

[24] K Srinivasan and P Levis ldquoRSSI is under appreciatedrdquo in Pro-ceedings of the 3rd Workshop on Embedded Networked Sensors(EmNets rsquo06) May 2006

[25] J Latvala J SyrjarinneH Ikonen and JNiittylathi ldquoEvaluationof RSSI-based human trackingrdquo in Proceedings of the EuropeanSignal Processing Conference (EUPSICO rsquo00) vol 10 pp 2273ndash2276 Tampere Finlande July 2000

[26] J Small A Smailagic and D Siewiorek ldquoDetermining userlocation for context aware computing through the use of a wire-less LAN infrastructurerdquo Project Aura Report httpwwwicescmuedureports040201pdf

[27] P Bergamo and G Mazzi ldquoLocalization in sensor networkswith fading and mobilityrdquo in Proceedings of the 13th IEEE Inter-national SymposiumonPersonal Indoor andMobile Radio Com-munications September 2002

[28] W Afric B Zovko-Cihlar and S Grgic ldquoMethodology of pathloss calculation using measurement resultsrdquo in Proceedings ofthe 14th International Workshop on Systems Signals and ImageProcessing (IWSSIP rsquo07) and 6th EURASIP Conference Focusedon Speech and Image Processing Multimedia Communicationsand Services (EC-SIPMCS rsquo07) pp 257ndash260 June 2007

[29] M Bshara and L van Biesen ldquoLocalization in wireless networksdepending on map-supported path loss model a case study onWiMAX networksrdquo in Proceedings of the 2009 IEEE GLOBE-COMWorkshops pp 1ndash5 December 2009

[30] Y S Lu C F Lai C CHu YMHuang andXHGe ldquoPath lossexponent estimation for indoor wireless sensor positioningrdquoKSII Transactions on Internet and Information Systems vol 4no 3 pp 243ndash257 2010

[31] R Stoleru T He and J A Stankovic ldquoWalking GPS a practicalsolution for localization in manually deployed wireless sensornetworksrdquo in Proceedings of the 29th Annual IEEE InternationalConference on Local Computer Networks (LCN rsquo04) pp 480ndash489 November 2004

[32] R Singh M Guainazzo and C S Regazzoni ldquoLocation deter-mination using wlan in conjuction with GPS network (GlobalPositioning System)rdquo in Proceedings of the IEEE 59th VehicularTechnology Conference (VTC rsquo04) pp 2695ndash2699 May 2004

[33] A Ibrahim and D Ibrahim ldquoReal-time GPS based outdoorWiFi localization system with map displayrdquo Advances in Engi-neering Software vol 41 no 9 pp 1080ndash1086 2010

[34] E HechtOptics AddisonWesley ReadingMass USA 4th edi-tion 2001

[35] P M Shankar Introduction to Wireless Systems JohnWiley andSons New York NY USA 2001

[36] F P Fontan and P M EspineiraModeling theWireless Propaga-tion Channel John Wiley and Sons New York NY USA 2008

[37] W C Y Lee and Y S Yeh ldquoOn the estimation of the second-order statistics of log-normal fading in mobile radio environ-mentrdquo IEEE Transactions on Communications vol 22 no 6 pp869ndash873 1974

[38] E D Kaplan Ed Understanding GPS Principles and Applica-tions Artech House Norwood Mass USA 1996

[39] F van Diggelen ldquoGNSS accuracy lies damn lies and statisticsrdquoGPS World vol 18 no 1 pp 26ndash32 2007

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



However RSS levels are highly unpredictable and theformulation of a path loss model (PLM) as function ofdistance is a complex issue This complexity is derived fromthe fact that the received power level is a combination ofdifferent signal propagation mechanisms such as reflectiondiffraction and scattering and absorption losses Due to theseimpairments which depend on the surrounding environ-ment shadowing and multipath fading are produced As aconsequence estimation errors can be introduced for anyRSS-based localization algorithm

In recent years RSS-based localization algorithms havebeen the subject of an increasing interest due to the wideavailability of 80211bg transceivers and the proliferation ofWireless Local Area Networks (WLANs)

