Properties of Indoor Received Signal Strength for WLAN Location Fingerprinting

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1 Propertes of Indoor Receved Sgnal Strength for WLAN Locaton Fngerprntng Kamol Kaemarungs and Prashant Krshnamurthy Telecommuncatons Program, School of Informaton Scences, Unversty of Pttsburgh E-mal: Abstract Indoor postonng systems that make use of receved sgnal strength based locaton fngerprnts and exstng wreless local area network nfrastructure have recently been the focus for supportng locatonbased servces n ndoor and campus areas. A knowledge and understandng of the propertes of the locaton fngerprnt can assst n mprovng desgn of algorthms and deployment of poston locaton systems. However, most exstng research work gnores the rado sgnal propertes. Ths paper nvestgates the propertes of the receved sgnal strength reported by IEEE 82.b wreless network nterface cards. Analyses of the data are performed to understand the underlyng features of locaton fngerprnts. The performance of an ndoor postonng system n terms of ts precson s compared usng measured data and a Gaussan model to see how closely a Gaussan model may ft the measured data. Keywords: ndoor, measurement, modelng, postonng system, wreless LANs. Introducton Indoor postonng systems that use locaton fngerprnts and exstng wreless local area network (WLAN) nfrastructure have been demonstrated for ndoor areas [] where the global postonng system (GPS) does not work well [2]. The fngerprntng technque s smple to deploy compared to technques usng angle of arrval (AOA) and tme dfference of arrval (TDOA). Instead of dependng on accurate estmates of angle or dstance to determne the locaton, locaton fngerprntng assocates locatondependent characterstcs such as the receved sgnal strength (RSS) wth a locaton and uses these characterstcs to nfer the locaton. In ths case, there s no need for specalzed hardware at the moble staton (MS) besdes the wreless network nterface card (NIC) and the exstng WLAN nfrastructure can be reused easly. Before a postonng system can estmate the locaton, a locaton fngerprnt database or a rado map [3] must be constructed. Each entry n the database s a mappng between a poston and a locaton fngerprnt. The locaton fngerprnt can be an average value as n the RADAR system [] or probablstc [3]. In the average approach that we consder n ths paper, the locaton fngerprnt s a vector R of the average RSS values from multple access ponts (APs) at a partcular locaton L. A typcal vector R = (r, r 2,, r N ) conssts of N RSS values from N APs. The rado map contans all such RSS vectors for a grd of locatons n the ndoor area. For postonng, a MS obtans a sample RSS vector P = (, 2,, N ). The Eucldean sgnal dstance between the P and R for each R n the database s computed. The locaton s then estmated to be that L for whch the Eucldean dstance s the smallest. Note that the vector P s random. An error s made when the smallest Eucldean dstance occurs for a locaton L that s not the one at whch the sample P was collected. Errors occur because the measured RSS vector s a sample of a random vector whle only the average RSS vector s stored n the rado map. Understandng the statstcal propertes of the locaton fngerprnt (RSS vector) s mportant for the desgn of postonng systems for several reasons. It can provde nsghts nto how many access ponts are needed to unquely dentfy a locaton [3] wth a gven accuracy and precson, whether preprocessng of the RSS measurements can mprove the accuracy and so on. Exstng lterature on ndoor postonng systems focuses manly on the accuracy performance and mprovement of the locaton estmaton algorthm and gnores the study of the RSS random vector. Knowledge of the RSS propertes can n fact enable the development of better algorthms to classfy a measured RSS vector P as belongng to a partcular

2 z z locaton L. Although a varety of statstcal rado propagaton models exst, they were developed wth sgnal coverage, communcatons capablty and data rate n mnd. Moreover, the relatonshp between RSS values from multple APs s not understood very well. The dstrbuton of RSS values, ther standard devaton, ther temporal varaton, and the (n)dependence of RSSs from multple access ponts (APs) are mportant for understandng and modelng the performance of fngerprnt based ndoor postonng systems. For nstance, the dstrbuton of the RSS s sad to be normally dstrbuted n dbm accordng to the study n [5]. However, our prelmnary study and the study n [6] showed otherwse. Ths artcle presents data analyses of the RSS n an ndoor envronment wth postonng n mnd. Secton 2 descrbes the measurement setup. Secton 3 explores the effect of user s body, the effect of user s orentaton, the statonarty and