Analysis of the impact of some network parameters on the accuracy of RSS-based geometric positioning methods

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1 Analyss of the mpact of some netwok paametes on the accuacy of RSS-base geometc postonng methos Folasae.M. Dahuns 1, Bay Dwolatzky 1 an Anne Love School of Electcal an Infomaton Engneeng 1, School of Mathematcs Unvesty of Wtwatesan, Pvate Bag 3, Wts 5, South Afca emal:{ahuns.folasae@stuents.wts.ac.za 1, bay.wolatzky@wts.ac.za 1, anne.love@wts.ac.za } Tel: , Fax: Abstact: The accuacy of Receve Sgnal Stength (RSS)-base postonng methos s hghly vaable ue to ts epenence on vaous vayng paametes such as the weless envonment, topology of the netwok, popagaton moel utlze etc. In ths pape, smulate ata was analyze to examne the effect stances an numbe of BSs use has on postonng accuacy base on fou RSS-base geometc postonng methos. Thee s elatvely vayng ffeences that the topologes of the netwok have on the accuacy of the postonng algothms. The RSSbase Geometc algothms consee nclue the Cente of Gavty, the Cente of Tlateaton, the Least Squae an the Tlateaton algothms. Inex Tems: Receve Sgnal Stength, locaton accuacy, base statons, stance, geometc methos I. INTRODUCTION The Feeal Communcatons Commsson (FCC) of the Unte State of Ameca (USA) n 1996 aopte a epot that enfoce moble opeatos n the USA to pove an elve weless emegency sevce (E911) [1,]. A vaant of the USA s E911 was also ntouce n Euope by the Euopean Emegency foum n 3 enfocng locaton enhance 11 (E-11) emegency sevces. The E911 was a majo ve of locaton-base sevces (LBS) to enhance effectve locaton base emegency sevce elvey [] an to avo heavy fnes by the Govenment of the USA. Ths has lea to a we ange of eseach to exploe methos of povng accuate postonng of moble staton (MS) an mpove qualty of LBS povson to moble uses. In evelopng countes, most of the netwok nfastuctues ae GSM netwoks. Smat phones ae not affoable to most an only a few uban busness aeas have 3G coveage. Ths has lea moble opeatos to epen lagely on netwok-base postonng methos fo the povson of LBS to uses. Cuently most eseach cae out on postonng technologes s geae towas evelope countes. Lttle eseach s cae out on futhe mpovng netwok-base postonng methos whch mght be moe applcable n evelopng countes. RSS measuements ae ealy avalable to all MSs (pat of the hanoff algothm) wth no exta cost to the uses an lttle mofcaton on the moble opeato s netwok [4]. If the popagaton moel s known, powe measuements can be mappe to a stance measuement an LBSs can be mae avalable usng RSS-base postonng methos. The majo challenge wth RSS-base postonng algothms s the estmaton eo whch s hghe than obtane n othe localzaton methos whch utlze smat phones an/o satellte postonng. The movement of the MS also ntouces a fast fang eo facto to the measuements whch hampes mappng RSS measuements coectly to stance measuements. One of the majo postonng technques employe to etemne the locaton of the MS use the conventonal RSS metho. Geneally, the moble s sgnal s eceve at seveal eceves wth known postons. Afte ecepton, the stance chaactestcs of the sgnal ae combne wth the known postons of the eceves an ths nfomaton s use to solve the MS s poston. Ths pape nvestgates the elatonshp between stance an postonng eo estmate by usng some Receve Sgnal Stength (RSS)-base geometc postonng methos. The RSS-base metho wll fulfll the nee fo postonng n evelopng countes whee smat phones ae not ealy avalable an the majo netwok