A Bayesian Sampling Approach to In-Door Localization of Wireless Devices Using Received Signal Strength Indication

Transcription

1 Deartmet of Comuter Scece a Egeerg Uverty of Texa at Arlgto Arlgto, TX 7609 A Bayea Samlg Aroach to I-Door Localzato of Wrele Devce Ug Receve Sgal Stregth Icato Vay Sehar ehar@ce.uta.eu Techcal Reort CSE Th reort wa alo ubmtte a a M.S. the.

2 A BAYESIAN SAMPLING APPROACH TO IN-DOOR LOCALIZATION OF WIRELESS DEVICES USING RECEIVED SIGNAL STRENGTH INDICATION The member of the Commttee arove the mater the of Vay Sehar Dr. Mafre Huber Suervg Profeor Dr. Gergely Zaruba Suervg Profeor Mr. Dav Leve

3 Coyrght by Vay Sehar 2003 All Rght Reerve

4 A BAYESIAN SAMPLING APPROACH TO IN-DOOR LOCALIZATION OF WIRELESS DEVICES USING RECEIVED SIGNAL STRENGTH INDICATION by VINAY SESHADRI Preete to the Faculty of the Grauate School of The Uverty of Texa at Arlgto Partal Fulfllmet of the Requremet for the Degree of MASTER OF SCIENCE IN COMPUTER SCIENCE AND ENGINEERING THE UNIVERSITY OF TEXAS AT ARLINGTON December 2003

5 ACKNOWLEDGEMENTS Frt a foremot, I woul lke to thak my aret a famly for ther uort a ecouragemet that mae all th oble. I woul lke to offer ecal thak to my uervg rofeor Dr. Mafre Huber a Dr. Gergely Zaruba for ther cotet hel, uort, a fug throughout th eeavor. Ther atece, exerece, a kowlege have bee valuable throughout my reearch, a I am truly grateful for th. I woul lke to thak Mr. Dav Leve for cooerato wth the acce ot h offce, a for beg o my commttee. I woul alo lke to thak Shvarama Krha for hel wth ata collecto the mle of the ght, Mchael Browlow, formerly at the AI lab, UTA, for helg me get tarte wth FLTK a varou Lux ue, a Pama Srvaa for hel wth ettg u PCMCIA a the ecal wrele car rver o Lux. November 8, 2003 v

6 ABSTRACT A BAYESIAN SAMPLING APPROACH TO IN-DOOR LOCALIZATION OF WIRELESS DEVICES USING RECEIVED SIGNAL STRENGTH INDICATION Publcato No. Vay Sehar, M.S. The Uverty of Texa at Arlgto, 2003 Suervg Profeor: Dr. Mafre Huber a Dr. Gergely Zaruba A evce are becomg more a more tellget, a augmete by the ablty to commucate wth other evce va wrele chael, locato aware comutg gag mortace. I fact, the localzato roblem ha bee etfe a a key roblem moble robotc a t lay a fuametal role varou ucceful moble robot ytem. Locato awaree alo lay a mortat role ubqutou comutg evromet wth tremeou otetal eroal avgato a ecurty ytem, evce targetg eole wth ablte, health-care, etc. For examle, a moble evce coul be mae caable of rovg a uer wth recto wth a large bulg real-tme, by "kowg" where the uer at reet relatve to the bulg. v

7 We rooe a robabltc aroach to "global" localzato wth a home evromet wth mmal fratructure requremet. Global localzato a flavor of localzato whch the evce uaware of t tal oto a ha to eterme the ame from cratch. Localzato erforme bae o the Receve Sgal Stregth Icato RSSI, whch rove by ay off the helf wrele etwork aater, a the oly eor reag ug Bayea flterg o a amle et erve by Mote- Carlo amlg. The frt te volve bulg wrele gal tregth ma the home evromet. The ma bult by vg the area to cell wth reefe meo a collectg a umber of reag each cell. Thee reag form a amle et for Sequetal Mote-Carlo amlg. Next, a oteror robablty trbuto for the locato of the wrele evce comute over the etre area ug Mote Carlo amlg bae Bayea Flter, alo kow a Partcle Flter. Locato etmate may the be eterme from th trbuto ug the maxmum ety ot or other arameter eeg o the etmate eee. We cu theory a reearch leag to the rooe metho a rove reult of mulato a real-lfe exermet. v

8 TABLE OF CONTENTS ACKNOWLEDGEMENTS... ABSTRACT... LIST OF ILLUSTRATIONS... v v x Chater. INTRODUCTION.... Motvato Alcato Doma PREVIOUS WORK Wrele Sgal Proagato Backgrou Localzato BAYESIAN FILTERING Itroucto to Flter Stochatc Etmato a State-Sace-Moel Bayea Flter Recurve Bayea Flter Precto Meauremet Uate Cotrat : Markov Proce Cotrat 2: Memory Le Chael... 7 v

9 4. MONTE CARLO SAMPLING BASED APPROACH TO BAYESIAN FILTERING Samlg from a Arbtrary Dtrbuto Mote Carlo Itegrato Imortace Samlg Sequetal Imortace Samlg Degeeracy Meaure of Degeeracy Reamlg Geerc Partcle Flter PARTICLE FILTER MODELS State-ace-moel for the Partcle Flter Referece Frame for the Partcle Flter Meauremet Moel for the Partcle Flter Wrele Ma Other Meauremet Movemet Moel for the Partcle Flter IMPLEMENTATION Exermetal Setu The Evromet Harware Setu Software Setu v

10 6..3. Oeratg Sytem a Drver Smulato Methoology The Trag Phae Bulg the Wrele Ma The Localzato Phae Program Italzato Rug the Smulato The Meauremet Uate The Moel Uate Locato Etmate Etmate : Sum of Ivere Dtace Etmate 2: Hghet Partcle Dety Crcle wth Gve Rau Etmate 3: Hghet Partcle Dety Crcle wth Gve Rau Etmate 4: Mea of All the Partcle EXPERIMENTAL RESULTS Smulate Walk Through Etmato Error Partcle Flter Performace Wth a Wthout Oretato Recore Walk Through Etmato Error Lve Walk Through x

11 8. CONCLUSIONS AND FUTURE WORK Cocluo Future Work REFERENCES BIOGRAPHICAL INFORMATION x

12 LIST OF ILLUSTRATIONS Fgure Page 2. Tragulato Algorthm, equetal mortace amlg Algorthm 2, reamlg Algorthm 3, geerc artcle flter Partcle lacemet trbuto The evromet Wrele ma for the outhwet acce ot outh Sgal tregth trbuto a cell Movemet ath for the mulate walk through wth velocte Smulato ahot mulate walk through moe Error lot for locato Error lot for oretato Average error locato mulate walk through moe Average error oretato mulate walk through moe Average error locato wthout oretato Movemet ath of the moble oe recore walk through moe Smulato ahot recore walk through moe Average error locato recore walk through moe x

