research article multidimensional optimization of signal space...

Research ArticleMultidimensional Optimization of Signal Space DistanceParameters in WLAN Positioning

Milenko BrkoviT and Mirjana SimiT

School of Electrical Engineering University of Belgrade Bulevar kralja Aleksandra 73 11120 Belgrade Serbia

Correspondence should be addressed to Mirjana Simic miraetfrs

Received 25 August 2013 Accepted 12 February 2014 Published 16 March 2014

Academic Editors D De Vleeschauwer and W Yu

Copyright copy 2014 M Brkovic and M Simic This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Accurate indoor localization of mobile users is one of the challenging problems of the last decade Besides delivering high speedInternet Wireless Local Area Network (WLAN) can be used as an effective indoor positioning system being competitive bothin terms of accuracy and cost Among the localization algorithms nearest neighbor fingerprinting algorithms based on ReceivedSignal Strength (RSS) parameter have been extensively studied as an inexpensive solution for delivering indoor Location BasedServices (LBS) In this paper we propose the optimization of the signal space distance parameters in order to improve precisionof WLAN indoor positioning based on nearest neighbor fingerprinting algorithms Experiments in a real WLAN environmentindicate that proposed optimization leads to substantial improvements of the localization accuracy Our approach is conceptuallysimple is easy to implement and does not require any additional hardware

1 Introduction

Possession of the information about user location in radionetworks where the user mobility is assumed completes thegoal of service availability not only at the right time but alsoin the right place The idea of user positioning in radio net-works originated in cellular networks for safety purposesEmergency call services (such as 911 and 112) are the bestexample since users are not always able to provide preciseinformation of their location to emergency dispatchers Thisis the main reason why regulatory agencies in the USA andthe EU required mobile network operators to implementlocation services in their networks Later the informationabout mobile user location opened new commercial possibil-ities for mobile network operators A large number of appli-cations in radio networks based on user location informationin outdoor environment initiated development of similarapplications for indoor environment Some of the indoor LBSare inventory tracking location detection of products storedin a warehouse location detection of medical personnel orequipment in a hospital location detection of firemen ina building on fire virtual tourist guides in museums andgalleries and so forth [1] Although the indoor positioning

implies positioning in various short-range technologies [2]as bluetooth RFID (Radio Frequency IDentification) IrDA(Infrared Data Association) UWB (Ultra Wide Band) andso forth WLAN is the most common technology in indoorenvironment and therefore is used for indoor positioning themost often

Regardless of the type of radio technology there are foursignal parameters which can be used for user positioning inradio networks [3] AOA (Angle Of Arrival) TOA (Time OfArrival) TDOA (TimeDifference Of Arrival) and RSS AOAparameter is very sensitive to the NLOS (Non-Line-Of-Sight)propagation conditions and multiple propagation beingthe main characteristics of indoor propagation [4] AlsoAOA requires considerable hardware modifications on thetransmitterreceiver and therefore is not suitable for indoorpositioning Time as a parameter (either TOA or TDOA) isgenerally very reliable positioning parameter but like AOAnot suitable for indoor conditions The main problem here isthe demand for high resolution of time measurement This isa consequence of the wave propagation at the speed of lightover small distances inside buildings This leaves RSS as theonly parameter available to estimate the distance accordingto a propagation model

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 986061 6 pageshttpdxdoiorg1011552014986061

2 The Scientific World Journal

Signal propagation in indoor environments is a complexprocess and propagation modeling requires large numberof input parameters Building type infrastructure wallthickness windows layout and size of the rooms all havesignificant influence on signal propagation Even knowledgeof all these parameters cannot guarantee good estimation ofthe RSS because the number and position of people movingwithin the building also affect the signal level Therefore themost challenging issue for indoor positioning based on RSSparameter is the unstable RSS value due to the multipatheffect caused by reflection diffraction and diffusion on theindoor scattering-rich walls which causes a time-varyingRSS even at a fixed location [5] However despite numerousdrawbacks RSS parameter is the most common choice forpositioning in indoor environment mainly due to lack ofalternative