nfastuctue s GSM. [3]. II. RSS-BASED POSITIONING ALGORITHM A. RSS measuement moel/poblem Fomulaton RSS s a sgnal paamete such that powe o enegy of a sgnal tavellng between a BS an a MS contans nfomaton elate to the stance between them. A mathematcal elatonshp between the RSS an the path loss moel s use to estmate the stance [5, 6]. Conseng two mensonal postonng; let the tue locaton of the MS = [x m,y m ] T an the coonates of the th BS =[x,y ] T, = 1,.N. whee N s the total numbe of tansmttng BSs wth aequate eceve sgnal level qualty at the MS between 9Bm an -114Bm accong to GSM specfcatons [6]. The stance between the MS an th BS, enote by s gven by

2 = 1 ( xm x ) + ( ym y ) Whee = 1, N, numbe of heaable tansmttes The nose-fee RSS o eceve powe at the th BS, enote by P, s expesse n [5, 7] P P = k, = 1, N t Whee P t s the tansmtte powe, powe, s the popagaton constant, P s the eceve k enotes othe factos that affect the eceve powe nclung antenna heght, antenna gan, measuement nose etc. The ange elate measuement can then be moelle, as expesse n [8], by t P ˆ = k + n 3 = + n 4 ˆ = ( xm x ) + ( ym y ) + n, = 1, N 5 Whee n = measuement nose n by the th BS, s obtane by fnng the path loss slope by measuement [5, 7]. The effect of multpath popagaton (eflecton, ffacton, absopton an efacton) cannot be totally mtgate. B. Geometc RSS-base methos Geometc ntepetatons of etemnstc nfomaton fom the RSS measuements ae use to estmate the MS poston. The geometc appoach s futhe classfe nto empcal an popagaton moel base appoaches. The fome technque s base on gtal maps of a specfc aea an ths eques extensve on-ste measuements an calbatons. It s also computatonally ntensve, eque a lot of man powe an lose ts valty wth tme, because of changes n popagaton contons ove tme. The latte s consee n ths pape an eeme best to ft the nee of evelopng countes that ae often pose wth computatonal powe challenges an lack of aequate pofessonal expetse. Zhou et al (3) popose the algothm Cente of Gavty, whch we call the COG algothm fo locaton estmaton as the weghte mean of the locatons of the sevng BS an the neghboung BSs [8]. COG assumes that the elaton between RSS an the stance between the MS an the BS s base on an nvese squae law. The popotonalty elatonshp was as R -, whee s the popagaton constant taken nto account because of the envonmental facto, R s the eceve sgnal stength an s the stance between the MS an the BS. Cente of Tlateaton (whch we call the COT) appoach was also popose by Zhou et al. (3). Ths algothm was base on constuctng thee (3) ccles usng RSS an locaton of the tansmttng BSs. The ntesecton of the ccles s calculate to estmate the locaton of the MS [8]. It assumes that the popotonalty elatonshp between stance fom MS to BS an RSS s base on an nvese squae law, whch s (Ɲ + R) -, whee s the popagaton constant, Ɲ s the nomalzaton constant, R s the eceve sgnal stength at MS fom BS. Lneazaton base Least Squae (whch we call the LS) metho s utlze when the numbe of nepenent equatons s geate than the numbe of unknown paametes. The LS metho can be apple to optmze the eunant measuements to obtan mpove locaton estmates [9]. Tlateaton (whch we call the TRI) metho uses thee stance measuements fo thee BSs an the known locatons to calculate the unknown MS poston. Gven the stance measuement of each BS to the ecevng MS, the BS s locate at the cente of the stance aus an the MS can be locate somewhee on the ccle. In most cases, two ccles wll coss each othe at two ponts, poucng two solutons, a th