Indoor Navigation without the use of GPS utilizing Intelligent Data Algorithms

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1 Idoo avigaio wihou he use of GS uilizig Iellige Daa Algoihms Sco M. Gif e Sae Gea Valley School of Gaduae ofessioal Sudies 30 Eas Swedesfod Road, Malve, A 9355, USA smg80@psu.edu Asac avigaio i oday s wold is domiaed y he Gloal osiioig Sysem (GS). GS is ecomig commecially ad socially acceped as he es posiio epoig sysem. While his sysem offes uses upecedeed posiio accuacies, GS magially woks idoos. The GS sysem elies o saellies o solve fo a use s posiio. These saellies have a vey low sigal powe ad mos eceives have oule acquiig/ackig idoos due o he sigifica amou of osucios. To solve his polem, a mehodology is discussed o pefom idoo avigaio wih commecially availale pas. Thee sepaae daa souces ae comied i his idoo avigaio sysem: a ieial avigaio sysem, disace/wall sesos, ad a digial map of he uildig. Also povided i he pape, ae he esuls fom a sofwae simulaio of he idoo avigaio sysem. y ielligely comiig he hee sepaae daa souces, ee accuacies ha a sadaloe GS eceive ca e achieved (0.5 mees vs. 5 mees). Keywods Idoo avigaio, Ieial avigaio Sysem, IS, Disace Sesos, Wall Sesos Ioducio The Gloal osiioig Sysem (GS) is a ioxicaig sysem, offeig a use eal-ime 5-mee hoizoal asolue RMS (oo-mea-squae) posiio accuacy. GS woks y measuig he disace fom a use s cue locaio o muliple saellies i oi. These disaces ae called pseudoages. Fom he pseudoages, a posiio soluio is fomulaed. u he saellie sigals have low powe, so GS does o always wok idoos. Jus ecause GS does o wok well idoos, does o mea ha idoo avigaio is o waed. Idoo avigaio will have a affec o a wide vaiey of applicaios: waches, lapops, DAs, cell phoes, ec. Maye soo, whe a peso isa-messages a fied, hei cue locaio will also pop up. Idoo avigaio is o a ew idea; oo hoyiss have ee doig small-scale idoo avigaio fo may yeas. The sysems used have mosly elied o simple dead eckoig. Simple dead eckoig is easy ad he devices ae usually small wih lile powe cosumpio. omally wih his mehod, posiio accuacies quickly degade ove ime. Aleaive o cheap dead eckoig is o use a Ieial avigaio Sysem (IS). A IS is a moe complex dead eckoig sysem ha seses moio ad oaios diecly. Accuae ISs of he pas have ee limied o miliay vehicles o elaively high value commecial applicaios such as commecial ailies. These devices wee expesive ad lage ad o suied fo ooics, huma weaig, o ohe small applicaios. Oly uil ow has echology ee eady o ake o he idoo avigaio polem. Smalle ad fase compues allow fo moe poweful algoihms. ompues ca soe huge amous of daa, such as a digial map of a uildig. Sesos have also goe moe accuae ad less expesive. A IS adequae fo his ask ca e ough elaively

2 cheaply. Wih he comig age of Mico-Eleco-Mechaical Sysems (MEMS), a aveage IS will also e vey small ad uoiceale. Disace sesos (o deec a disace o a ojec) ae commecially availale wih sumee accuacies. Idoo avigaio File Theoy Fug of a IS, disace sesos, ad a digial map of a uildig wih a idoo avigaio file will povide he soluio o he idoo avigaio polem. The compoes will o fucio accuaely aloe. The IS posiio accuacies will gow uouded ove a sho amou of ime. The disace sesos will o kow wha diecio hey ae seg wihou IS aiude oupus. The digial map povides he esimaed ages fo he disace seso age measuemes. Wihi he oveall idoo avigaio file is he disace seso file. This file specifically compues he use s hoizoal posiio fom he diffeece ewee measued ad esimaed ages. This idoo avigaio sysem is coceed wih a use s hoizoal posiio ad o veical. The use is assumed o always e o he same floo of he uildig. The idoo avigaio file i Figue ielligely comies he daa souces ad keeps he posiio uceaiies elaively low. Figue Idoo avigaio File lock Diagam. Ieial avigaio Sysem The mai pupose of a ieial avigaio sysem fo he idoo avigaio file is o deemie he oieaio of he disace sesos. The IS also has he eefi of eig ale o deemiig a use s velociy ad posiio. To do all of his, a IS usually icopoaes six sesos: hee acceleomees ad hee gyoscopes. Acceleomees measue he uses acceleaio while he gyoscopes measue oaio ae. The mai ypes of ISs ae gimaled ad sapdow. I a gimaled sysem, he gyoscopes mechaically oae he acceleomees, keepig he acceleomee axis aliged wih he avigaio coodiae fame. The avigaio coodiae fame is he plae age o he Eah s suface a a give locaio (also efeed o as he local age fame). I a sapdow sysem, hee ae o movig pas. I is up o he compue o esolve he acceleaio io he avigaio coodiae fame. Today, almos all sysems ae sapdow ecause he compuaio powe is availale ad hee ae o movig pas; hus esulig i a smalle, lighe, low cos sysem. To ge posiio, he IS has o iegae he use s acceleaios as measued y he acceleomees. This is doe i he avigaio coodiae fame. This way he sysem ca keep ack of how much he use has moved Eas, oh,