tme-dependence, and the dstrbuton of the RSS. The ndependence of the RSS from multple APs s also analyzed n Secton 3. An approxmate model for the RSS s appled to the study of the precson performance of postonng systems n Secton 4 to evaluate the sutablty of a Gaussan approxmaton. We conclude the paper n Secton Measurement setup A standard laptop computer equpped wth an Ornoco WLAN card and clent manager software was used to collect samples of RSS from APs nsde the School of Informaton Scences (IS) buldng at the Unversty of Pttsburgh. The WLAN card s plugged nto the PCMCIA slot on the rght sde of the laptop. The buldng has 8 floors and APs nstalled opportunstcally. The dmenson of each floor s approxmately 76 ft 2 ft (23 m 37 m). All APs are from Lucent s WAVELAN and are equpped wth Ornoco WLAN cards. The rado frequency channels of IEEE 82.b are n the 2.4 GHz band whch s shared by other equpment n the ndustral, scentfc, and medcal (ISM) band such as Bluetooth. The number of non-overlappng channels for 82.b s three [7]. We observe that the RSS value reported by the WLAN card s an average value over a samplng perod and n ntegral steps of dbm. The receved sgnal senstvty of the WLAN card also lmts the range of the RSS to be between -93 dbm and dbm [8]. Nevertheless, the hghest typcal value of the RSS s approxmately -3 dbm at one meter from any AP. The clent manager software s a ste survey tool whch provdes the lnk qualty and AP montorng capabltes. 2.. Expermental desgn The measurement n each of the studes n Secton 3.2 s done by samplng the RSS data every one second. The vector of RSS data at each locaton forms the locaton fngerprnt wth at most three RSS elements n the vector. Four locatons of measurement are chosen on the fourth floor of the IS buldng as shown n Fgure denoted as L, L2, L3, and L4. The user s orentaton corresponds to the arrows at each locaton n ths fgure. The locatons of APs on ths floor are labeled as SIS4, SIS4, and SIS48. The rado channels used for each AP are channel, 6, and, respectvely. There s one more AP on the ffth floor labeled as SIS5 wth channel number 6, but there s no AP on the thrd floor. The MS has a drect lne-ofsght to one of the APs only at L2. The data were collected four tmes wth a perod of approxmately one hour each for every locaton and at dfferent hours of the day. The total number of RSS samples would be 4 locatons 4 hours 3 APs = 48. However, n our experments only 46 RSS data samples were collected because at L we can receve sgnals from only two APs at best SIS GIS Lab North UP DN 4a L 496 SIS 4 4-Wreless Lab L2 L3 z UP SIS 5 DN SIS L4 z 4 Fgure. The fourth floor of the IS buldng wth the locatons of APs and the orentaton of measurements 3. Propertes of the receved sgnal strength Indoor rado propagaton s dffcult to predct because of the dense multpath envronment and propagaton effects such as reflecton, dffracton, and scatterng [9]. Multpath fadng causes the receved sgnal to fluctuate around a mean value at partcular locaton. The receved sgnal s usually modeled by the combned effects of large-scale fadng and small-scale fadng []. The large-scale-fadng component (of nterest here) descrbes the sgnal attenuaton as the 42

3 sgnal travels over a dstance and s absorbed by materal such as walls and floors along the way to the recever. Ths component predcts the mean of the RSS and usually has a log-normal dstrbuton []. Small-scale fadng explans the dramatc fluctuaton of the sgnal due to multpath fadng. If there s no lneof-sght (NLOS) component, the small-scale fadng s often modeled wth a Raylegh dstrbuton. If there s a lne-of-sght (LOS) component, the small-scale fadng s modeled wth a Rcan dstrbuton. However, these models are focused on understandng the mpact of rado propagaton on recever desgn and sgnal coverage rather than from the perspectve of ndoor postonng systems. The nvestgaton of RSS data n ths secton s dvded nto four parts. All measurements were done at fxed locatons. Frst, we consder the effect of the user s presence on a sngle RSS set (ths s the set of RSS samples from one AP at a fxed locaton obtaned over tme). Second, we nvestgate the statstcal propertes of a sngle RSS set (the dstrbuton, the statonarty, the tme-of-day dependency, etc.). Thrd, we study the propertes of multple RSS sets (bascally RSS values from multple APs). We evaluate whether each RSS set s ndependent from the others and whether they all exhbt the same statstcal propertes. We also observed that n some locatons the sgnal from certan APs s not present all the tme. Fnally, we compare the dfferences between the RSS fngerprnts (these are vectors wth RSS sets as ther components) of two locatons. 