ccle pouce by the th base staton nomally esolves the ambguty [9]. The fou afoe-mentone RSS-base algothms ae nvestgate n ths pape to analyze the effect the stance of the BSs elatve to the MS on the accuacy of the postonng algothms. It shoul be note that RSS measuements ae vey unelable n uban an bult up aeas ue to multpath an othe foms of ntefeence [9]. Ths s why ths pape s analyss s base on ual envonment wth bulngs spasely locate on even tean. The typcal cell sze of the ual envonment s between 1km an 35km [1]. A. System Smulaton III. METHODOLOGY. Cellula netwok The cellula system smulate n ths pape s a seven cell topology an each cell has a BS locate at ts cente an a cell aus of 3km. Ths s shown n Fgue 1. The BSs ae at the cente of each cell an ncate by tangles an the cell coveage by ccles. The BSs numbee 1 7 fo BS1- BS7 espectvely y BS6 BS x BS4 BS5 Fgue 1: Cellula netwok topology BS BS3 BS1

3 The stance between each BS s 3km whch s about thee quates of the cell sze, to allow fo ovelappng of the cells n oe to ensue that thee ae aeas whee all the cells ovelap, unlke the nomal hexagon cell shape. Due to the symmetcal natue of the cell aangements, the antenna chaactestcs at BS 1 wll be epesentatve of the values at the othe neghbong BSs. Only one MS s consee because the elatonshp smulate s not epenent on the ensty of the netwok. An omn-ectonal antenna s assume fo the MS an also fo the BSs. The smulaton s pefome by assumng that the MS wll be the ecevng antenna an postonng calculatons wll be cae out n the MS. It s also assume that the MS can eceve RSS fom seven BSs. Theefoe the nomal hexagonal cell topology cell sze was change to ccula to enable the BSs to ovelap on each othe. The BSs ae locate at (3.,.), (14.3, 18.), (-5.1,.4), (-.7, 1), (-.7,-1), (-5.1,-.4), (14.3,-17.) fo BS 1,, 4, 6, 7, 5 an 3 espectvely (all unts n km).. Movement of MS The MS s assume to move n a hozontal lne though the sevng BS (BS1) wth MS n a stat poston, whee L s the length of the se of the heptagon smulate. Stat poston S = - (L + ((1/) * L)). Fnal poston F = (L + ((1/) * L)). The MS une conseaton moves n the path ncate by the aow n Fgue. The stance between each movement s etemne by the numbe of moves (locaton ponts) eque to move fom S to F. In Fgue, we have use 11 moves, each of whch s ncate by a small squae. y BS6 BS4 S BS1 F BS ffeent stances elatng to the MS poston an the eo ntouce by havng no ecton, s now elmnate.. Dstance Depenent fang The stance epenent fang s moelle as a ual pecton by the Okumua Hata path loss moel fo open aea o ual aea pecton (PL OA ) [11]: PL OA = PLU - a(hms) x (Log1( fc)) x Log1 ( ) The baselne moel whch s the uban pecton fo path loss (PL U ) s gven by the Equaton PL U - a(h (B) = x log1 (f MS ) + ( x log1 h BS c ) x log1h ) x Log1() BS 7 whee f c s the tansmttng fequency n MHz, h BS s the base staton heght above the tean n metes, h MS s the antenna heght above the tean n metes, s the stance between the tansmtte (BSs) an eceve (MS) n klometes, a(h MS ) s the moble antenna heght coecton facto fo ffeent envonments. Notng that the path loss s gven by the tansmtte sgnal subtacte fom the eceve sgnal ( P TX PRX = PLOA ), the eceve sgnal stength can be calculate gven all the othe paametes. The path loss moel s use to estmate the aveage eceve powe of the tansmtte sgnal at the MS. Keepng all othe paametes constant, the eceve sgnal stength changes wth stance fo any envonment une conseaton base on the path loss moel use. Wth the cell sze, the Okumua