Complex indoor radio propagation in practice reducesthe indoor positioning techniques to two the locationproximity (also known as Cell-ID) and fingerprinting [6]Cell-ID is the simplest positioning technique based on thefact that the location of the nearest transmitter (in case ofWLAN location of the access point AP) is assigned to anunknown userterminal location This method has all theadvantages and only one drawbackmdashpoor accuracy Finger-printing technique ismore complex compared to Cell-ID butincreases positioning accuracy Location fingerprinting refersto techniques thatmatch the fingerprint of a set of radio signalpropagation characteristics that are location dependent [1]

A number of various location fingerprinting-based posi-tioning algorithms are available probabilistic methods [7]neural networks [8] space segmentation [9] support vectormachines [10] and 119870 nearest neighbor (KNN) as one of thebasic algorithms [11] KNN uses the online RSS to search for119870 closestmatches of known locations in signal space from thepreviously built database By averaging these119870 location can-didates with or without adopting the distances in signal spaceas weights an estimated location is obtained [1]

The algorithm proposed in this paper improves precisionof WLAN positioning based on nearest neighbor finger-printing algorithms by applying optimization of the param-eters of the metric used to compute the difference in radiofingerprints Experimental results in a real indoor WLANenvironment show that the optimization of signal spacedistance computational parameters results in higher posi-tioning accuracy compared to the traditional approach

The rest of the paper is structured as follows Section 2illustrates basic principles for the location fingerprintingsystem Section 3 describes the optimization of the param-eters used to compute the difference in radio fingerprintsIn Section 4 we describe the experimental environmentSection 5 presents experimental results and analyses Finallythe conclusion is given in Section 6

2 Fingerprinting Positioning Algorithm

Fingerprinting is a positioning method that relies upon adatabase of collected location dependent radio signal param-eters that constitute a ldquofingerprintrdquo of a specific location

Location of the mobile unit is determined comparing a set ofradio signal parameters the mobile unit observes to availabledatabase

The first step in fingerprinting is to collect a set of locationdependent parameters of radio signals received by themobileuser (MU) from the access points The access points areassumed to have fixed spatial positions In WLAN thelocation-dependent parameter readily available is the valueof the received signal strength of available access points at theconsidered point in space To build the database of locationfingerprints in the area of interest a set of reference points(RPs) has to be selectedThe RPs should be uniformly spreadin the area of interest [12] that is the area in which thepositioning service is being implemented This area is alsocalled the ldquotest bedrdquo area [13]

The process of collecting the database of fingerprints isnamed the training phase Result of the training phase is thedatabase containing a set of 119899RP coordinates (119909RP119896 119910RP119896) 119896 isin1 119899RP accompanied by the corresponding ordered setof observed RSS levels that originate from all of the availableaccess points indexed by 119894 119894 isin 1 119899 The set of measuredRSS levels is conveniently stored in a vector

997888997888rarrRSSRP119896 = [RSSRP1198961RSSRP1198962 RSSRP119896119899] (1)

The vector 997888997888rarrRSSRP119896 is a fingerprint of the location specified by(119909RP119896 119910RP119896)

After the system is trained that is the database offingerprints that correspond to the RPs is collected in thepositioning phase of the algorithm for each positioningrequest the mobile unit measures the vector of RSS param-eters it observes 997888997888rarrRSSMU

997888997888rarrRSSMU = [RSSMU1RSSMU2 RSSMU119899] (2)

and compares it to the database obtained in the training phaseof themethod An appropriate algorithmdetermines locationof the mobile unit which is the most likely

21 Metric for the Difference in Radio Fingerprints Manyalgorithms can be used to estimate position of the mobileunit The basic one is the nearest neighbor in signal space(NNSS or NN) [11] First the signal distance between the RSSvector observed by the mobile unit (2) and the RSS vectorsin the database (1) is computed In this paper we proposegeneralized signal space distance defined as