3.. Effects of user s presence on RSS In ndoor postonng systems based on WLANs, the user typcally carres the moble staton equpped wth a wreless NIC. The effect of the user s presence close to the antenna plays a sgnfcant role n the mean value and the spread of the average RSS values. An observaton was made n [] that the user s orentaton caused a varaton n RSS level up to 5 dbm Effect of user s body. To study the effect of the user s body, we performed measurement of the sgnal from SIS4 at locaton L nsde the room IS 4a n Fgure. The dstance between the transmtter (AP) and the recever (MS) s approxmately 7 m and the MS does not have a clear lne-of-sght to the AP. The data were recorded for two hours. Durng frst hour, the user was present, whle no user was present n the second hour. The results were analyzed by plottng hstograms of the RSS for both hours. The results are shown n Fgure 2. Frequency Frequency (a) Dstrbuton of RSS when user s present Average receved sgnal strength n dbm (b) Dstrbuton of RSS when user s not present Average receved sgnal strength n dbm Fgure 2. Comparson of hstograms of RSS Fgure 2-a and 2-b depct the dfference between these two dstrbutons. The user s body nfluences the RSS dstrbuton by spreadng the range of RSS values by a sgnfcant amount. The standard devaton s ncreased from approxmately.68 dbm to 3. dbm when the user s present. The mean changes from dbm to -7.6 dbm wth the user s body present. Clearly, t s essental to collect data for the rado map based on the applcaton. When the postonng system s supposed to cater to real users, t s essental to have the user present whle collectng the RSS values for the fngerprnt and to take nto account the effect of human s body. For applcatons that make use of sensors wthout a human presence the data should reflect that envronment Effect of user s orentaton. Because the resonance frequency of water s at 2.4 GHz and the human s body conssts of 7% water, the RSS s absorbed when the user obstructs the sgnal path and causes an extra attenuaton [6]. To study the effect of user s orentaton, we performed another measurement at the locaton L2 nsde the room IS 4 n Fgure. In ths case, there s a lne-of-sght between the transmtter (SIS4) and recever and the dstance between them s approxmately 2 ft (6 m). Sgnals from SIS4 and SIS5 were also present at ths locaton wth non lne-of-sght dstances of 36 ft ( m) and 22 ft (7 m), respectvely. The measurement was done wth four orentatons (facng North, West, South, and East of the buldng) for a perod of 5 mnutes each. The results of the statstcs of the RSS values from the three transmtters are shown n Tables, 2, and 3. The orentatons that user body blocks the drect path between the AP and MS are marked wth astersks.

4 Table. LOS RSS (dbm) from SIS4 wth dfferent orentaton Statstcs North West South* East Sample Mean Standard Devaton Skewness For the LOS case (Transmtter SIS4) n Table, when the user was facng south and the AP was behnd the user, the sample mean of the RSS was lower at dbm compared to the hghest RSS of dbm when the user faced west. The results show that the RSS can be attenuated by 9.32 db n our case due to the obstructon from the body. Ths suggests that the user s orentaton s crucal and should be ncluded n computng the user locaton nformaton as ponted out n []. The attenuaton by the body of the user can even completely block the RSS from a NLOS AP as shown n Table 2 when there was no RSS nformaton at all durng the perod that the person s back was turned towards the transmtter SIS4. Ths means that the locaton fngerprnt at the same locaton may lack one RSS value n the vector f the user s orentaton s dfferent. The sgnal from SIS5 s also attenuated by 5.8 db between the hghest and the lowest RSS levels n Table 3. Table2. NLOS RSS (dbm) from SIS4 wth dfferent orentaton Statstcs North West* South East Sample Mean N/A Standard Devaton.84 N/A Skewness.5 N/A.9 -. Table3. NLOS RSS (dbm) from SIS5 wth dfferent orentaton Statstcs North West* South East Sample Mean Standard Devaton Skewness In what follows, we restrct the study and focus on the RSS propertes when the user s present and facng one drecton arbtrarly Statstcal propertes of the RSS Tradtonally, the average RSS s beleved to be log-normally dstrbuted accordng to popular largescale fadng models []. The mean value s generally predctable and beleved to follow one of several standardzed path loss models dscussed n [9]. However, there are some conflctng conclusons regardng the RSS dstrbuton measured at the software level by the wreless NIC for ndoor rado propagaton n [5] and [6]. Moreover, the standard devaton and the statonarty of the RSS are not understood very well Dstrbuton of receved sgnal strength. The results n [5] are based on a fve second samplng