This approach exploits existingWLAN infrastructure andprecludes the use of additional hardware such as badges andwearable sensors see [15 16] In fact the IEEE 80211 stand-ard provides the means to obtain the signal strength via theReceived Signal Strength Indicator (RSSI) This indicator isdefined as ldquoa mechanism by which RF energy is to be mea-sured by the circuitry on a wireless NIC This numeric valueis an integer with an allowable range of 0ndash255 (a 1-byte value)rdquo[17] Similar metrics are defined for the IEEE 802154 andIEEE 802151 standards

The node localization algorithms within previous litera-ture are referred to as GPS-free or GPS-less algorithms Thelack ofGPS use can be explained by commondrawbacks attri-buted to several causes such as signal availability costantenna size and energy consumption Nowadays some ofthese arguments are no longer true GPS chips can be ubiquit-ously found in mobile devices such as smart phones handhelds and tablets While GPS chips are available in manydevices there are still many others that do not have it Theexisting GPS positioning capability could be used to estimatethe PLEs of WLAN access points and the derived PLMemployed to enable GPS-free location services

In this paper we propose a PLE estimationmethod whichuses the RSSI provided by a 80211bg transceiver in com-bination with data collected from a commercial grade GPSreceiver The method builds ray tracing models for typicalpropagation scenarios such as urban canyon and non-urbancanyon cases and uses them to formulate the design matrixof an observationmodelThe propagation scenarios take intoaccount the shadowing and multipath effects The observa-tions are composed of RSSI readings and GPS data The sys-tem of equations of the design matrix is linearized usingTaylor series and then solved through least squares Themain contribution of this work is the formulation of a para-metric mathematical model which improves the PLE accu-racy by using the Equivalent Isotropic Radiated Power (EIRP)and Effective Antenna Aperture (EAA) parameters calculatedbefore obtaining the PLE A second contribution is the com-bination of GPS data and RSSI readings in order to identifythe RSSI long term behavior

Depending on the transmitterrsquos power antenna heightand coverage area the RF environments where the devices aredeployed can be classified as macrocell microcell and pico-cell In microcell environments the transmitting power of theradios ranges from 01 to 1 watt the RF coverage area ranges

from 200 to 1000m and the transmitterrsquos height is low (3 to10 meters) [18] Environments within buildings are classifiedas picocells Indoor-to-outdoor configurations are environ-ments with walls blocking the signal and are characterizedby a wall attenuation factor The algorithm proposed in thiswork is tailored to microcell RF environments with indoor-to-outdoor coverage configurations therefore models suchas Okumura-Hata Lee or Walfisch-Bertoni are not treatedhere From this point forward when we refer to a blindnode we mean a device (smart phone hand held tablet orlaptop) whose position needs to be estimated when we referto anchor or beacon or landmark nodes we mean accesspoints (APs) for whose position are already known

The paper is organized as follows Section 2 reviews thelocalization algorithms based on RSSI only and algorithmswith RSSI-GPS collaboration In Section 3 we present theproposed method Section 4 presents the implantation of themethod in real world conditions In Section 5 the accuracy ofthe experimental results is discussed and finally conclusionsand future work are presented in Section 6

2 Related Work

This section is divided in two parts The first part reviewspapers related to either empirical or theoretical RSSI-basedmodels In the second part techniques that rely on both RSSIand GPS to derive power-distance models for node local-ization are examined Note there are other methods for RF-based localization such as fingerprinting [19 20] andBayesianNetworks [21 22]These techniques and some others excludePLE estimation and are not reviewed in this paper