119871119902119898 = (

119899

sum

119894=1

1003816100381610038161003816RSSRP119898119894 minus RSSMU1198941003816100381610038161003816

119902)

1119902

(3)

where 1 le 119898 le 119899RP and 119899RP is the number of RPs available inthe database For 119902 = 2 generalized distance of (3) reducesto the Euclidean distance while for 119902 = 1 the distance isthe Manhattan distance The metric maps a difference of RSSvectors to a single real number

After the signal space distances from the observed RSSvector to the vectors available in the database are computedthe minimum is found

119871119902 min = min1le119898le119899RP

119871119902119898 (4)

The Scientific World Journal 3

which determines the reference point 119897 which is in the radiosignal space the closest to mobile unit

119871119902119897 = 119871119902 min (5)

Coordinates of this reference point (119909RP119897 119910RP119897) are assigned asan estimate of the mobile unit coordinates

(119909MU 119910MU) = (119909RP119897 119910RP119897) (6)

Although heuristic in nature the nearest neighbor searchis natural and obvious However the positioning ultimatelyrelies on only one RSS vector in the database Another issueis opened in the case where more than one of the vectorsin the database satisfies (5) A response to these issues is ageneralizedmethod named119870 nearest neighbors (KNN)Thealgorithm determines a set 119878NN of119870 reference points with theRSS vector 997888997888rarrRSSRP119896 closest to the RSS vector observed by themobile unit 997888997888rarrRSSMU and assigns estimate of the mobile unitposition according to

119909MU =1

119870

119870

sum

119894=1

119909RP 119878NN 119894

119910MU =1

119870

119870

sum

119894=1

119910RP 119878NN 119894

(7)

In this manner all of the reference points in the 119878NN have thesame influence in determining the mobile unit position

To include the information about the radio distance fromthe mobile unit to the reference points in 119878NN anotheralgorithm to compute the estimated position of the mobileunit is proposed as

119909MU =sum119870

119894=1((1119871119902119878NN 119894

) 119909RP 119878NN 119894)

sum119870

119894=1(1119871119902119878NN 119894

)

119910MU =sum119870

119894=1((1119871119902119878NN 119894

) 119910RP 119878NN 119894)

sum119870

119894=1(1119871119902119878NN 119894

)

(8)

This method of estimating the mobile unit coordinates takesinto account both119870 nearest neighbors as well as their signalspace distance to the mobile unit Similar to KNN but withthe weighting scheme (inverse of the signal space distanceas a weight) this method is known as 119870 weighted nearestneighbors (KWNN) [14]

All three of the considered algorithms are heuristic innature and require database of radio fingerprints observedin a set of reference points The algorithms that include 119870nearest neighbors require somewhat more complex databasesearch algorithm Common to all three of the algorithms isthe dependence of the positioning result on themetric used tocompute the difference in radio fingerprints characterized bythe exponent 119902

22 Received Signal Strength Value Assigned to UnavailableAccess Points Another relevant issue in the fingerprinting

approach is the RSS value assigned to the access points thatare effectively unobservable by the mobile unit Since theRSS is measured in dB absence of the signal corresponds tominus infinity causing the difference measure (3) to divergeevery time when some of the access points represented in theRSS vector are not observable This problem is heuristicallypatched by assuming a low finite RSS value for the accesspoints that are not observable The assumed value will belabeled as 119899119900119860119875 The value chosen for 119899119900119860119875 affects the resultof (3) propagating further to affect the positioning resultThus 119899119900119860119875 effectively appears as an indirect parameter of thesignal space distance metric

3 Multidimensional Optimization

The metric used to compute the difference in radio finger-prints parameter 119902 usually takes a value of 1 or 2 so wehaveManhattan or Euclidean distance respectively althoughthere is no physical limitations referring to the values thatparameter 119902 could take By varying this parameter within areasonable range we will try to reduce the positioning error