perod over long duratons of fve hours, 2 hours, and one month. Here, they conclude that the RSS s lognormally dstrbuted (normal or Gaussan n db) due to the smlarty of the medan, the mean, and the mode. However, they dd not ndcate whether the user was present all the tme durng the measurements. Thus, we suspect that the dstrbuton of the RSS n db that could be observed n realty may not be normally dstrbuted as descrbed n [5]. A recent study of a 45- second measurement perod wth the user s presence n [6] ponted out that the RSS dstrbuton was non- Gaussan and asymmetrc. Moreover, the hstograms n [6] depcted that there could be multple modes wth one domnant mode n the dstrbuton. The means and the modes were often dfferent n ther results. The results of our experment showed a smlar trend as n [6]. The hstogram n Fgure 2-a has two modes wth one domnant mode when the user s present. A vsual test of Fgure 2-a confrms that the RSS does not come from a normal dstrbuton and a norm-plot test s also nonlnear. Out of the 46 RSS elements that we collected from four locatons (L to L4), most of the hstograms show that the RSS does not ft the normal dstrbuton. Only a few hstograms showed a good normal approxmaton. We observed that the RSS dstrbuton tended to be left-skewed n our measurement results. The hstograms that are strongly left-skewed are usually the ones wth the strongest RSS out of the three APs at a partcular locaton. The dstrbuton of RSS wth the user n Fgure 2-a s also skewed to the left. The leftskew property seems to occur n most of our measurements as reported by the skewness n Tables, 2, and 3. Ths property s usually observed when the data have an upper bound whch s the case for the attenuated RSS measurement. In a comparson of the 46 dstrbutons, we saw that 39 of them had dstrbutons that were left-skewed whle fve of them were almost symmetrc and only two of them were rght-skewed. The left-skew s the effect of the range lmtaton mposed by the maxmum RSS at each locaton. Because of the complexty of the rado propagaton, the dstrbuton of RSS s dffcult to model and ft to well-known dstrbutons. The authors n [6] conclude that they rather record the dstrbuton of the RSS than reduce t to only the mean value. We

5 beleve that t would be a great beneft f we could fnd a representatve or approxmate dstrbuton of the underlyng RSS process for understandng locaton fngerprntng. Ths s part of our ongong research The standard devaton of the RSS. The results n Table, 2, and 3 also reveal an nterestng trend n the second order statstcs of the RSS values. The standard devatons are qute smlar for a sgnal from the same AP at a partcular locaton except when the user s orentaton blocks that AP. The man dfference between the three APs s the dstance to the measurement pont L2. Comparng the three tables, the results ndcate that the farther the AP s from the MS or the lower the receved sgnal level s, the smaller the degree of standard devaton. Note that wthn the same table the RSS data whch s blocked by the user has a smaller standard devaton. Ths occurs as a result of the sgnal attenuaton by the user s body and the smaller range of RSS between the maxmum and mnmum recevable sgnal level. A lnear regresson plot (Fgure 3) between the sample mean of the RSS and the standard devaton collected from 46 dstrbutons llustrates the trend. Ths observaton suggests that the RSS values from the same AP at two dfferent locatons may be dffcult to dstngush for postonng purposes when the RSS level s hgh n whch case t tends to have a large degree of varaton. A good communcatons sgnal may not result n a good postonng sgnal. On the other hand, two nearby locatons mght be easly dentfed f both have low RSS levels and smaller sgnal varatons. Ths good postonng case usually occurs n ndoor locatons wth NLOS. Ths s rather counter-ntutve snce the farther apart the WLAN recever s from the AP, the worse the measurement accuracy or the larger the sgnal varaton should be as suggested by [5]. Sample Standard Devaton n dbm Sample Mean RSS Lnear Regresson s Y =.497 X Sample Mean of RSS n dbm Fgure 3. The relatonshp between average RSS and ts standard devaton Statonarty of the RSS. Assumng that the ergodc theorem s appled accordng to the Wener defnton of statonarty [], we analyze the statonarty of the RSS element by breakng the seres of RSS measurements nto separate peces over dfferent tme ntervals. A random process s sad to be statonary when t meets two condtons. Frst, ts mean and varance reman the same over tme. Second, ts autocovarance functon has the same shape for each separate tme-seres. We nvestgated ths property over two tme scales: peces of 5 mnutes wthn the same hour and peces of one hour over fve dfferent