Hata moel was use to calculate estmate sgnal stength at stances whee the MS s locate. v. Othe Paametes As the MS moves, the stance between the MS an the BSs changes. The RSS s ectly elate to the stances as shown n Equaton 6, theefoe the RSS changes wth changes n stance. Snce we ae nteeste n the elatonshp between stance an poston eo, all othe nput paametes wee kept constant an only the MS was move though a peefne path. Fgue 3 shows a block agam of the smulate system BS7 Coonate of MS, sevng an neghbou BS BS x Fgue : Smulate movement of MS The stances of MS to BSs whle appoachng BS fom left s enote as postve whle stances to the ght of BS1 ae enote as negatve. If no ecton s use, t s possble, fo example to calculate the poston mmeately befoe an afte BS1 as the same stance whch when elate to each othe ntouces atonal eo. If ecton s use then these above postons wll have BS3 Receve sgnal stength Tansmtte sgnal Popagaton moel Tmng Avance Estmate poston of MS Actual poston of MS Antenna Chaactestcs of sevng an neghbou BS Fgue 3: Block agam of the smulate system Eo of locaton algothm

4 IV. SIMULATION RESULT The elatonshp between the vaables une conseaton s pesente n thee ways; lnea plots, system entfcaton an cuve fttng analyss. Lnea plots wee use to analyze the elatonshp between the stance between the BSs an MS wth poston eo fom the estmate MS locatons. All smulatons wee cae out usng A. Ba analyss Fgue 4 shows a plot of postonng eos fo locaton algothms une conseaton whee each MS locaton s enote wth just the x-axs (the y-axs) s zeo. Fom Fgue 1, t s obseve that BS1 s symmetcal n aangement to the othe BSs theefoe the elatonshp wth the postonng eo s expecte to be smla. Eo COG COT TRI LS MS Poston Fgue 4: Ba analyss of the elatonshp between postonng eos wth movng locatons of MS The Tlateaton algothm postonng eo elatonshps wth stances fom BSs to MS ae qute smla to those obtane usng the LS postonng eo. Ths can be obseve fom Fgue 4. TRI s calculate wth just thee BSs whle LS metho s calculate usng seven BSs an yet the elatonshp looks smla. Ths mples that paametes fom the fst thee BSs ae the most mpotant fo calculatng locaton usng LS metho when conseng ths cellula netwok stuctue. COT an COG gave smla elatonshp wth MS poston fom Postons 1 5 but afte ths, COT gave hghe locaton eo that COG ths mght be ncatve of the elatonshp n the change of stances between MS an BSs. It shoul also be note that ue to the symmetcal natue of the BS aangements the values of, 4 an 6 ae the same as the values of 3, 5 an 7 espectvely. Table 1 shows the values of 1 7 wth the coesponng locaton of MS.. Dstances between base statons an MS wth postonng eo Vayng postons of the MS affects the stance between the MS an the BSs. Fom Table 1 an Fgue 4, the postonng eos best follows 1. Ths ncates that the eo of postonng obtane fo ths patcula cellula netwok shown n Fgue s ectly popotonal to 1. Table 1: 1-7 an coesponng MS locaton Locaton of MS 1 an 3 4 an 5 6 an 7 Pos Pos Pos Pos Pos Pos Pos Pos Pos Pos Pos Numbe of base statons analyss Ths pat of the eseach helps to bette unestan the mpact the numbe of BSs use fo estmaton of the locaton has on the postonng eo obtane fom the locaton algothms une conseaton. Fgue 5 shows the gaphcal elatonshp between vayng MS poston, numbe of base statons an COG, LS, COT an TRI postonng eos. The postonng eos ae least when the numbe of BSs nvolve n estmatng the MS locaton ae seven (7), whch can be seen MS poston s between 5 an 7. Numbe of base statons Eo MS Poston COG COT TRI LS MS Poston Fgue 5 shows the elatonshp between numbe of BSs, postonng eos an MS locaton It wll be notce that as the MS moves towas BS1, fom poston 1 to 5, the postonng eo all euces sgnfcantly fom the value of 3km to 5km fo COT an fom 5km to neglgble fo LS. As the MS moves close to BS1 an futhe away fom BS 6 an 7, the poston eo nceases. Ths ncease s qute sgnfcant wth COT an