Whenmeasuring the RSS parameters at one point it oftenhappens that signal strength of some APs is below the thresh-old and the device simply does not detect a signal from theAPThe question is what RSS value should be assigned for theseAPs so that numerical value of the signal space distance canbe calculated In the previous section we called this param-eter 119899119900119860119875 Most commonly this parameter is assigned valueof the noise level but we will optimize its value in order toincrease positioning accuracy

Multidimensional optimization is a process of findingoptimal values of the signal space distance parameters 119902and 119899119900119860119875 in order to maximize accuracy of the WLANpositioning In this paper we performed multidimensionaloptimization for all considered algorithms (NN KNN andKWNN) and the results are presented in Section 5

4 Experimental Setup

Measurements required for the experimental analysis of fin-gerprinting positioningmethod are performed in hallways ofthe School of Electrical Engineering University of Belgradeusing the WLAN available there The experimental area is ofthe size 147m times 66m The WLAN infrastructure consists ofeight APs placed to provide the best signal coverageThe APsare Cisco Aironet 1230G high capacity with omnidirectionalantennas supporting 80211g WLAN standard on 24GHzwith 50mW of power All of the APs are placed 02mbeneath the ceilingThe building plan is presented in Figure 1Positions of the APs are marked with red dots and redrectangle shows the area where the measurements wereconducted The building is with narrow hallways and lot ofwalls and windows where prediction of wave propagation isvery difficult

Fingerprinting database is formed from RSS measure-ments collected at 147 RPs uniformly distributed in themiddle of the hallways (red rectangle in Figure 1) and 2mapart from each other Thirty-seven test points (TPs) are also


AP1 AP2 AP3 AP4

AP5AP6 AP7

AP8

Figure 1 Experimental test bed

0 200 400 600 800 1000 1200 1400 1600d (cm)

0

2

4

6

8

10

12

14

16

n

Figure 2 Histogram of the positioning error for NN algorithmwithout optimization

located on the rectangle however outside of strictly defineduniform schedule at every 2m and they are used to checkaccuracy of the implemented positioning method Measure-ments were performed in a real workday environment withN5010 Dell laptop and DV1501Wireless-NWLANHalf-MiniCard network card using inSSIDer 20

5 Experimental and Optimization Results

The first method to be considered in this paper is theNN algorithm The measurement results are first processedwithout multidimensional optimization Mean positioningerror obtained by NN algorithm defined as

120575 =1

119873

119873

sum

119894=1

radic(119909MU minus 119909MUactual)2+ (119910MU minus 119910MUactual)

2 (9)

is 120575 = 43439 cm where (119909MUactual 119910MUactual) are actualcoordinates of the mobile unit and 119873 is the number of testpointsThis value is obtained for the parameter value 119899119900119860119875 =minus100 dBm (equal to the receiver sensitivity) and Euclideandistance (119902 = 2) Figure 2 shows a histogram of thepositioning error for the NN algorithm

0 200 400 600 800 1000 1200 1400 16000

2

4

6

8

10

12

14

16

d (cm)

n

Figure 3 Histogram of the positioning error for NN algorithmwithoptimization

Optimization of a signal space distance parameters 119902and 119899119900119860119875 is performed applying the brute force algorithmin order to obtain the minimum average positioning errorThe resulting mean positioning error in the case of NNalgorithm with optimization is 120575 = 27003 cm Optimizationof the signal space distance parameters results in the meanpositioning error reduction of about 40 without any effortin the fingerprint database generation only by applyingthe optimization process Figure 3 shows histogram of thepositioning error for NN algorithm with multidimensionaloptimization The obtained optimal values of the parametersare 119902 = 11 and 119899119900119860119875 = minus81 dBm Figure 4 showsmean posi-tioning error dependence of the positioning parameters 119902 and119899119900119860119875