13 7. Average error oretato recore walk through moe Lve walk through x

14 CHAPTER INTRODUCTION The boom wrele etwork over the at few year ha gve re to a large umber of avalable moble tool a ther alcato are becomg more a more ohtcate by the year. Wrele etwork have become a crtcal art of the etworkg fratructure a are avalable mot cororate evromet, arort, hog mall, cafe, etc. There eve talk about WF eable cte, wth Par, Frace, beg oe of the frt target ee [7]. The fact that wrele etworkg eable moblty a key factor bulg tellget moble evce to erform may route tak. Smart evce a home that are caable of ajutg themelve to rove maxmum comfort to a uer are lowly becomg realty. Wth growg ema for the eloymet of uch ytem, etwork reearcher are u agat a fuametal a well-kow roblem the fel of robotc: etermato of hycal oto of a moble oe ug ucerta eor localzato. Locato awaree alo lay a mortat role the evelomet of ubqutou comutg evromet wth tremeou otetal eroal avgato a ecurty, health-care, ablty a, etc. May commercal a reetal etablhmet are alreay eque wth off-the-helf wrele Etheret IEEE 802.b a may off the helf moble evce ow avalable are wrele Etheret eable. Thee evce are caable of meaurg gal tregth of receve acket a

15 art of ther taar oerato, a th the outle our reearch towar ug th gal tregth, the Receve Sgal Stregth Icato RSSI, to relably eterme the locato of a evce. A gfcat cotrbuto of th the woul be to how that reaoable etmate may be acheve ug RSSI reag from a gle acce ot, eeg o the tructural ymmetry a locato of the acce ot the evromet.. Motvato May oular locato etmato techque lke RADAR RAo Detecto A Ragg [2] a GPS Global Potog Sytem [22] have bee roucto for everal year ow. Both thee techque rely o the tme take by rao wave for roagato a a farly rece locato etmate relatve to the locato of the trackg evce may be ealy eterme by calculatg fferece th roagato tme. Other metho to eterme the locato of moble boe clue LASER Lght Amlfcato by Smulate Emo of Raato a SONAR Sou NAvgato a Ragg. Thee metho are alo wely ue commercal a utral equmet to etmate locato of moble boe oor, uerwater, or other lace. Oe mortat requremet for thee a other SONAR or LASER bae evce to fucto that the target ee to be wth the recever le of ght. Th factor revet, or at leat retrct, the ue of uch ytem oulate area where uch a le of ght may ot be avalable. Th lmtato everely reuce the feablty of ucceful eloymet a ubqutou comutg evromet where moble evce target may be wearable or mlate a caot rema wth the recever' le of 2

16 ght. RSSI reag from a Rao Frequecy RF evce, o the other ha, are avalable from the evce wthout the ee for a le of ght. Whle RF wave are caable of eetratg may hycal bouare or tructure, thee o affect the RSSI reag, albet a omewhat rectable faho. Th rectablty make t oble to ma RSSI reag from a fxe acce ot to a rego, a th make localzato ug wrele Etheret feable. Whle our reearch focue o a offce evromet, we mata eough geeralty to aly the reult to ay oor evromet. The roagato of wave gal are affecte everal o-trval way a oor evromet, caug oe, terferece, multle ath effect, ea ot, etc, a caue the behavor of oor wrele chael to be hghly ucerta. Uer thee crcumtace, a localzato ytem woul have to overcome the hgh ucertaty a o o wthout ug exeve equmet..2 Alcato Doma Aother trog motvatg factor the alcato area of the rooe techque. Phycal locato ata from moble oe woul allow may oftware ackage to rove a whole rage of feature that we rarely ee. Feature lke beg able to walk acro your houe wth TV cree each room wtchg to the chael you are watchg, or a robotc vacuum cleaer ruhg off to clea a coffee ll wth momet of the ll, woul be commolace. You woul alway be able to rt to the earet rter from your wrele eable lato, rreectve of your hycal locato the offce bulg, or you woul be able to ak your PDA to gve auble recto 3

17 to your 0:00a aotmet or to your eat a arlae. Icororatg may uch coveece feature to evce woul become trval, oce accurate a relable formato o the hycal locato of the evce avalable. Locato etmato woul lay a mortat role the formato ecurty area, a far a hycally trackg uauthorze acce to rvate wrele etwork cocere; t woul be eay to locate a uauthorze uer relatve to a acce ot earet to hm. Locato aware evce woul alo a mrovg reoe tme urg emergece. For examle, whe omeboy trouble make a 9 call from a cell hoe, a the hycal locato of the cell hoe vble o the 9 oerator comuter cree, t woul a recue ut to reach the caller fater tha f they were to earch for the caller. Other otetal alcato clue better call traffc routg algorthm for cellular hoe, evelomet of better acceblty a for able eole, healthcare equmet, etc. 4

18 CHAPTER 2 PREVIOUS WORK I th chater, we brefly trouce the behavor a charactertc of wrele gal, followe by a troucto to reearch o localzato ug wrele gal tregth by other eole a reearch grou. 2. Wrele Sgal Proagato I th ecto, we trouce factor affectg the roagato of Rao Frequecy wave a coequetly affectg Receve Sgal Stregth Icato meauremet a oor evromet. IEEE 802. a famly of IEEE taar for a wrele etworkg rotocol ege to rove wrele ervce comarable to revou wre IEEE 802 ecfcato. The ecfcato cover everythg from the hycal meum mcrowave rao a IR moulato techque to lk-layer mlemetato. Comlete ecfcato of the taar are avalable at htt:// IEEE 802., whe ue over wrele rao lk, make ue of a techology calle rea ectrum. Lke ay gal roagato techology, IEEE 802. ucetble to oe a other terferece from the evromet. Sce mcrowave frequece ue by IEEE 802. ~2.4GHz are ulcee, they are ucetble to terferece from a whole rage of ource lke corle telehoe, mcrowave ove, etc. Alo, ce every IEEE 802. caable-car mlemet the ame chg coe, 5

19 rea ectrum oe ot offer ay heret ecurty feature. For a better ecrto of rect equece rea ectrum a t charactertc, the reaer ecourage to refer to [8]. Whle Rao Frequecy RF wave are caable of eetratg hycal bouare lke wall a other obtacle uch a furture, reece of uch bouare ha a gfcat effect o the gal tregth. The reece of huma beg a et alo affect gal tregth gfcatly, ce water aborb rao wave the 2.4GHz rage. Due to thee factor, roagato of wrele gal affecte everal otrval way a oor evromet, wth oe, terferece, multle ath effect, etc., beg commolace. For the rooe metho, we ee to cotruct wrele ma of the evromet uer coerato. Whle we rove a etale exlaato of wrele ma chater 5, t uffcet for the reaer to kow that thee ma are cotructe bae o the aumto that wrele gal tregth acro a area follow a kow trbuto of ome ort. Sce obtacle lke huma a et are moble, a ce oor a wow are ot etrely tatoary obtacle, the trbuto of gal tregth acro the evromet may ot be cotet over tme. Thee factor reer the behavor of wrele chael hghly ucerta a t vtal for ay techque coerg the ue of gal tregth to overcome th ucertaty. 6