21 PLE from RSSI Measurements The study of RSSI fordifferent purposes is not a new idea Some of these purposesare the optimization of the coverage area of wireless networks[23] assessment of links quality for multihop routing pro-tocols [24] and so forth The use of RSSI as a means fornode localization estimation in a WLAN dates back to 2000For example [25] proposes the use of an Extended KalmanFilter (EKF) to cope with the noise in the measurementsand to maintain a position estimate in harsh conditionsThey conducted an empirical experiment to relate signalstrength to distance between base and mobile stations Theshortcoming of this work is that it is designed to work withinpredefined surroundings in this case an office The accuracyis one room In [26] authors propose a lookup-table methodfor node position triangulation They also conducted datacollection to empirically correlate distance to signal strengthThe shortcoming of this works is that it requires an extensivesurvey at different points in a predefined environment and theconsequent table size In [27] authors proposed an optimalaveraging window length of RSSI samples to cope with fadingof the power and mobility of the nodes By modeling thechannelrsquos fading with a Rayleigh distribution they obtained afactor (1199032)whichmultiplies theRSSI samples (119908)The authorsreported a lower boundmean error of 25mwith119908 = 50Themain drawback is that thismethod is intended for rectangularareas where bacons are placed optimally





10(1198891)


10(1198892)

(1)


2687 lowast log10(119889)




PL (119889) = PL (1198890) minus 10120572log

10(

119889

1198890

) + 119883120590 (2)


0) is a path loss


120590is



120572 =

minussum119899

119894=1(PL (119889

119894) minus PL (119889

0))

sum119899

119894=110 (log 119889

119894)

(3)














1and 120579

2


1= tan 120579

1 and119898

2= tan 120579

2





3 Proposed Solution


119875119903=

1

119889120572 (4)






RSSI and GPS

data

Fast variations

Slow variations

PLE estimation

[[[[

1199011199031(119889)

119901119903119899(119889)

]]]]

119911 = 120573 +




z = 119867 (x) 120573 + k (5)









119875119903= 0119860119903 (6)


0 =

1

2

|119890|2

120120587

(7)


119860119903=

1205822sdot 119892119903

4120587 sdot 119897119903

(8)




0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(a)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(b)



119875119903(1198890) = 119860

119903

1003816100381610038161003816119890119879(1198890)1003816100381610038161003816

2

2120578

(9)


119879and rep-


119879= 1198900+ 1198901+ 1198902+ 1198903) The term 119890

0represents the




1198900= radic

60119901119892

119897

119890(minus1198951198961198890)

1198890

1198901= radic

60119901119892

119897

GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

1198902= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

1198903= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198893)

1198890+ 1198893

(10)




3are the additional



119860119903

100381610038161003816100381610038161003816100381610038161003816

radic60119901119892

119897

(

119890(minus1198951198961198890)

1198890

+ GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

+WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

+119882119877

119890minus119895119896(1198890+1198893)

1198890+ 1198893

)

100381610038161003816100381610038161003816100381610038161003816

2

(2120578)minus1

(11)



system is

z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + k (12)




119905


119905and


z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + n (13)



Table 1


ENA 131 N 566263617E 70093253

242

ENE 136 N 566266942E 70084148

235

NM 110 N 566254219E 70093153

231

KNB 125u N 566244524E 70080563

240

KNB 132 N 566242101E 70079860

241

MC 184 N 566245213E 70087963

252

MC 197 N 566247447E 70092779

255



119901119903(119889) = (119901


10(

120582

4120587

))

+ 120574 sdot 10 sdot log10(119889)

(14)







1205881= radic(119909

1minus 119909119906)2

+ (1199101minus 119910119906)2

+ (1199111minus 119911119906)2

1205882= radic(119909

2minus 119909119906)2

+ (1199102minus 119910119906)2

+ (1199112minus 119911119906)2

120588119899= radic(119909

119899minus 119909119906)2

+ (119910119899minus 119910119906)2

+ (119911119899minus 119911119906)2

(15)

where (1199091 1199101) (1199092 1199102) and (119909



1 1205882 120588

119899are


119906Δ119910119906




119901 (119909119906+ Δ119909119906 119910119906+ Δ119910119906 119906+ Δ119911119906)

= 119901 (119909119906 119910119906 119906) +

120597119901 (119909119906 119910119906 119906)

120597119909119906

Δ119909119906

+

120597119901 (119909119906 119910119906 119906)