In order to evaluate the effect of optimization for KNNand KWNN algorithm we performed the same analyses asin the case of NN algorithm In Table 1 mean positioningerror is presented In the case without optimization in theconsidered WLAN environment increase of parameter 119870slightly increases the mean positioning error

Multidimensional optimization of parameters 119902 and119899119900119860119875 is also performed for KNN and KWNN algorithms inorder to minimize mean positioning error Results shown in


1

12

14

16

18

2

minus70minus90

minus110minus130

No AP value (dBm)q minus150

Mea

n po

sitio

ning

erro

r (cm

)

260

300

340

380

420

Figure 4 Mean positioning error dependence of the signal spacedistance parameters 119902 and 119899119900119860119875

Table 1 Mean positioning error 120575 for KNN and KWNN algorithmwithout optimization

119870120575 (cm)

KNN KWNN2 48877 440293 52820 478504 62025 526425 70762 55466

Table 2 show that optimization leads to a reduction in meanpositioning error both for KNN and KWNN algorithm butalso depends on the value of parameter119870 The best results ofmultidimensional optimization are achieved for119870 = 2 wherethemean positioning error is reduced by about 48 for KNNand by about 36 for KWNN algorithm which yields fromthe data presented in Tables 1 and 2

Optimal values of the optimization parameters 119902 and119899119900119860119875 are different for different algorithms and differentvalues of the parameter 119870 and they are given in Table 3

Presented experimental results show that the most con-venient positioning choice for the considered indoor WLANenvironment is KNN algorithm (with119870 = 2) with optimizedparameters 119902 = 11 and 119899119900119860119875 = minus77 dBm In this casemean positioning error reaches the minimum value of120575 = 25289 cm This represents maximum accuracy limit offingerprinting-based positioning method for given indoorWLAN environment In this manner any indoor WLANenvironment can be characterized by the set of signalspace distance parameter values 119902 119899119900119860119875 which guaranteethe highest possible indoor positioning accuracy At thismoment it remains an open questionwhether there is a phys-ical explanation for the optimal values of these parameters orit is just an empirical result

Table 2 Mean positioning error 120575 for KNN and KWNN algorithmwith optimization

119870120575 (cm)

KNN KWNN2 25289 283373 29693 331174 37639 376445 49648 44414

Table 3 Dependance of the optimal 119902 and 119899119900119860119875 values on thealgorithm type and parameter 119870

119870 119902 noAP (dBm)

2 KNN 11 minus77KWNN 11 minus77




6 Conclusion

To improve precision of WLAN positioning based on tradi-tional fingerprinting nearest-neighbor algorithms the opti-mization of parameters used to compute the difference inradio fingerprints is proposed Experiments in a real WLANenvironment demonstrated usefulness of the optimizationprocess and significant improvements of the positioningaccuracy The numerical results show reduction of the meanpositioning error from about 20 to 48 for all of the con-sidered algorithms Furthermore optimal values of the opti-mization parameters guarantee the highest possible indoorpositioning accuracy and can be used as a unique position-ing characteristic of any indoor WLAN environment Theapproach is conceptually simple is easy to implement anddoes not require any additional hardware time or effortcompared to traditional fingerprinting positioning process

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to thank Professor Predrag V Pejovicof the Faculty of Electrical Engineering University of Bel-grade for his valuable comments on the paper

References

[1] H Liu H Darabi P Banerjee and J Liu ldquoSurvey of wirelessindoor positioning techniques and systemsrdquo IEEE Transactions


on Systems Man and Cybernetics C vol 37 no 6 pp 1067ndash10802007

[2] A Bensky Wireless Positioning Technologies and ApplicationsArtech House 2008

[3] A Melikov Ed Cellular Networks Positioning PerformanceAnalysis Reliability InTech 2011