20 2.2 Backgrou Localzato Several aroache to the localzato roblem have bee uer vetgato for a whle. May of thee aroache rely o roretary techque a ether requre the ue of atoal equmet for eloymet or rely o ome tguhg charactertc ecfc to the evromet whch the ytem eloye. For examle, cellular hoe may ue GPS ytem tegrate to the moble termal or ue gal tregth meauremet to tragulate ther oto relatve to fxe bae tato [9, 20]. Fgure 2.: Tragulato [4] Several ytem that make ue of uch techque for localzato have bee rooe a uccefully eloye for a oor evromet. Thee ytem are bae o well-etablhe ytem lke: frare tramtter a recever ytem [23] LASER tramtter a recever ytem 7

21 RADAR tramtter a recever ytem [2] Ultraoc eor a actuator ytem SONAR [25] Rao Frequecy IDetfcato RFID ytem for cloe roxmty localzato [28] Smle hycal cotact bae actuator ytem [27] Comuter vo bae ytem[26] All of thee ytem requre the ue of fratructure ecfcally for the uroe of localzato, a equmet for th fratructure rarely avalable off the helf. Due to the boom wrele etworkg a hgh ema for wrele etworkg fratructure, everal rouct that eable wrele etworkg ug IEEE 802., Bluetooth, a other rotocol are avalable off the helf ay eghborhoo comuter tore worlwe. Such evce ca be ftte o almot ay moble evce avalable toay, a we ca exect wrele etwork to lay a gfcat role the future of ubqutou comutg. Therefore, t wll be far to aume that ay uer or evce eeg locato trackg caablte alreay wrele eable. A a coequece, techque to erve locato etmate from Receve Sgal Stregth Icato RSSI of wrele gal are raly gag oularty a are becomg more a more rece a ohtcate. RSSI bae localzato techque geerally cot of two hae: A trag hae a a etmato hae. I the trag hae, a mag of ome k etablhe betwee wrele gal tregth a varou reefe oto the evromet, whch tycally acheve through collectg RSSI amle at the 8

22 reefe locato. I mot cae, the evromet ve to cell orer to efe thee locato. I the etmato hae, a etmate of the target locato comute ug the gal tregth mag a.k.a. wrele ma va robabltc or etermtc techque cue below. RSSI bae locato etmato techque are broaly ve to etermtc a robabltc techque, both of whch requre o atoal fratructure. For the ue of a etermtc techque, the hycal area makg u the evromet frt ve to cell. Next, the trag hae execute whch reag are take from everal fxe, kow acce ot. A fally, localzato erforme be executg a etermato hae, whch the mot lkely cell electe by etermg whch cell the ew meauremet ft bet ee [5]. The reaer referre to [3] a [34] for more formato o etermtc localzato techque. O the other ha, robabltc techque cotruct a robablty trbuto over the target locato for the hycal area makg u the evromet. I orer to etmate the locato of the target, fferet arameter lke the moe of the trbuto or the area wth hghet robablty ety may be ue. Whle robabltc techque rove more reco, a trae-off betwee comutato overhea a reco trouce. We outle ome robabltc techque rooe the at the followg aragrah. A extee Kalma flter [] bae aroach reete [9], whch a attemt mae to etmate the tra cell oto of a cellular evce ug RSSI reag from bae tato. Th etmate, combato wth movemet atter ata 9

23 a velocty vector, ue to etmate the ext cell crog. Such a ytem woul rove very ueful to otmze cellular acket routg algorthm. Th work coul be coere oe of the earlet to aly tattcal metho to localzato ug RSSI meauremet. A Bayea flter bae aroach rooe [33], whch the author utlze a Bayea belef etwork to erve a oteror robablty trbuto over the target locato. The tate-ace over all oble locato of the target oe cretze a the ue to evelo a Bayea belef etwork, gve the cotoal robablte of a RSSI reag beg meaure at each oble locato a 2 a a- ror robablty trbuto of the oe beg at a fferet locato. The oteror trbuto the erve by vertg th Bayea etwork. The comutatoal overhea volve th techque very hgh. Aother mlar rooto [32] cot of evelog the Bayea etwork bae oly o the troget ubet of acce ot rather tha all of them. Other techque have bee rooe makg ue of atoal techque or algorthm, lke mache learg, whch mrove the reco of the etmate at the cot of creag comutato overhea. The techque rooe th the a robabltc aroach ug recurve Bayea flter bae o Sequetal Mote Carlo Samlg a.k.a. Partcle flter. The rooe techque comute a oteror trbuto of the target locato ug Sequetal Imortace Samlg ee chater 4. The Sequetal Imortace Samlg techque caable of ug a arbtrary a-ror trbuto to comute the requre 0

24 oteror trbuto. Th metho le comutatoally teve a ute to a oor wrele eable evromet where taar trbuto of RSSI reag may ot be avalable. We rocee to rove a etale ecrto of the rooe metho clug exermet coucte a reult the followg chater.

25 CHAPTER 3 BAYESIAN FILTERING We attemt a robabltc aroach to localzato where the ytem attemt to eterme the robablty that the target may be locate at ay ot acro the evromet. After ormalzg th robablty acro the area, the mot lkely locato of the target may be eterme by comutg the area wth maxmum ety or other arameter eeg o the etmate eee. To track movemet of the moble oe cotuouly, we mly geerate uch a robablty trbuto wth a cotuou amlg ero of oe/ec or le. I th work, we ue Sequetal Mote Carlo Samlg bae Bayea flter to cature a follow the robablty trbuto of the target locato. A arbtrary a- ror trbuto covergg to a gle moe of the amle trbuto ca be ue th metho. I th chater, we cu the theory beh utlzg flter for etmato clug Bayea flter a recurve Bayea flter followe by Mote Carlo Samlg bae aroache to Bayea flterg clug Imortace Samlg a Sequetal Imortace Samlg Partcle flter the ext chater. 3. Itroucto to Flter The ctoary efe a flter the Comuter Scece oma a "A rogram or route that block acce to ata that meet a artcular crtero". Here, we ue a 2

26 flter to etmate a a-yet ukow tate of a ytem bae o meauremet from a kow tate, or et of tate, of the ytem. Such a roce, better kow a etmato, volve a "rogram or route" that comute a et of oble future tate of a gve ytem bae o meauremet from a kow et of tate. Ay etmato roce hghly alcato ecfc a, more ofte tha ot, t eceary to eal wth oy ature of meauremet. Th oe tattcal ature or ca effectvely be moele a uch, whch lea to tochatc etmato metho Stochatc Etmato a State-Sace Moel A frt cocer woul be to evelo a coveet a tractable mathematcal rereetato of the ytem uer tuy. A tate-ace moel jut uch a otato, eveloe to make otatoally tractable aaly feable. If a yamc roce ecrbe by a th orer fferece equato of the form 0,,,, = + + u o where: u rereet a zero-mea raom oe roce a o, -,, -+ are tal value rereete by zero-mea raom varable wth kow covarace [5] how that th oe u tattcally eeet from the roce to be etmate. Coequetly, we may rewrte the above fferece equato a: { G x A u + = Μ 3 2 Μ Μ Μ Μ Μ Μ ϖ 3