120597119910119906

Δ119910119906+

120597119901 (119909119906 119910119906 119906)

120597119909119906


(16)






1= 439158 meters

1205882= 605400 meters and 120588



119906= 700900 and 119911

119906= 11124 (red color




(dB)


(a)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(b)

0 50 100 150 200 250minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60


(dB)

(c)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(d)


(dB)


(e)

0 005 01 015 02minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(f)










111991121199113sdot sdot sdot 119911119899]



Table 2


ONE N 566262236E 70089486

62863 37488

TWO N 56624691E 70084036

73534 15291

THREE N 566250343E 70091576

36885 14245

Average 57760 22341








2


rms2= radic120590

2

119909+ 1205902

119910 (17)



119909and 1205902119910





2and HDOP are

shown in Table 2



Table 3


RMS2 Mean HDOP


385868419143

157322 07866


517475704132

322975 17112


30094391

60423 05857

Average 18024 10278


2


2










References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













10(1198891)


10(1198892)

(1)


2687 lowast log10(119889)




PL (119889) = PL (1198890) minus 10120572log

10(

119889

1198890

) + 119883120590 (2)


0) is a path loss


120590is



120572 =

minussum119899

119894=1(PL (119889

119894) minus PL (119889

0))

sum119899

119894=110 (log 119889

119894)

(3)














1and 120579

2


1= tan 120579

1 and119898

2= tan 120579

2





3 Proposed Solution


119875119903=

1

119889120572 (4)






RSSI and GPS

data

Fast variations

Slow variations

PLE estimation

[[[[

1199011199031(119889)

119901119903119899(119889)

]]]]

119911 = 120573 +




z = 119867 (x) 120573 + k (5)









119875119903= 0119860119903 (6)


0 =

1

2

|119890|2

120120587

(7)


119860119903=

1205822sdot 119892119903

4120587 sdot 119897119903

(8)




0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(a)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(b)



119875119903(1198890) = 119860

119903

1003816100381610038161003816119890119879(1198890)1003816100381610038161003816

2

2120578

(9)


119879and rep-


119879= 1198900+ 1198901+ 1198902+ 1198903) The term 119890

0represents the




1198900= radic

60119901119892

119897

119890(minus1198951198961198890)

1198890

1198901= radic

60119901119892

119897

GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

1198902= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

1198903= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198893)

1198890+ 1198893

(10)




3are the additional



119860119903

100381610038161003816100381610038161003816100381610038161003816

radic60119901119892

119897

(

119890(minus1198951198961198890)

1198890

+ GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

+WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

+119882119877

119890minus119895119896(1198890+1198893)

1198890+ 1198893

)

100381610038161003816100381610038161003816100381610038161003816

2

(2120578)minus1

(11)



system is

z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + k (12)




119905


119905and


z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + n (13)



Table 1


ENA 131 N 566263617E 70093253

242

ENE 136 N 566266942E 70084148

235

NM 110 N 566254219E 70093153

231

KNB 125u N 566244524E 70080563

240

KNB 132 N 566242101E 70079860

241

MC 184 N 566245213E 70087963

252

MC 197 N 566247447E 70092779

255



119901119903(119889) = (119901


10(

120582

4120587

))

+ 120574 sdot 10 sdot log10(119889)

(14)







1205881= radic(119909

1minus 119909119906)2

+ (1199101minus 119910119906)2

+ (1199111minus 119911119906)2

1205882= radic(119909

2minus 119909119906)2

+ (1199102minus 119910119906)2

+ (1199112minus 119911119906)2

120588119899= radic(119909

119899minus 119909119906)2

+ (119910119899minus 119910119906)2

+ (119911119899minus 119911119906)2

(15)

where (1199091 1199101) (1199092 1199102) and (119909



1 1205882 120588

119899are


119906Δ119910119906




119901 (119909119906+ Δ119909119906 119910119906+ Δ119910119906 119906+ Δ119911119906)

= 119901 (119909119906 119910119906 119906) +

120597119901 (119909119906 119910119906 119906)