hours. After dvdng the seres of measurement data of RSS n Fgure 2-a wthn the same hour nto groups of 5 mnutes, the RSS dstrbuton wthn each quarter s observed to follow a smlar dstrbuton wthn the same group. Table 4 lsts the summary statstcs wthn each quarter. These results suggest that the RSS dstrbuton may be statonary or tme ndependent snce the means and the sample varances of each quarter are very close together. The correlograms n Fgure 4 depct the same shapes for each quarter ndcatng that the second condton s also met for ths tme scale. Autocorrelaton Table 4. Mean and standard devaton of RSS wth user (dbm) Statstcs st Qtr. 2 nd Qtr. 3 rd Qtr. 4 th Qtr. Mean Standard Devaton Sample Varance Correlogram of st Quarter Tme lag n second Correlogram of 3rd Quarter Autocorrelaton Tme lag n second Autocorrelaton Correlogram of 2nd Quarter Tme lag n second Correlogram of 4th Quarter Autocorrelaton Tme lag n second Fgure 4. The correlograms of RSS wthn the same hour

6 The one-hour tme scale study was made for a sgnal measured at L over dfferent tmes of day. Table 5 shows a consstent mean, but nconsstent varance values of the RSS. Therefore, the test for the frst condton for statonarty fals and we conclude that the RSS random process n ths case s nonstatonary. Fgure 5 llustrates sample paths of average receved sgnal strength values from the three access ponts measured at locaton L3 over a perod of one hour. Observe that the sample mean from SIS4 abruptly changes to another value (-7 to -6 dbm) whch confrms our concluson on the non-statonary property. Ths s common due to the changng ndoor envronment such as n ths case when a person walked nto the room and sat n the mddle of the room IS 4 after approxmately 3 mnutes nto our experment. Notce that the rest of the receved sgnals from other APs located outsde the room are not affected by ths event. Although the statonary assumpton may not be vald over all tme scales, there s some evdence that we could assume statonarty over small tme scale for modelng purposes. Table 5. Tme dependency of RSS (dbm) from SIS4 wth user s presence Statstcs AM 2AM 2PM 8PM PM Mean Standard Devaton Sample Varance Average receved sgnal strength n dbm AP (ss4) AP2 (ss4) AP3 (ss5) Tme n second Fgure 5. Samples of RSS from three APs Tme dependency of receved sgnal strength. The summary of statstcs n Table 5 suggests that there s some dependency of RSS on the tme of day. Ths s due to the dynamcs of the ndoor envronment. To understand the property better, we requre more measurements and ths s part of our ongong research work Propertes of multple RSSs at a partcular locaton Ths subsecton analyzes the dependency of multple RSSs from multple APs. Ths s to confrm an ntuton that the RSS from multple APs are actually ndependent. The second part of ths subsecton dscusses the effect of nterference on the RSS when there s another AP transmttng n the same frequency channel Independence of multple RSSs. The average of the RSS from each AP s a value of a locaton fngerprnt vector. To verfy statstcal ndependence between these values, a measurement of multple RSS samples was collected at locaton 3 (L3) n Fgure where the MS can receve sgnals from three APs smultaneously durng an afternoon hour. The dstances from the three APs SIS4, SIS4, and SIS5 were approxmately 8, 5, and meters. We took RSS measurements for approxmately one hour wth the user s presence and the sample paths of RSS levels are showed n Fgure 5. The standard devatons from each AP were 5.67, 2.23, and.8, respectvely. The means were , -8.23, and dbm. The correlaton values between each par of RSS data are C (SIS4,SIS4) = -.2, C (SIS4,SIS5) =.3, C (SIS4,SIS5) = -.3. Therefore, we can conclude that the RSS from the APs are uncorrelated Interference from multple APs. There are two APs n our experment that use the same frequency channel number 6, whch are SIS4 and SIS5. One may thnk that the RSSs from both APs mght nterfere wth each other and cause dffculty n formng the locaton fngerprntng. However, our ntal results as calculated by the correlaton ndcate that both RSSs are ndependent and do not nterfere wth the recepton of each other. Ths s due to the way n whch the 82. MAC operates where a transmsson s ether not heard or s deferred f a competng transmsson exsts Propertes of RSS at dfferent locatons Generally, the RSS falls lnearly wth the log of the dstance between the transmtter and the recever. Ths subsecton wll not focus on ths common knowledge but wll nstead nvestgate how the samples of RSS fngerprnts at dfferent locatons may look lke. We plot the RSS patterns n two dmensons n order to analyze the clusterng of the RSS data. The clusterng of two RSS data at two locatons s plotted n Fgure 6.