27 where: A rereet meauremet from the + th tate of the ytem, rereet the th tate of the ytem, rereet obervato erve from tate, u rereet the oe the meauremet. We ca ow wrte the above tate-ace moel a geeral form a: = A + Gu, + = H + ν where: H rereet the meauremet or obervato erve from teral tate + Lterature commoly refer to thee two equato a the roce moel a meauremet moel reectvely whch form the ba for mot lear etmato moel, uch a the Bayea flter. The ea to etmate the tate of a lear ytem, gve acce to oe or more outut rouce by the ytem. A commo aroach to th roblem to ue a tate-ace moel ecrbe above. 3.2 Bayea Flter The roblem we are tryg to olve ca be cat the framework of attemtg to etmate the evolvg tate of a ytem gve meauremet that are tochatcally relate to t. We wll rove a etale ecrto of the ytem tate later. For ow, let the tate of the ytem be eote by at tme t = t where t the amlg terval. Thu {, 2,, } a equece of tate at t t, 2 t,..., t. Owg to oe the tate evoluto roce or heret ucertaty the evoluto of the 4

28 roce telf, may be regare a a raom varable. Let eote a meauremet rouce by the ytem at tme t = t a a mlar otato {, 2,, } eote a equece of meauremet. For the uroe of trackg or motorg a gve tochatc ytem, we are attemtg to etmate t evolvg tate ug meauremet collecte at each amlg terval. Sce a raom varable, a oteror ety fucto of the form may be ue to covey all formato rove by. A Bayea Flter algortm a techque that rouce uch a etmate for each =,2,, gve. Gve uch a oteror trbuto, t eay, at leat cocetually, to rouce ay ere tattc of. For examle, we may ealy comute a cotoal mea ug the formula. = 3.3 Recurve Bayea Flter A recurve Bayea flter algorthm moe the cotrat that the etmate of houl be geerate ug oly the revou oteror ety - - a the mot recet meauremet. Th way, we coveetly avo torg the etre meauremet equece a reuce the amout of comutato erforme. Coer a two te roce roucg the ere oteror trbuto a outut by takg ut. The two te are exlae a follow: a a 5

29 3.3. Precto Th te ma the revou oteror trbuto - - to a recto ety. =, 3. Th te alo kow a the moel uate, ce t uate the tate ace moel bae o recto Meauremet Uate Th te combe a ew obervato wth the recto ety - to comute the ere oteror ety., = 3.2 The eomator the uate te eterme by tegratg the umerator:, =. Uo examg the above equato, we otce the reece of the term, a, that requre all revou meauremet collecte. Thu, to erform Bayea Flterg recurvely, we mut moe ome cotrat o our tochatc roce. Thee cotrat mut be uch that revou meauremet are ot ue the above equato Cotrat : Markov Proce We frt aume that the tate equece Markova,.e.: 3.3 = 6

30 Ay raom roce a to be Markov f the future of the roce gve the reet eeet of the at,.e. the reet tate cota the etre at Cotrat 2: Memory Le Chael A eco aumto we make that obervato occur through a memory le chael,.e. aume to be eeet of all tate but a alo all other meauremet. I.e.: = =. 3.4 The recto te ow reuce a follow: =, = Alyg the above aumto, = Ug Baye rule, = 3.5 The meauremet uate te alo reuce a follow:, = Alyg Baye rule, we get 7

31 , = Alyg Cotrat 2, we get = Alyg Baye rule aga, we get = = 3.6 We may ow ue a Recurve Bayea Flter of the form ecfe by equato 3.6 cojucto wth a Sequetal Mote Carlo amlg bae techque to comute the tegral our recto te equato 3.5. The followg chater cue the theory beh Mote Carlo amlg a Partcle Flter. 8

32 CHAPTER 4 MONTE CARLO SAMPLING BASED APPROACH TO BAYESIAN FILTERING 4. Samlg from a Arbtrary Dtrbuto The two-te Recurve Bayea Flter ecrbe the revou chater make ue of a tegral of the form g g I = 4. where g a fucto of the tate. I equato 3.5, we woul ee to tegrate th equato over multmeoal ace a alo, may be multvarate, or otaar, a ooe to a taar form lke a Gaua trbuto. Such tegrato ot ealy tractable a coul ealy reer telf comutatoally feable. Coequetly, tea of eekg a aalytc oluto, we ca comute a aroxmate oluto by Mote Carlo tegrato [0], []. 4.. Mote Carlo Itegrato Mote Carlo tegrato amle the tate ace at raom eeet of the umber of meo []. A a raom amlg techque, the tegral oluto requre the ablty to raw eeet amle { } from. Coequetly, a otaar ca reet ubtatal ffculty for Mote Carlo tegrato. 9

33 The ma tak of a Mote Carlo metho to geerate eeet amle from a target trbuto uch a. Due to the reao reete above, rawg amle rectly from the trbuto ot feable, ecetatg a rect aroach. Thee rect amle may be raw from a trbuto other tha [3]. We wll ue g to eote a Prooal Dtrbuto from whch we are able to raw amle. The Strog Law of Large Number SLLN, whch aert that a equece of cumulatve um of raom varable become o-raom whe ormalze by a arorate equece of o-raom umber a whe aroachg the lmt, guaratee the valty of th aroxmato Imortace Samlg Th amlg metho requre that g > 0 wheever > 0, to avo tuato where rego of tate ace where o-zero caot be mae by amle raw from g. The cuo th ecto raw uo work reete [2]. where: w = We ca rewrte Equato 4. a g I g = g g 4.2 g 4.3 Now, N eeet amle { } may be raw accorg to g a we ca aroxmate equato 4.2 by Mote Carlo tegrato a 20

34 I N N g = g N = w 4.4 where: w w Th et w = {w, w 2,, w N } referre to a the mortace weght. Equato 4.4 may be rewrtte a where: = δ I N N g g w = δ 4.5 = δ the Drac Delta fucto. If the emrcal raom meaure geerate by amle raw from g eote by N the: N N = w Ug equato 4.6, equato 4.2 a 4.5 may be relate a I = g g g = N N δ 4.6 where the aroxmato mrove a N,.e. a the umber of amle choe creae. Thu mortace amlg rove a mea of bulg a emrcal aroxmato to a oteror trbuto eve f the revou oteror caot be ue for amlg. 4.2 Sequetal Imortace Samlg Th algorthm a Mote Carlo metho that form the ba for mot Sequetal Mote Carlo Flter a alo kow by the followg ame ee [4]: 2

35 Boottra Flterg, Partcle Flter, Iteractg Partcle Aroxmato, Coeato Algorthm, a Survval of the Fttet. The revou ecto emotrate that Imortace Samlg may be ue to geerate a raom meaure N N that aroxmate a true oteror trbuto. ot oly cota a et of raom value, a.k.a. uort ot, but alo the mortace weght of each uort ot. The comlete ecfcato of the trbuto N = { w } N, = For our Bayea Flterg cotext, each uort ot, eote by a raomly geerate Sequece of State. The raom meaure raw rereete by N w N, = a ecfe by the et { } where the u-ormalze weght ecfe by equato 4.3 atfy w = 4.7 g Gve the latet meauremet, the algorthm execte to traform { w } to { N } w, =. If the trbuto choe uch that t may be factore a: g g g =, N, =