120597119909119906

Δ119909119906

+

120597119901 (119909119906 119910119906 119906)

120597119910119906

Δ119910119906+

120597119901 (119909119906 119910119906 119906)

120597119909119906


(16)






1= 439158 meters

1205882= 605400 meters and 120588



119906= 700900 and 119911

119906= 11124 (red color




(dB)


(a)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(b)

0 50 100 150 200 250minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60


(dB)

(c)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(d)


(dB)


(e)

0 005 01 015 02minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(f)










111991121199113sdot sdot sdot 119911119899]



Table 2


ONE N 566262236E 70089486

62863 37488

TWO N 56624691E 70084036

73534 15291

THREE N 566250343E 70091576

36885 14245

Average 57760 22341








2


rms2= radic120590

2

119909+ 1205902

119910 (17)



119909and 1205902119910





2and HDOP are

shown in Table 2



Table 3


RMS2 Mean HDOP


385868419143

157322 07866


517475704132

322975 17112


30094391

60423 05857

Average 18024 10278


2


2










References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













1and 120579

2


1= tan 120579

1 and119898

2= tan 120579

2





3 Proposed Solution


119875119903=

1

119889120572 (4)






RSSI and GPS

data

Fast variations

Slow variations

PLE estimation

[[[[

1199011199031(119889)

119901119903119899(119889)

]]]]

119911 = 120573 +




z = 119867 (x) 120573 + k (5)









119875119903= 0119860119903 (6)


0 =

1

2

|119890|2

120120587

(7)


119860119903=

1205822sdot 119892119903

4120587 sdot 119897119903

(8)




0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(a)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(b)



119875119903(1198890) = 119860

119903

1003816100381610038161003816119890119879(1198890)1003816100381610038161003816

2

2120578

(9)


119879and rep-


119879= 1198900+ 1198901+ 1198902+ 1198903) The term 119890

0represents the




1198900= radic

60119901119892

119897

119890(minus1198951198961198890)

1198890

1198901= radic

60119901119892

119897

GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

1198902= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

1198903= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198893)

1198890+ 1198893

(10)




3are the additional



119860119903

100381610038161003816100381610038161003816100381610038161003816

radic60119901119892

119897

(

119890(minus1198951198961198890)

1198890

+ GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

+WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

+119882119877

119890minus119895119896(1198890+1198893)

1198890+ 1198893

)

100381610038161003816100381610038161003816100381610038161003816

2

(2120578)minus1

(11)



system is

z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + k (12)




119905


119905and


z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + n (13)



Table 1


ENA 131 N 566263617E 70093253

242

ENE 136 N 566266942E 70084148

235

NM 110 N 566254219E 70093153

231

KNB 125u N 566244524E 70080563

240

KNB 132 N 566242101E 70079860

241

MC 184 N 566245213E 70087963

252

MC 197 N 566247447E 70092779

255



119901119903(119889) = (119901


10(

120582

4120587

))

+ 120574 sdot 10 sdot log10(119889)

(14)







1205881= radic(119909

1minus 119909119906)2

+ (1199101minus 119910119906)2

+ (1199111minus 119911119906)2

1205882= radic(119909

2minus 119909119906)2

+ (1199102minus 119910119906)2

+ (1199112minus 119911119906)2

120588119899= radic(119909

119899minus 119909119906)2

+ (119910119899minus 119910119906)2

+ (119911119899minus 119911119906)2

(15)

where (1199091 1199101) (1199092 1199102) and (119909



1 1205882 120588

119899are


119906Δ119910119906




119901 (119909119906+ Δ119909119906 119910119906+ Δ119910119906 119906+ Δ119911119906)

= 119901 (119909119906 119910119906 119906) +

120597119901 (119909119906 119910119906 119906)

120597119909119906

Δ119909119906

+

120597119901 (119909119906 119910119906 119906)

120597119910119906

Δ119910119906+

120597119901 (119909119906 119910119906 119906)

120597119909119906


(16)