[4] K Pahlavan X Li and J-PMakela ldquoIndoor geolocation scienceand technologyrdquo IEEE Communications Magazine vol 40 no2 pp 112ndash118 2002

[5] S-H Fang T-N Lin and K-C Lee ldquoA novel algorithm formultipath fingerprinting in indoorWLANenvironmentsrdquo IEEETransactions onWireless Communications vol 7 no 9 pp 3579ndash3588 2008

[6] G Sun J Chen W Guo and K J R Liu ldquoSignal processingtechniques in network-aided positioning a survey of state-of-the-art positioning designsrdquo IEEE Signal Processing Magazinevol 22 no 4 pp 12ndash23 2005

[7] T Roos P Myllymaki H Tirri P Misikangas and J SievanenldquoA probabilistic approach to WLAN user location estimationrdquoInternational Journal of Wireless Information Networks vol 9no 3 pp 155ndash164 2002

[8] R Battiti T L Nhat and A Villani ldquoLocation-aware com-puting a neural network model for determining location inwireless LANsrdquo Technical Report DIT-02-0083 Department ofInformation and Communication Technology University ofTrento Trento Italy 2002

[9] M Simic and P Pejovic ldquoAn algorithm for determining mobilestation location based on space segmentationrdquo IEEE Communi-cations Letters vol 12 no 7 pp 499ndash501 2008

[10] Z-L Wu C-H Li J K-Y Ng and K R P H Leung ldquoLocationestimation via support vector regressionrdquo IEEE Transactions onMobile Computing vol 6 no 3 pp 311ndash321 2007

[11] P Bahl and V N Padmanabhan ldquoRADAR An in-buildingRF-based user location and tracking systemrdquo in Proceedingsof the 19th Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo00) pp 775ndash784March2000

[12] A Kupper Fundamentals of Positioning in Location-BasedServices Fundamentals and Operation John Wiley and Sons2005

[13] B Li J Salter AGDempster andC Rizos ldquoIndoor positioningtechniques based on wireless LANrdquo in Proceedings of theAuswireless Conference 2006

[14] R BattitiM Brunato andAVillani ldquoStatistical learning theoryfor location fingerprinting in wireless LANsrdquo Technical ReportDIT-02-0086 Department of Information CommunicationTechnology University of Trento Trento Italy 2002

International Journal of

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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



Signal propagation in indoor environments is a complexprocess and propagation modeling requires large numberof input parameters Building type infrastructure wallthickness windows layout and size of the rooms all havesignificant influence on signal propagation Even knowledgeof all these parameters cannot guarantee good estimation ofthe RSS because the number and position of people movingwithin the building also affect the signal level Therefore themost challenging issue for indoor positioning based on RSSparameter is the unstable RSS value due to the multipatheffect caused by reflection diffraction and diffusion on theindoor scattering-rich walls which causes a time-varyingRSS even at a fixed location [5] However despite numerousdrawbacks RSS parameter is the most common choice forpositioning in indoor environment mainly due to lack ofalternative

Complex indoor radio propagation in practice reducesthe indoor positioning techniques to two the locationproximity (also known as Cell-ID) and fingerprinting [6]Cell-ID is the simplest positioning technique based on thefact that the location of the nearest transmitter (in case ofWLAN location of the access point AP) is assigned to anunknown userterminal location This method has all theadvantages and only one drawbackmdashpoor accuracy Finger-printing technique ismore complex compared to Cell-ID butincreases positioning accuracy Location fingerprinting refersto techniques thatmatch the fingerprint of a set of radio signalpropagation characteristics that are location dependent [1]

A number of various location fingerprinting-based posi-tioning algorithms are available probabilistic methods [7]neural networks [8] space segmentation [9] support vectormachines [10] and 119870 nearest neighbor (KNN) as one of thebasic algorithms [11] KNN uses the online RSS to search for119870 closestmatches of known locations in signal space from thepreviously built database By averaging these119870 location can-didates with or without adopting the distances in signal spaceas weights an estimated location is obtained [1]