36 The obtag a amle g a follow: Draw g, Set { }, = Gve the factorzato equato 4.8, we oly ee to raw N amle urg each meauremet uate. The mortace weght may be mlfe ug the factorzato a follow:, = g g w, = g g Coerg the Markov roerty of 0 a the cotoal eeece of gve 0,, w g w = 4.9 Sce we o ot wh to mata a htory of meauremet a, we mut remove all coto bae o. Th yel: 2 = = j j j j g g g 0, We ca ow wrte equato 4.9 a, w g w =

37 Th form utable for ue Recurve Bayea flter a the algorthm yel a emrcal ety trbuto a N N = w = δ 4. The fferece betwee th form a that ecfe by equato 4.6 that the weght w equato 4. are ormalze. Th trbuto aroxmate the oteror trbuto a 2 2 N = w [, 2 ] We ummarze the ecrto thu far by a euo coe ecrto from [4]: FOR = TO N END FOR DRAW g, Ag the artcle a weght, w, accorg to equato 4.0 N N [{ w } ] SIS[ {, w }, ], = Fgure 4.: Algorthm, equetal mortace amlg 4.3 Degeeracy A commo roblem wth the Sequetal Imortace Samlg flter Degeeracy, where, after a few terato, all but oe artcle wll have eglgble weght. Coequetly, a gfcat amout of comutato et o uatg artcle that cotrbute gfcatly lttle to the aroxmato of, - urg 24

38 each terato. Th alo reult ecreag the qualty of aroxmato a the algorthm rocee Meaure of Degeeracy A coveet meaure of egeeracy woul be the Effectve Samle Sze, N eff, efe a: N eff N = + Var ω where ω = referre to a the true weght. g, Whle t ot oble to meaure N eff exactly, a etmate Nˆ eff = N w = 2 where w the ormalze weght. Coequetly, N eff N a, egeeracy creae a N eff get maller. 4.4 Reamlg Reamlg a metho ue to reuce the effect of egeeracy wheever we oberve a gfcat amout of the ame. The rcle beh reamlg to comletely remove artcle wth gfcat weght a cocetrate o thoe wth gfcat weght. Th accomlhe by rawg N eeet amle from N equato 4., the true oteror trbuto we are tryg to 25

39 aroxmate wth the Sequetal Imortace Samlg algorthm, wheever egeeracy fall below ome threhol N τ.e. f N eff < N τ. The roceure ca be ecrbe by the mag ˆ ˆ j j uch that Pr = w { ˆ, wˆ } = where: N, = N N = ˆ j eote the tate vector before reamlg a eote the tate vector after reamlg Becaue reamlg raw from a true oteror a aroxmate ee, the reamle weght rema uform throughout. Thu, by cotructg a raom meaure where all uort ot have a weght of, reamlg revet egeeracy the N Sequetal Imortace Samlg. Equato 4.3 cate that reamlg te to multly thoe tate wth gfcat weght whle carg thoe wth eglgble weght. Aga, we ummarze the ecrto thu far by a euo coe ecrto from [4]: 26

40 N [ ] RESAMPLE[ {, w } ] j j j N { w, }, = j= = INITIALIZE CDF: c = 0 FOR = 2 TO N END FOR Cotruct CDF: c c + w = = DRAW A STARTING POINT u Υ [ 0 N ], FOR j = TO N MOVE ALONG THE CDF: u = u + N j j WHILE u j > c = + END WHILE j ASSIGN SAMPLE: = j ASSIGN WEIGHT: w N = ASSIGN PARENT: j = END FOR Fgure 4.2: Algorthm 2, reamlg 4.5 Geerc Partcle Flter Algorthm that cororate Imortace Samlg have gae mortace over the at ecae. The term artcle flter revalet for uch algorthm a we wll 27

41 aot th term th reort. The uort ot et { N } = wll be referre to a artcle. A euo coe ecrto for uch a algorthm from [4] rove below: FOR = TO N END FOR DRAW g, Ag the artcle a weght, w, accorg to equato 4.0 N [ w ] CALCULATE TOTAL WEIGHT: = SUM { } FOR = TO N END FOR N N [{ w } ] PF[ {, w }, ] NORMALIZE w, = = = = t w t = CALCULATE N eff USING Nˆ eff = N w = 2 IF N eff < N τ END IF RESAMPLE USING Algorthm 2 Fgure 4.3: Algorthm 3, geerc artcle flter 28

42 CHAPTER 5 PARTICLE FILTER MODELS I the revou chater, we reete the Sequetal Imortace Samlg algorthm uo whch Partcle Flter are bae a a uortg algorthm to revet egeeracy the Sequetal Imortace Samlg algorthm. I th chater, we cu the tate a meauremet moel ue our artcle flter. 5. State-ace Moel for the Partcle Flter A how the revou chater, a artcle flter allow for a hgh egree of flexblty a far a the tate moel cocere. The flter caable of halg ubtatally comlex tate moel clug thoe that are o-lear a o- Gaua. Th allow the ue of a moel that correctly rereet a roce f t oble to cotruct oe rather tha oe that aroxmate the correct moel to a lear or Gaua ytem. Th roerty of artcular teret to u ce a moel rereetg wrele gal tregth trbuto woul be ether lear or Gaua. We are rmarly terete trackg the locato of a wrele eable moble oe or evce a oor evromet a ee to evelo a val movemet moel for t. Here, we efe the locato of the moble oe term of t oto ace a oretato relatve to referece frame ecrbe later. The movemet moel woul ee o the aget carryg the moble oe,.e., the movemet moel for a huma carryg a hahel comuter coerably fferet from that for a wrele eable 29

43 robot that erform houehol chore. Whle we have eveloe a movemet moel for a huma carryg a lato comuter our work, mofyg the ytem to cororate a fferet moel relatvely effortle. For our uroe, we moel the moble oe a a boy wth three egree of freeom [5]. Two of thee ecfy locato of the moble oe the evromet coere a the thr ecfe oretato of the moble oe. Gve thee egree of freeom, t oble to ecfy moto of the moble oe by varato t locato a oretato over tme. We cu ecfc of the tate vector the followg chater. 5.. Referece Frame for Localzato of the Moble Noe To ecfy the tate of ay movg object, t eceary to efe a referece frame that fxe ace relatve to the target object. Sce we are rmarly terete oor localzato of moble evce, we efe the hycal tructure of the oor evromet a a referece frame. A ecfc ot the evromet choe a the org a the locato of the moble oe may be ecfe term of Cartea coorate wth reect to th org. Thee coorate form the frt two egree of freeom our tate ace moel ecrbe above. Whle we are reetly ot terete a thr meo heght of the moble oe a far a t locato cocere, ag uch a meo to the artcle flter alo relatvely effortle. A eco referece frame eceary to ecfy oretato of the moble oe. To ecfy oretato comletely, we frt ee to ecfy a teral referece frame that chage oretato wth reect to a exteral referece frame. A traghtforwar 30