1= 439158 meters

1205882= 605400 meters and 120588



119906= 700900 and 119911

119906= 11124 (red color




(dB)


(a)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(b)

0 50 100 150 200 250minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60


(dB)

(c)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(d)


(dB)


(e)

0 005 01 015 02minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(f)










111991121199113sdot sdot sdot 119911119899]



Table 2


ONE N 566262236E 70089486

62863 37488

TWO N 56624691E 70084036

73534 15291

THREE N 566250343E 70091576

36885 14245

Average 57760 22341








2


rms2= radic120590

2

119909+ 1205902

119910 (17)



119909and 1205902119910





2and HDOP are

shown in Table 2



Table 3


RMS2 Mean HDOP


385868419143

157322 07866


517475704132

322975 17112


30094391

60423 05857

Average 18024 10278


2


2










References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(a)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

100


119910(m

)

(b)



119875119903(1198890) = 119860

119903

1003816100381610038161003816119890119879(1198890)1003816100381610038161003816

2

2120578

(9)


119879and rep-


119879= 1198900+ 1198901+ 1198902+ 1198903) The term 119890

0represents the




1198900= radic

60119901119892

119897

119890(minus1198951198961198890)

1198890

1198901= radic

60119901119892

119897

GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

1198902= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

1198903= radic

60119901119892

119897

WR119890minus119895119896(1198890+1198893)

1198890+ 1198893

(10)




3are the additional



119860119903

100381610038161003816100381610038161003816100381610038161003816

radic60119901119892

119897

(

119890(minus1198951198961198890)

1198890

+ GR119890minus119895119896(1198890+1198891)

1198890+ 1198891

+WR119890minus119895119896(1198890+1198892)

1198890+ 1198892

+119882119877

119890minus119895119896(1198890+1198893)

1198890+ 1198893

)

100381610038161003816100381610038161003816100381610038161003816

2

(2120578)minus1

(11)



system is

z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + k (12)




119905


119905and


z =[

[

[

[

1198751199031(119889)

119875119903119899(119889)

]

]

]

]

120573 + n (13)



Table 1


ENA 131 N 566263617E 70093253

242

ENE 136 N 566266942E 70084148

235

NM 110 N 566254219E 70093153

231

KNB 125u N 566244524E 70080563

240

KNB 132 N 566242101E 70079860

241

MC 184 N 566245213E 70087963

252

MC 197 N 566247447E 70092779

255



119901119903(119889) = (119901


10(

120582

4120587

))

+ 120574 sdot 10 sdot log10(119889)

(14)







1205881= radic(119909

1minus 119909119906)2

+ (1199101minus 119910119906)2

+ (1199111minus 119911119906)2

1205882= radic(119909

2minus 119909119906)2

+ (1199102minus 119910119906)2

+ (1199112minus 119911119906)2

120588119899= radic(119909

119899minus 119909119906)2

+ (119910119899minus 119910119906)2

+ (119911119899minus 119911119906)2

(15)

where (1199091 1199101) (1199092 1199102) and (119909



1 1205882 120588

119899are


119906Δ119910119906




119901 (119909119906+ Δ119909119906 119910119906+ Δ119910119906 119906+ Δ119911119906)

= 119901 (119909119906 119910119906 119906) +

120597119901 (119909119906 119910119906 119906)

120597119909119906

Δ119909119906

+

120597119901 (119909119906 119910119906 119906)

120597119910119906

Δ119910119906+

120597119901 (119909119906 119910119906 119906)

120597119909119906


(16)






1= 439158 meters

1205882= 605400 meters and 120588



119906= 700900 and 119911

119906= 11124 (red color




(dB)


(a)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(b)

0 50 100 150 200 250minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60


(dB)

(c)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(d)


(dB)


(e)

0 005 01 015 02minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(f)










111991121199113sdot sdot sdot 119911119899]



Table 2


ONE N 566262236E 70089486

62863 37488

TWO N 56624691E 70084036

73534 15291

THREE N 566250343E 70091576

36885 14245

Average 57760 22341








2


rms2= radic120590

2

119909+ 1205902

119910 (17)