7 RSS of SIS4 n dbm Locaton 2 Locaton RSS of SIS4 n dbm Fgure 6. RSS fngerprnts wth two elements The plot n Fgure 6 contans all possble vectors P = [ 2 ] for L2 and L3 wth on the x-axs and 2 on the y-axs. We see that the locaton fngerprnts can be separated by some dscrmnant functon or clusterng technque. Note that L3 conssts of 3,666 samples and L2 conssts of 3,465 samples. Only certan patterns are present whch mples that there are fewer unque fngerprnts for each locaton. Fgure 7 shows the densty of each fngerprnt. Ths vsual study suggests that we may use the center of the cluster as a representaton of the locaton fngerprnt nstead of the dstrbuton tself as these locatons can be clearly separated. Fgure 7 suggests that only two APs are suffcent to dstngush between locatons for a system wth small number of postons and coarse locaton granularty. Two locatons become dffcult to dentfy f ther patterns are closer together and exhbt large varatons due to the nature of standard devaton of the RSS. Increasng the number of APs s one way to further separate two locaton fngerprnts. Frequency ss4 (dbm) L L2 6 5 ss4 (dbm) Fgure 7. Frequency of occurrence of RSS patterns Implcatons on postonng algorthms The data analyses n the prevous secton have two major mplcatons on selectng potental postonng algorthms. Frst, we observed that the RSS sample vectors exhbt clusterng (they are concentrated around the center of a cluster wth the greatest frequency of occurrence beng roughly at the center as n Fgure 7). Ths explans why the accuracy performance of all postonng algorthms evaluated n [2] s smlar. Both the support vector machnes (SVMs) approach and the k-nearest neghbors (or equvalently Eucldean dstance) approach provde smlar accuracy and precson. The reason s that locaton fngerprnts can be smply represented by vectors of average RSSs. Second, to perform any analytcal performance evaluaton of pattern classfers, we eventually need a model of locaton fngerprnts. In the followng secton we suggest a smple model of locaton fngerprnts and compare t wth the emprcal ones from ths study based on our prevous work n [3]. 4. Modelng of RSS for locaton fngerprnts and performance of the Eucldean dstance Although our prelmnary fndng suggests that the RSS dstrbuton s not normal, some of them could be approxmated by a normal dstrbuton. In an attempt to model ndoor postonng systems [3], we assumed a frst cut Gaussan model of the RSS. A locaton fngerprnt s denoted as a vector of N features of RSS, e.g. X = (x, x 2,, x 3 ). Here, we lst the assumptons made n [3] that are partally supported by the work here. Each RSS feature n fngerprnt s normally dstrbuted and statonary over a small tme scale. The sample standard devatons of all RSS features are assumed to be constant and unque for each RSS. (We dd not model the varaton n standard devaton for each RSS feature.) The mean of the RSS can be used as the fngerprnt as samples of the RSS vector exhbt clusterng. All RSS features n each locaton fngerprnt are mutually ndependent (whch s confrmed by our measurement n Secton 3.3). We compare the locaton estmaton performance usng ths smplfed model wth the one usng emprcal dstrbutons obtaned from the measurement results of ths paper. The smple locaton estmaton algorthm utlzes the Eucldean dstance. The number of access ponts N s three. The mathematcal

8 expresson for the accuracy was developed n [3]. We use the expressons to predct the performance of two smplfed postonng systems n ths secton. 4. Two-locaton system As an example of a system wth only two locaton fngerprnts, we select the measurement data of locatons L2 and L3 for analyss. Note that these are ncely dstngushable. Let R = (r, r 2,, r 3 ) and S = (s, s 2,, s 3 ) be the locaton fngerprnts (mean values of the RSSs from the APs) of L2 and L3, respectvely. The actual physcal dstance between the two locatons s 8 ft (5.5 m). Table 6 summarzes the locaton fngerprnts and ther standard devatons. Table 6. Fngerprnts of two-poston system (dbm). Locaton Statstcs SIS4 SIS4 SIS5 L2 Mean STD L3 Mean STD Usng a Monte Carlo smulaton to generate the samples of locaton fngerprnts based on the emprcal dstrbutons, we compare the error of locaton detecton gven