44 choce for the exteral referece frame woul be the Earth, whch mata a fxe oretato a far a the moble oe coere. The recto the huma face whle carryg the lato coere the teral referece frame for our exermet. I the cae of a robot, a utable teral referece lae may be choe mlarly. A artcular recto choe to rereet 0 a oretato exree wth reect to th recto. Thu, f the uer a to be have a oretato of 0 whe he facg North, he woul have a oretato of 80 whe he face South a 270 whe he face wet. I the followg ecto, we ecrbe the evelomet of meauremet a moto moel bae the tate-ace moel cue above. 5.2 Meauremet Moel for the Partcle Flter A tycal wrele commucato ytem cot of two oe exchagg formato wth each other va a wrele roagato meum tycally ar. For th rooal to work, t eceary that oe of thee oe be at a fxe locato at all tme a we requre a etu where the moble oe, or target, commucate wth oe or more wrele acce ot, eal. Such a etu tycal mot bulg a home where wrele teret acce avalable va 802.a/b/g, Bluetooth, or other techologe. A acce ot uch a etu wll tycally reo to a robe acket from a oe wth a robe reoe acket. The oe ca the extract the Receve Sgal Stregth Icato RSSI reag from th robe reoe acket to bul our meauremet moel. 3

45 5.2. Wrele Ma To etmate the locato of a moble oe from a Receve Sgal Stregth Icato reag, a tattcal rereetato of the ame acro the oor evromet eceary. Bulg uch a rereetato volve collectg a umber of RSSI reag from each acce ot at every oble locato the oor evromet. Thee reag woul rereet a wrele ma of the evromet a form the meauremet moel for the artcle flter. Sce t feable ractce to collect reag at every oble locato the moble oe may be, t eceary to cretze the hycal area of the evromet by vg t to cell. Th trouce a trae-off betwee reco localzato a cell ze. Sce we are alo terete etmatg oretato of the moble oe, we ee to cotruct uch wrele ma for every oretato the oe may take. Aga, th ractcally feable a t eceary to cretze oretato. We rereet a wrele ma tule by oe et of reag from each acce ot er cell er oretato. : x y, θ,{ AP, AP,, }, 2 where: x & y rereet Cartea coorate of a hycal ot o the ma θ rereet oretato at that hycal ot AP, AP 2,, AP k rereet vector cotag the et of reag collecte from acce ot, 2,, k AP k 32

46 5.2.2 Other Meauremet Whle we emotrate that, t oble to localze a moble oe ug RSSI reag aloe, ue of atoal arameter the meauremet moel may mrove trackg effcecy a accuracy. For examle, f the moble oe a wrele eable robot, oe coul ealy cotruct a movemet moel bae o velocty a accelerato. It the oble to mrove erformace of the artcle flter by cororatg uch a moel to t. Aga, t relatvely eay to cororate atoal moel to the artcle flter eve f the moel ot Gaua or eve o-lear. 5.3 Movemet Moel for the Partcle Flter A tycal movemet moel rereetg the moto of a moble oe woul cot of velocty a/or accelerato arameter. Cotructo of uch moel traghtforwar, coerg that moel rereetg huma moto are realy avalable. I ato, t oble to cororate avalable moel for moble robot or other evce to the artcle flter, ce there are o retrcto o learty or comlexty of the moel. For our uroe, we aume that the target movemet follow a Gaua velocty moel. Followg th aumto, we ck a ormally trbute raom varable to uate the locato of each artcle urg the moel uate te. The robablty trbuto a how fgure

47 Fgure 5.: Partcle lacemet trbuto Fgure 5. how the robablty of artcle lacemet f the curret locato of the artcle the ceter of the hae crcle. The robablty cate by the hae: Darker the hae, hgher the robablty that the artcle move to that locato after the meauremet uate te. Sce the target oe caot cro wall, the artcle are retrcte from crog wall too. Coequetly, fgure 5. oe ot cate robablte acro wall. A movemet moel aumg that the target accelerato follow a Gaua trbuto may alo be ue. I th cae, we ck a ormally trbute raom varable a the accelerato a uate the locato of each artcle by comutg the tace the target woul travel urg the amlg terval. Wth th, we rocee to our mlemetato of the artcle flter the ext chater. 34

48 CHAPTER 6 IMPLEMENTATION I th chater, we ecrbe the mlemetato of our artcle flter wth the moel exlae the revou chater. 6. Exermetal Setu The area ue to make u the evromet cot of four corror a a louge. Two wrele acce ot are etu the evromet a we ue a lato wth a wrele aater a the target oe. We ecrbe each of thee etal below. 6.. The Evromet The area we coer for ettg u a evromet the thr floor, Neerma Hall at UTA. The evromet cot of four corror, oe louge, a two wrele acce ot are etu at the e aroxmately of the outh corror. We ve the etre area to 88 cell orer to evelo wrele ma of the evromet a ecrbe the revou chater. We chooe locato for the acce ot a ecrbe orer to mmze tructural ymmetry the evromet. Structural ymmetry woul reult a wrele ma that exhbt etcal RSSI roerte at more tha oe ot acro the evromet. Ug uch a wrele ma to comute oteror trbuto of the oe locato woul reult a mult-moal trbuto that woul make etmatg the locato ffcult. The evromet wth the acce ot locato a cell a how Fgure

49 Fgure 6.: The evromet 6..2 Harware Setu Whle we ue a IEEE 802.b wrele Etheret etwork, the rooe metho work wth ay wrele techology rovg RSSI reag a art of taar oerato. A huma oerator carryg a Dell Lattue C60 lato wth a Lucet Oroco Slver PCMCIA WF aater IEEE 802.b coucte our exermet. Th artcular car ue the IEEE Oroco WaveLAN chet. The two acce ot we ue alo ue the Lucet Oroco IEEE 802.b chet Software Setu Whle t oble to wtch the car to romcuou moe, extract RSSI formato from all comg acket a clafy them bae o MAC are, uch a metho woul oly guaratee a cotuou tream of acket from the acce ot to whch the comuter curretly attache. To get acce to beaco that all the acce 36

50 ot e out everal tme a eco, we mae ue of a ecal rver wrtte by Moutafa Youef [6]. Th rver, wrtte for the Lux PCMCIA rver 82365, rove a terface for acce ot cag through the wy rogram, whch art of the Lux Wrele Tool ackage. The wy rogram mofe to erform cag cotuouly a ether wrte all RSSI reag to a fle or fee them to our mulato rogram ecrbe below Oeratg Sytem a Drver Coerg the rver metoe above, the oeratg ytem we chooe Lux. I artcular, we ue ReHat Lux 7.3 to tall the bae ytem a etu all other rogram eceary by comlg them. Sce the efault kerel rove the yeta ocket PCMCIA rver, t wa eceary to recomle the kerel wthout PCMCIA PCMCIA rver were the comle oute of the kerel tree a talle. We the comle the ecal rver wrtte by Moutafa Youef, ame mwavela_c. For the cag fuctoalty to work, we ee the wy rogram artcularly from Wrele Tool vero 20. Suort for acce ot cag ext ether earler vero, or later vero Smulato To evaluate our rooal, we have eveloe a crete evet mulato rogram C++ that mmc the movemet of a moble oe wth the evromet. Th rogram feature a GUI wrtte ug the Fat Lght Tool Kt for C++ FLTK..3, that grahcally lay the locato trackg ytem we rooe. Th mulato lay the curret locato a oretato of the moble oe the 37