119909and 1205902119910





2and HDOP are

shown in Table 2



Table 3


RMS2 Mean HDOP


385868419143

157322 07866


517475704132

322975 17112


30094391

60423 05857

Average 18024 10278


2


2










References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 1


ENA 131 N 566263617E 70093253

242

ENE 136 N 566266942E 70084148

235

NM 110 N 566254219E 70093153

231

KNB 125u N 566244524E 70080563

240

KNB 132 N 566242101E 70079860

241

MC 184 N 566245213E 70087963

252

MC 197 N 566247447E 70092779

255



119901119903(119889) = (119901


10(

120582

4120587

))

+ 120574 sdot 10 sdot log10(119889)

(14)







1205881= radic(119909

1minus 119909119906)2

+ (1199101minus 119910119906)2

+ (1199111minus 119911119906)2

1205882= radic(119909

2minus 119909119906)2

+ (1199102minus 119910119906)2

+ (1199112minus 119911119906)2

120588119899= radic(119909

119899minus 119909119906)2

+ (119910119899minus 119910119906)2

+ (119911119899minus 119911119906)2

(15)

where (1199091 1199101) (1199092 1199102) and (119909



1 1205882 120588

119899are


119906Δ119910119906




119901 (119909119906+ Δ119909119906 119910119906+ Δ119910119906 119906+ Δ119911119906)

= 119901 (119909119906 119910119906 119906) +

120597119901 (119909119906 119910119906 119906)

120597119909119906

Δ119909119906

+

120597119901 (119909119906 119910119906 119906)

120597119910119906

Δ119910119906+

120597119901 (119909119906 119910119906 119906)

120597119909119906


(16)






1= 439158 meters

1205882= 605400 meters and 120588



119906= 700900 and 119911

119906= 11124 (red color




(dB)


(a)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(b)

0 50 100 150 200 250minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60


(dB)

(c)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(d)


(dB)


(e)

0 005 01 015 02minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(f)










111991121199113sdot sdot sdot 119911119899]



Table 2


ONE N 566262236E 70089486

62863 37488

TWO N 56624691E 70084036

73534 15291

THREE N 566250343E 70091576

36885 14245

Average 57760 22341








2


rms2= radic120590

2

119909+ 1205902

119910 (17)



119909and 1205902119910





2and HDOP are

shown in Table 2



Table 3


RMS2 Mean HDOP


385868419143

157322 07866


517475704132

322975 17112


30094391

60423 05857

Average 18024 10278


2


2










References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











(dB)


(a)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(b)

0 50 100 150 200 250minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60


(dB)

(c)

0 005 01 015 02minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(d)


(dB)


(e)

0 005 01 015 02minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20


(dB)

(f)










111991121199113sdot sdot sdot 119911119899]



Table 2


ONE N 566262236E 70089486

62863 37488

TWO N 56624691E 70084036

73534 15291

THREE N 566250343E 70091576

36885 14245

Average 57760 22341








2


rms2= radic120590

2

119909+ 1205902

119910 (17)



119909and 1205902119910





2and HDOP are

shown in Table 2



Table 3


RMS2 Mean HDOP


385868419143

157322 07866


517475704132

322975 17112


30094391

60423 05857

Average 18024 10278


2


2










References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














111991121199113sdot sdot sdot 119911119899]



Table 2


ONE N 566262236E 70089486

62863 37488

TWO N 56624691E 70084036

73534 15291

THREE N 566250343E 70091576

36885 14245

Average 57760 22341








2


rms2= radic120590

2

119909+ 1205902

119910 (17)



119909and 1205902119910





2and HDOP are

shown in Table 2



Table 3


RMS2 Mean HDOP


385868419143

157322 07866


517475704132

322975 17112


30094391

60423 05857

Average 18024 10278


2


2










References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 3


RMS2 Mean HDOP


385868419143

157322 07866


517475704132

322975 17112


30094391

60423 05857

Average 18024 10278


2


2










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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