that L2 s the correct locaton wth the analytcal mathematcal formulaton n [3] and smulatons wth a Gaussan dstrbuton wth the same means and standard devatons. The probablty of ncorrectly pckng locaton L3 nstead of L2 s Pe. For a system wth two postons, Pe can be found from the probablty of returnng the correct locaton (Pc) as: c Pe Pc erf, () c N 2 c 2r c 2 2 s r, and r s N where,, N ( 2 ) 2. We performed 2 smulatons of, samples each. The results are summarzed n Table 7. The Gaussan approxmaton provdes an optmstc error performance for the system. The analytcal result from () exactly calculates Pe. The emprcal dstrbutons have a worse performance because there are some samples of RSS fngerprnts that are closer to the locaton L3 s fngerprnt than L2 s fngerprnt. Fgure 6, whch represents the projecton of all fngerprnts nto the plane of two features, clearly explans the cause of the worse performance because there are some RSS patterns on the left-sde of the plot that may be wrongly nterpreted as correspondng to L3. Table 7 also shows the results when we consder only two APs (SIS4, SIS5) and one AP (SIS4) n whch the error probabltes are hgher. Table 7. Probablty of returnng ncorrect locaton at 95% C.I. for two-locaton system. Scenaro 3 APs 2 APs AP Emprcal.22e e-5.79e-3 3.2e-5 6.9e e-5 Gaussan.24e e-6.4e e e-3 4.6e-5 Analytcal.24e-3.4e-3 7.5e Twenty fve-locaton system The second system we consder conssts of 25 locaton fngerprnts where we measured the real locaton fngerprnts from a grd of 25 postons. The grd spacng s approxmately meter. The locaton area of 6 m 2 covers part of the room IS4 and part of the corrdor as showed n Fgure 8. Each poston s labeled by the square box North Soft Wall Room IS Fgure 8. Grd of system wth 25 locatons Due to space lmtaton, we wll not lst the measured locaton fngerprnts here. Note that the measurement s done for only one orentaton of the user (facng north). Each poston can receve sgnals clearly from all three APs (SIS4, SIS4, SIS5) and there are approxmately,2 samples of each RSS measured over fve mnutes at a rate of four samples per second. We assume that the current MS s locaton s at the center of the map. A smulaton was done n the same manner as the two locaton system. The results are summarzed n Table 8. In order to fnd the exact analytcal expresson, we need to fnd the jont probablty densty of multple locaton fngerprnts whch s rather cumbersome. We argue n [3] that ths can be avoded by resortng to an approxmaton

9 of the probablty of returnng an erroneous locaton. Ths consders only the locaton fngerprnts of M N = 8 nearest neghborng postons n two-dmensons and the correct locaton. The approxmaton works for a large number of access ponts and can be wrtten as: Pe Pc j. (2) jm N Table 8. Probablty of returnng ncorrect locaton at 9% C.I. for 25 locatons. Scenaro 3 APs 2 APs AP Emprcal.67.46e e e-3 Gaussan.85.67e e e-3 Approxmaton The overall performance results n ths system are worse than the prevous one because there are more locatons to be compared wth and the spacng between the locatons s much closer. Dependng on the standard devaton of each RSS feature, t s possble that the fngerprnt patterns overlap. The results wth a Gaussan model are worse than those wth the emprcal model and appear to be rather pessmstc n ths case. Ths can be explaned as follows: the Gaussan model tends to spread the fngerprnt patterns evenly around the mean value whle the real fngerprnt patterns are asymmetrc and more concentrated around ther means n some cases. The analytcal approxmaton s hghly pessmstc and not approprate n ths case. In summary the Gaussan model provdes a probablty of an erroneous report on the same order as one would expect wth real RSS samples, but could be ether optmstc or pessmstc. 