5 COG agan but to a vayng egee, moe wth COT than COG. V. FURTHER WORK AND CONCLUSION The numbe of BSs can be kept constant so that the paametes affectng locaton eos can be euce an then analyze futhe. Wth a eucton n the numbe of epenent factos fo locaton eo, system entfcaton can be cae out n oe to efne a mathematcal moel fo the elatonshp between postonng eo an stance. Ths mght be use to mofy the locaton algothms an mpove the accuacy. Futhe analyss can then be cae out aganst the mofe (wth geomety mathematcal moels) an unmofe postonng algothm. Ths smulaton s cae out to analyze the elatonshp between the MS elatve stances to BSs, postonng eo an the numbe of BSs. Fom the analyss, t was scovee that the elatonshp between elatve stances to BSs an eo fo ffeent locaton metho s ffeent whch makes t mpotant to nclue the geomety analyss fo an mpove netwok-base locaton algothm. The postonng eo s also epenent on the numbe of BSs avalable fo locaton estmaton. Refeences 1. Y. Zhao, Stanazaton of moble phone postonng fo 3G systems, IEEE Communcatons Magazne. July,, pp ,.. Feeal Communcaton Commsson: Guelnes fo Testng an Vefyng the Accuacy of Weless E911 Locaton Systems, OET Bulletn no. 71, Apl. Pesentaton avalable onlne, last assesse 6 th Octobe, 8: sevces/enhance911/achves/oet71.pf. 3. Gpsy: Locaton sevces an accuacy: An analyss fo fel wok applcatons. Pesentaton avalable onlne, last assesse th Octobe, 8: ons /ocs/gpsy_4_7.pf. 4. J. Wess: On the Accuacy of a Cellula Locaton System Base on RSS Measuements, IEEE Tansactons on Vehcula Technology, Vol. 5, No. 6, pp , K. W. Cheung H. C. So, W. K. Ma, Y. T. Chan: Receve sgnal stength base moble postonng va constane weghte least squaes, Poceengs: Intenatonal Confeence on Acoustcs, Speech, an Sgnal Pocessng, pp , Apl S. Gezc: A Suvey on Weless Poston Estmaton, Weless Pesonal Communcaton, Vol. 44 No 3, pp. 63-8, H. L. Song: "Automatc Vehcle Locaton n Cellula communcatons Systems", IEEE Tansacton on Vehcula Technology, Vo1. 43 No. 4 pp. 9-98, J. Zhou, K. M. Chu an J. K. Ng: Povng Locaton Sevces wthn a Rao Cellula Netwok usng Ellpse Popagaton Moel, Poceengs: 19th Intenatonal Confeence on Avance Infomaton Netwokng an Applcatons, pp 57-66, Apl K. Yu, I. Shap an Y. J. Guo: Goun Base Weless Postonng, IEEE Pess Sees on Dgtal an Moble Communcaton,, John Wley an Sons Lt, fst eton, chaptes 5 an 8, T. Kos, M. Ggc an G. Ssul (6) Moble Use Postonng n GSM/UMTS Cellula Netwoks, Poceengs: 48th Intenatonal Symposum ELMAR- 6, pp , June 6.Golsmth: Weless Communcatons by Cambge Unvesty Pess. 1 st eton, 5 Chapte : pp Folasae Mojsola Dahuns s a postgauate stuent n the Faculty of Engneeng an the Bult Envonment at Unvesty of the Wtwatesan, South Afca. He eseach nteests nclue weless netwok optmzaton, aolocaton technques an geogaphcal nfomaton system. She s a stuent membe of the IEEE. Pof. Bay Dwolatzky s a Pofesso of Softwae Engneeng at the Unvesty of Wtwatesan, Johannesbug (RSA). Hs eseach nteests ae softwae evelopment usng object-oente pogammng technques, esgn an mplementaton of softwae fo contol engneeng applcatons an softwae ntegaton fo lage systems.