The algorithm proposed in this paper improves precisionof WLAN positioning based on nearest neighbor finger-printing algorithms by applying optimization of the param-eters of the metric used to compute the difference in radiofingerprints Experimental results in a real indoor WLANenvironment show that the optimization of signal spacedistance computational parameters results in higher posi-tioning accuracy compared to the traditional approach

The rest of the paper is structured as follows Section 2illustrates basic principles for the location fingerprintingsystem Section 3 describes the optimization of the param-eters used to compute the difference in radio fingerprintsIn Section 4 we describe the experimental environmentSection 5 presents experimental results and analyses Finallythe conclusion is given in Section 6

2 Fingerprinting Positioning Algorithm

Fingerprinting is a positioning method that relies upon adatabase of collected location dependent radio signal param-eters that constitute a ldquofingerprintrdquo of a specific location

Location of the mobile unit is determined comparing a set ofradio signal parameters the mobile unit observes to availabledatabase

The first step in fingerprinting is to collect a set of locationdependent parameters of radio signals received by themobileuser (MU) from the access points The access points areassumed to have fixed spatial positions In WLAN thelocation-dependent parameter readily available is the valueof the received signal strength of available access points at theconsidered point in space To build the database of locationfingerprints in the area of interest a set of reference points(RPs) has to be selectedThe RPs should be uniformly spreadin the area of interest [12] that is the area in which thepositioning service is being implemented This area is alsocalled the ldquotest bedrdquo area [13]

The process of collecting the database of fingerprints isnamed the training phase Result of the training phase is thedatabase containing a set of 119899RP coordinates (119909RP119896 119910RP119896) 119896 isin1 119899RP accompanied by the corresponding ordered setof observed RSS levels that originate from all of the availableaccess points indexed by 119894 119894 isin 1 119899 The set of measuredRSS levels is conveniently stored in a vector

997888997888rarrRSSRP119896 = [RSSRP1198961RSSRP1198962 RSSRP119896119899] (1)

The vector 997888997888rarrRSSRP119896 is a fingerprint of the location specified by(119909RP119896 119910RP119896)

After the system is trained that is the database offingerprints that correspond to the RPs is collected in thepositioning phase of the algorithm for each positioningrequest the mobile unit measures the vector of RSS param-eters it observes 997888997888rarrRSSMU

997888997888rarrRSSMU = [RSSMU1RSSMU2 RSSMU119899] (2)

and compares it to the database obtained in the training phaseof themethod An appropriate algorithmdetermines locationof the mobile unit which is the most likely

21 Metric for the Difference in Radio Fingerprints Manyalgorithms can be used to estimate position of the mobileunit The basic one is the nearest neighbor in signal space(NNSS or NN) [11] First the signal distance between the RSSvector observed by the mobile unit (2) and the RSS vectorsin the database (1) is computed In this paper we proposegeneralized signal space distance defined as

119871119902119898 = (

119899

sum

119894=1

1003816100381610038161003816RSSRP119898119894 minus RSSMU1198941003816100381610038161003816

119902)

1119902

(3)

where 1 le 119898 le 119899RP and 119899RP is the number of RPs available inthe database For 119902 = 2 generalized distance of (3) reducesto the Euclidean distance while for 119902 = 1 the distance isthe Manhattan distance The metric maps a difference of RSSvectors to a single real number

After the signal space distances from the observed RSSvector to the vectors available in the database are computedthe minimum is found

119871119902 min = min1le119898le119899RP

119871119902119898 (4)



119871119902119897 = 119871119902 min (5)


(119909MU 119910MU) = (119909RP119897 119910RP119897) (6)


119909MU =1

119870

119870

sum

119894=1

119909RP 119878NN 119894

119910MU =1

119870

119870

sum

119894=1

119910RP 119878NN 119894

(7)