51 lato, 2 the artcle the oteror trbuto geerate by the artcle flter, a 3 varou locato a oretato etmate erve from the artcle. The rogram caable of two moe of mulato a a lve moe a exlae below: Smulate walk through: I th moe, we mulate movemet of the moble oe lato through the evromet by reag a movemet fle. The movemet fle a ASCII fle cotag the ath the uer wll follow through the urato of the mulato. A raom RSSI reag from the wrele ma, eveloe the trag hae bae o the locato cell a oretato of the moble oe, gve to the artcle flter to geerate a oteror trbuto every 0.5 eco. The artcle flter the erform the meauremet a moel uate a lay etmate of the uer locato o the GUI. Recore walk through: I th moe, we make a oerator erform a walk through the evromet wth the moble oe. The lato recor all RSSI reag collecte by the mofe wy rogram to a fle urg the walk through. Next, we ru the mulato the recore walk through moe whch t rea RSSI reag off th fle a fee them to the artcle flter. The artcle flter the erform the recto a moel uate te a uate the artcle o the GUI. The artcle tur uate the etmate o the GUI, whch lay the etmate locato a oretato of the moble oe for the recore walk through. 38

52 Lve walk through: I th moe, a oerator erform a walk through whle the mulato rogram rug. The mofe wy rogram fee reag from all acce ot rectly to the artcle flter urg the walk through. The artcle flter the erform the recto a moel uate te a uate the artcle o the GUI. The artcle tur uate the etmate o the GUI, whch lay the etmate locato a oretato of the moble oe real-tme. The rogram make ue of object orete rogrammg cocet a feature a moular eg. Whle our emotrato lay the evromet ue our exermet, the moular eg allow a uer to chage eceary mulato arameter through a gle cofgurato fle a cutomze the rogram to mulate the rooe metho ay ere evromet. 6.2 Methoology Havg cue the comlete exermetal etu the revou ecto, we ow exla the methoology of our rooe metho. I our rooe metho, localzato of a wrele eable moble oe oe two hae: The Trag Phae The Localzato Phae 6.2. The Trag Phae Bulg the Wrele Ma The trag hae eetally cot of bulg a wrele ma of the evromet. It terme The Trag Phae ce th hae ha to be execute oly oce for a gve evromet. It eceary that the evromet rema cotet 39

53 from th hae to the localzato hae for localzato to work. Partcularly, t mortat that the acce ot rema the ame locato from th hae to the ext becaue the wrele ma eeet o the acce ot locato. We bul a eor ma or the wrele ma of the evromet by amlg the ace a gatherg ata at varou reefe ot the oor evromet. Th ma form a tattcal rereetato of the evromet bae o the two acce ot. To bul the ma, the floor area formg the oor evromet wa meaure a ve to cell of kow meo a how Fgure 6.. Samle et of 00 RSSI reag from each acce ot are collecte each cell. Reag from multle acce ot are collecte cocurretly o that covarace meaure betwee reag from fferet acce ot are val. Sce the huma boy aborb rao wave, the oretato of the oerator wth reect to the acce ot whle collectg reag affect the ma gfcatly. To utlze th charactertc for our beeft by ug t to rove oretato etmate, we collect reag for each of eght oretato North, Northeat a o o each cell. Th amle et form the ata for comutg the wrele ma for the artcle flter. The wrele ma telf comute o the fly by the mulato rogram a cue the followg ecto. Fgure 6.2 how a wrele ma of the evromet eveloe ug the outhwet acce ot. Th ma eote the gal tety trbuto acro the evromet wth the moble oe facg outh. Sgal tety eote by hag the evromet: Darker hae cate rego where the tety of the gal hgh, whle lghter hae cate rego wth lower tety. 40

54 Fgure 6.2: Wrele ma for the outhwet acce ot South The Localzato Phae I th ecto, we ecrbe the varou arameter a aumto that we ue for our mulator Program Italzato I the rogram talzato hae, we talze the mulato rogram arameter ecfc to our evromet. Fle cotag the wrele ma, the evromet arameter clug the cture for the GUI, etc. are loae, followe by talzg varou tattcal arameter lke lmt o varou value, mea, taar evato, etc. All te the talzato hae are rea off a gle cofgurato fle, whch a ASCII fle a uer ca ealy mofy to etu ere mulato arameter. The mulato executo moe alo ecfe the cofgurato fle. For the artcle flter to erve a oteror trbuto, t ee a ror trbuto form whch to reamle artcle weght. Whe the mulato rogre, the oteror trbuto comute the revou uate cycle ue a the ror trbuto. However, the begg, the artcle flter oe ot have a ror 4

55 trbuto avalable. Sce our tate-ace moel cot of three egree of freeom, the artcle flter wll ee to comute oteror trbuto for thee three meo. For mulato uroe, we talze all the three meo bae o a Uform trbuto,.e. the artcle are rea acro the etre evromet a uform maer Rug the Smulato I the revou ecto, we have ecrbe the three moe whch the rogram ca ru. The oly fferece betwee the three moe how we fee the latet reag to the artcle flter. Coerg that thee fferece are exlae the revou ecto, we rocee wth th cuo aumg that the ew reag are avalable. We ue the ew reag to geerate a trbuto for the locato of the target acro the evromet, followg whch the artcle flter erform the meauremet a moel uate te. Whle t feable to comute uch ety ma for all oble reag, th woul occuy a coerable amout of memory ce we have 00 reag amle x 88 cell x 8 oretato x 2 acce ot x 96 oble ew reag ma to comute, a o, we comute them o the fly The Meauremet Uate Oce the wrele ma are avalable, the artcle flter erform the meauremet uate te, whch we uate the weght of each artcle. For th, we frt comute the ety value for the curret reag from the wrele ma. Reag wth a cell eem to follow a Gaua trbuto a how Fgure 6.3 a therefore, we ue the Gaua robablty ety fucto 42

56 = X X V X X k T e V x 2 2 π. I th fucto, V eote the etermat value of the varace-covarace matrx, wth σ a the taar evato a the covarace betwee l a m,.e k k k k k V σ σ σ σ σ σ σ σ σ Μ Μ Μ 2 σ lm 2 = m m l l lm σ X the ata RSSI reag,.e., k X Μ 2 X the mea of X,.e. X k 2 Μ the k k AP = th reag the et of reag take from acce ot k, the umber of reag each cell of the wrele ma, 43

57 X T the traoe of X. After comutg th ety value for the curret reag, we ue th ety value a the weght of each artcle, a rocee a ecrbe the Sequetal Imortace Samlg algorthm Chater 3. Fgure 6.3: Sgal tregth trbuto a cell The Moel Uate Oce the meauremet uate erforme, all three meo of the artcle are uate bae o a zero-mea Gaua moel. The taar evato of thee moel are ecfe the cofgurato fle a may be mofe to ut the evromet. We the reamle the artcle bae o ther ew weght a ecrbe Reamlg algorthm Chater 4. A uformly trbute raom varable ue a the threhol N τ for egeeracy. 44