5. Conclusons We present an ntal analyss of the RSS values reported by an 82.b NIC commonly used n ndoor locaton systems based on locaton fngerprntng. We pont out that the user s presence should be taken nto account when collectng the locaton fngerprnt for user related locaton-based servces. The effect of user s orentaton s sgnfcant and the orentaton should be recorded n the database as demonstrated n []. We also analyze the statstcal propertes of the RSS and we fnd that t s statonary under certan crcumstances, but n general, such a concluson cannot be made. The dstrbuton of the RSS s not usually Gaussan, t s often left-skewed and the standard devaton vares accordng to the sgnal level. It s clear from our measurements that sgnals from multple APs are mostly ndependent and the nterference from other APs usng the same frequency does not have a sgnfcant mpact on the RSS pattern. The vsual presentatons of the RSS patterns n Secton 3.4 show that the fngerprnt can be grouped together as a set of clusters. More than one cluster may represent one locaton because of the multmodal dstrbuton of the RSS. In such a case, usng a smple Eucldean dstance as n [] to determne the locaton may classfy some patterns nto a wrong locaton easly. Ths causes poor performance of a postonng system that uses the Eucldean dstance. Fnally, n the last secton, we compare the error performance of a poston locaton system wth real locaton fngerprnts and a frst cut Gaussan model. The results ndcate that our model of locaton fngerprnts provde some approxmatons of the performance. The Gaussan model s ether optmstc or pessmstc but provdes values on the same order as a real system. The future work s to look for alternatve models for the dstrbuton of the RSS and to understand how they mpact poston locaton further. The results n ths paper and our prevous work could provde nsght on the mechansm behnd ndoor poston locaton systems based on locaton fngerprntng. In concluson, ths study steps back and nvestgates the RSS pattern n a greater detal. Ths study rases an mportant aspect of desgnng a locaton fngerprntng system that s to examne the propertes of the fngerprnt tself before applyng a pattern recognton technque to solve the postonng problem. Smple pattern recognton technques may be sutable and more effcent than more sophstcated ones. More extensve measurement campagns are needed to verfy some of the propertes lsted here. However, the lessons learned from ths study are used to support a theoretcal model of locaton fngerprnt whch n turn can be used to create a desgn framework of an ndoor postonng system [3]. Gven a framework and theoretcal explanaton, any future study and desgn of locaton fngerprntng system should be more effcent and less tme consumng. We could reduce the measurement tme n order to fne tune the system performance such as accuracy and precson to meet any requred crtera. 6. References [] P. Bahl and V. N. Padmanabhan, RADAR: An In- Buldng RF-based User Locaton and Trackng System, n Proc. IEEE INFOCOM, 2, pp [2] G. M. Djuknc, and R. E. Rchton, Geolocaton and Asssted GPS, IEEE Computer, vol. 2, pp , Feb. 2. [3] M. A. Youssef, A. Agrawala, and A. U. Shankar, WLAN Locaton Determnaton va Clusterng and

10 Probablty Dstrbutons, n Proc. IEEE PerCom, Mar. 23. [4] T. Roos et al., A Probablstc Approach to WLAN User Locaton, Int l Journal of Wreless Informaton Networks, vol. 9, pp , Jul. 22. [5] J. Small, A. Smalagc, and D. P. Seworek, (2, Dec.) Determnng User Locaton For Context Aware Computng Through the Use of a Wreless LAN Infrastructure. [Onlne at] aura/docdr/small.pdf. [6] A. M. Ladd et. al., Robotcs-Based Locaton Sensng usng Wreless Ethernet, n Proc. MOBICOM, 22, pp [7] The Insttute of Electrcal and Electroncs Engneers, Inc. IEEE Standards Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) specfcatons [8] Agere System Inc. (23, Feb.) Agere Product Bref: WaveLAN 82.b chp set. [Onlne] Avalable: [9] K. Pahlavan and P. Krshnamurthy, Prncples of Wreless Networks: A Unfed Approach, Prentce Hall PTR, Upper Saddle Rver, New Jersey, 22. [] B. Sklar, Raylegh fadng channels n moble dgtal communcaton systems: I. Characterzaton, IEEE Communcatons Magazne, vol. 35, pp. 9-, Jul [] J. M. Gottman, Tme-seres Analyss: A Comprehensve Introducton for Socal Scentsts, Cambrdge Unversty Press, New York, NY, 98. [2] R. Battt, M. Brunato, and A. Vllan. (22, Oct.) Statstcal Learnng Theory for Locaton Fngerprntng n Wreless LANs. Techncal Report DIT-2-86, Unverst a d Trento. [Onlne] Avalable: ~battt/archve/86.pdf [3] K. Kaemarungs, and P. Krshnamurthy, Modelng of Indoor Postonng Systems Based on Locaton Fngerprntng, n Proc. IEEE INFOCOM, May 24.