119909MU =sum119870

119894=1((1119871119902119878NN 119894

) 119909RP 119878NN 119894)

sum119870

119894=1(1119871119902119878NN 119894

)

119910MU =sum119870

119894=1((1119871119902119878NN 119894

) 119910RP 119878NN 119894)

sum119870

119894=1(1119871119902119878NN 119894

)

(8)













AP1 AP2 AP3 AP4

AP5AP6 AP7

AP8


0 200 400 600 800 1000 1200 1400 1600d (cm)

0

2

4

6

8

10

12

14

16

n





120575 =1

119873

119873

sum

119894=1


2 (9)


0 200 400 600 800 1000 1200 1400 16000

2

4

6

8

10

12

14

16

d (cm)

n






1

12

14

16

18

2

minus70minus90

minus110minus130


Mea

n po

sitio

ning

erro

r (cm

)

260

300

340

380

420



119870120575 (cm)

KNN KWNN2 48877 440293 52820 478504 62025 526425 70762 55466





119870120575 (cm)

KNN KWNN2 25289 283373 29693 331174 37639 376445 49648 44414


119870 119902 noAP (dBm)





6 Conclusion




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119871119902119897 = 119871119902 min (5)


(119909MU 119910MU) = (119909RP119897 119910RP119897) (6)


119909MU =1

119870

119870

sum

119894=1

119909RP 119878NN 119894

119910MU =1

119870

119870

sum

119894=1

119910RP 119878NN 119894

(7)



119909MU =sum119870

119894=1((1119871119902119878NN 119894

) 119909RP 119878NN 119894)

sum119870

119894=1(1119871119902119878NN 119894

)

119910MU =sum119870

119894=1((1119871119902119878NN 119894

) 119910RP 119878NN 119894)

sum119870

119894=1(1119871119902119878NN 119894

)

(8)













AP1 AP2 AP3 AP4

AP5AP6 AP7

AP8


0 200 400 600 800 1000 1200 1400 1600d (cm)

0

2

4

6

8

10

12

14

16

n





120575 =1

119873

119873

sum

119894=1


2 (9)


0 200 400 600 800 1000 1200 1400 16000

2

4

6

8

10

12

14

16

d (cm)

n






1

12

14

16

18

2

minus70minus90

minus110minus130


Mea

n po

sitio

ning

erro

r (cm

)

260

300

340

380

420



119870120575 (cm)

KNN KWNN2 48877 440293 52820 478504 62025 526425 70762 55466





119870120575 (cm)

KNN KWNN2 25289 283373 29693 331174 37639 376445 49648 44414


119870 119902 noAP (dBm)





6 Conclusion




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










AP1 AP2 AP3 AP4

AP5AP6 AP7

AP8


0 200 400 600 800 1000 1200 1400 1600d (cm)

0

2

4

6

8

10

12

14

16

n





120575 =1

119873

119873

sum

119894=1


2 (9)


0 200 400 600 800 1000 1200 1400 16000

2

4

6

8

10

12

14

16

d (cm)

n






1

12

14

16

18

2

minus70minus90

minus110minus130


Mea

n po

sitio

ning

erro

r (cm

)

260

300

340

380

420



119870120575 (cm)

KNN KWNN2 48877 440293 52820 478504 62025 526425 70762 55466





119870120575 (cm)

KNN KWNN2 25289 283373 29693 331174 37639 376445 49648 44414


119870 119902 noAP (dBm)





6 Conclusion




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

12

14

16

18

2

minus70minus90

minus110minus130


Mea

n po

sitio

ning

erro

r (cm

)

260

300

340

380

420



119870120575 (cm)

KNN KWNN2 48877 440293 52820 478504 62025 526425 70762 55466





119870120575 (cm)

KNN KWNN2 25289 283373 29693 331174 37639 376445 49648 44414


119870 119902 noAP (dBm)





6 Conclusion




Acknowledgment


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









research article multidimensional optimization of signal space...

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