58 A mortat factor that we caot gore urg the moel uate the wall of the bulg that make u the evromet. Sce t ot feable for a moble oe to a through wall, artcle crog wall o ot make ay ractcal ee. Coequetly, after uatg the meo of each artcle, we check to make ure that t oe ot cro ay wall. If a artcle crog a wall, t weght reage to zero a coequetly, t a goo a o-extet the oteror trbuto. Partcle wth zero weght are reamle urg the ext terato a the umber of artcle ket cotat throughout the mulato. Followg the moel uate, we comute varou etmate of the moble oe locato a oretato, whch are cue Secto We the uate the GUI wth ew locato of each artcle a ew etmate. We erform the meauremet a moel uate te oce every 0.5 eco a are able to track the moble oe movemet through the evromet Locato Etmate Whle the artcle flter geerate a oteror trbuto of artcle, each wth t ow locato coorate a oretato meaure, t u to a uer to extract a ere etmate from th trbuto. We have mlemete four uch etmate a thee are cue the followg ub-ecto Etmate : Sum of the Ivere Dtace Th metho comute the weght of each artcle wth reect to t tace from all other artcle. The tace from oe artcle to aother verte to rove a weght wth reect to the other artcle. Such weght are comute wth reect to 45

59 all other artcle a thee weght cumulatvely eterme the fal weght of the artcle. The weght of all artcle ue the flter are comute th way a the artcle wth the maxmum weght egate the bet etmate. Th metho ru O Etmate 2: Hghet Partcle Dety Crcle wth Gve Rau Lke Etmate, we comute a weght for each artcle a the artcle wth the hghet weght choe a the bet etmate. To comute the weght, crcle wth the gve rau cetere o each artcle are aume. The umber of artcle each uch crcle eterme a ue a the weght. The weght of all artcle the flter eterme mlarly. Th metho alo ru O 2. I our exermet we ue a crcle wth a mall rau 0.m for th etmate Etmate 2: Hghet Partcle Dety Crcle wth Gve Rau Th etmate the ame a Etmate 2, excet that a crcle wth a much larger rau ue. We ue a crcle wth a rau of m for th etmate Etmate 3: Mea of All the Partcle Ulke the revou etmate, o weght are comute th metho. The value of each meo of the artcle average acro all artcle a the reultg umber are ue a the bet etmate. Th metho ru O. Whle the artcle are retrcte from ag through wall, o uch retrcto are moe o the etmate to facltate accurate aaly a erformace tue. Coequetly, a etmate may come u wth a locato that oute of the evromet eeg o how the artcle are trbute acro the evromet. 46

60 CHAPTER 7 EXPERIMENTAL RESULTS I th chater, we cu varou exermet coucte a reet ther reult. We wll frt coer exermet wth the mulato rug the mulate walk through moe, followe by the recore walk through moe a fally, the lve walk through moe. I each cae, we reet the moble oe movemet ath a a ahot of the mulato GUI at varou tage through the roce. 7. Smulate Walk Through I th ecto, we reet reult of our exermet wth the mulato rug the mulate walk through moe. The mulate movemet ath of the moble oe a how Fgure 7.. We have eveloe a movemet ath wth the oe movg wth varyg velocte a how the fgure. Fgure 7.: Movemet ath for the mulate walk through wth velocte 47

61 The followg fgure how ahot of the mulato whle t rug. We ee that the artcle 3000 are able to follow the oe through the etre urato of the mulato. The actual moble oe locato rereete by a whte crcle, artcle oteror trbuto are rereete by mall re ot, a the varou etmate cue ecto through , the ame orer, are rereete by hae crcle gog from lghter to arker hae. 48

62 Fgure 7.2: Smulato ahot mulate walk through moe A oberve, eve wth the aumto that the RSSI reag a cell follow a bac Gaua trbuto, the ytem erform a far job of trackg the uer. 7.. Etmato Error Data from the varou locato a oretato etmate exlae ecto wa collecte urg the mulato ru a error etmato are eterme by comutg the fferece betwee true locato a oretato value a thoe rouce by the etmate. Fgure 7.3 a 7.4 how error lot for locato a oretato, reectvely, for oe mulato ru. 49

63 Fgure 7.3: Error lot for locato Fgure 7.4: Error lot for oretato I orer to aalyze the umber of artcle requre to obta etmate wth the ere reco, tral mulato were ru for the artcle flter ervg oteror 50

64 trbuto wth 200, 500, 800, 000, 500, 2000, 3000, 5000 a 0,000 artcle. Data for of thee ru were collecte for eght tral for each artcle umber value, a are ummarze below. The followg fgure, 7.5 how error lot for each etmate for locato average acro all the eght ru er artcle umber, a fgure 7.6 how error lot for oretato, alo average acro the eght ru for each etmate. Thee lot cate that reco mrove wth creae the umber of artcle ue the artcle flter. Fgure 7.5: Average error locato mulate walk through moe 5

65 Fgure 7.6: Average error oretato mulate walk through moe 7..2 Partcle Flter Performace wth a wthout Oretato To evaluate the erformace of the artcle flter wthout oretato, the mulato wa ru wth the artcle flter havg oly two meo oe each for x a y coorate. Ug th artcle flter, mulato were ru mlar to thoe ecrbe Secto 7.., by varyg the umber of artcle. The followg fgure, 7.7, how error lot for each etmate for locato average acro all the eght ru er artcle umber. Thee lot cate that attemtg to etmate oretato ug the artcle flter oe ot affect t erformace a far a etmatg locato cocere. 52

66 Fgure 7.7: Average error locato wthout oretato 53

67 7.2 Recore Walk Through I th ecto, we reet reult of our exermet wth the mulato rug the recore walk through moe. Whle everal ru were coucte th moe, we rocee to rove a etale aaly of oe ru th ecto. The movemet ath of the moble oe a how fgure 7.8 below. To how the true locato of the target, a mulate movemet ath fle wa eveloe wth velocte bae o the actual movemet urg the ru. The mulato raw a aroxmate locato for the moble oe ug th movemet ath fle urg each terato a alo ue to comute error the etmate. Coequetly, the error comute from the etmate are oly aroxmato of the actual error. Fgure 7.8: Movemet ath of the moble oe recore walk through moe Smulato ahot howg the aroxmate locato of the moble oe a the etmate ug the color cog a ecrbe Secto 7. are how Fgure

68 Fgure 7.9: Smulato ahot recore walk through moe Smlar to the mulate walk thru, the ytem erform a far job of trackg the uer the recore walk thru moe Etmato Error Fgure 7.0 a 7. how error lot for locato a oretato, reectvely, for over the ame equece of mulato ru ue Secto

69 Fgure 7.0: Average error locato recore walk through moe Fgure 7.: Average error oretato recore walk through moe 56

70 7.3 Lve Walk Through I th ecto, we mly how cture of the actual evromet wth me couctg a walk through a correo g ahot of the mulator GUI wow. Fgure 7.2: Lve walk through 57