3 ad Up. I a sapdow sysem, he acceleomees measue acceleaio i he ody coodiae fame. The ody coodiae fame is diecly elaed o he avigaio coodiae fame hough oll, pich, ad headig. As he IS oaes, so does he coodiae fame. The IS acceleomees measue acceleaio i he ody coodiae fame, u hey eed o e i he avigaio coodiae fame ce ha is whee a use s posiio is defied. The soluio o his is o use a diecio-coe-maix o oae he acceleaios fom he ody coodiae fame io he avigaio coodiae fame. Equaio shows he calculaio of oaig he acceleaio veco measued i he ody coodiae fame o a acceleaio veco i he avigaio coodiae fame. A = A () A is he acceleaio veco i avigaio coodiae fame. A is he acceleaio veco i ody coodiae fame. is he ody-o-avigaio diecio-coe-maix (defied lae). Equaio is o used ecause i is ee o asfom icemeal velociy ( V, delavees) fom ody o avigaio ha o go diecly fom acceleaio. Fied & Kayo (997) explai i as, The use of icemeal velociies isead of isaaeous acceleaio is impoa o peseve he coec velociy i he pesece of chagig acceleaio duig a samplig ieval. V () = A ( k ) d + A ()d () V (3) () = () V () Equaio iegaes A io ug apezoidal iegaio. Equaio is o vey useful fo he easo povided y May (00), I geeal, he acceleomees povide a pulse ai whose fequecy is popoioal o acceleaio. This pulse ai is accumulaed, ad heefoe, oly delavees ae availale ayway. Equaio 3 he oaes he V fom he ody coodiae fame io he avigaio coodiae fame. Equaio ad Equaio 3 do o ake io accou scullig eos. Scullig eos ae he eos due o he fac ha he diecio-coe-maix is also chagig wih ime. eglecig he effec of scullig will have a egligile effec due o he low accuacies of he sesos used i he IS fo his idoo avigaio file. V = V k + V () Equaio uses he use s posiio ( V () ( ) () (5) ( k ) = ( k ) + V ( k ) d + V ()d V o updae he use s velociy i he avigaio coodiae fame ( V ). Equaio 5 updaes ) fom velociy ( V ) ug apezoidal iegaio. If oll (φ ), pich (θ ), ad headig (ψ ) of he use ae kow, he diecio-coe-maix fom ody o avigaio is defied i Equaio 6 (Fael & ah,998). cos = ( ψ ) cos( θ ) ( ψ ) cos( φ ) + cos( ψ ) ( θ ) ( φ ) ( ψ ) ( φ ) + cos( ψ ) ( θ ) cos( φ ) ( ψ ) cos( θ ) cos( ψ ) cos( φ ) + ( ψ ) ( θ ) ( φ ) cos( ψ ) ( φ ) + ( ψ ) ( θ ) cos( φ ) ( θ ) cos( θ ) ( φ ) cos( θ ) cos( φ ) (6) ecause he IS uses gyoscopes, oll, pich, ad headig cao e compued diecly. The gyoscopes measue he ae of chage of oll, pich, ad headig. Iegaig hese aes idepedely o ge he desied aswe will o

4 wok ecause he coodiae fame is also oaig. So a pue oll ae measueme i oe ime fame may e coupled wih pich i he ex. To calculae fom oll, pich, ad headig aes, quaeios ae used. A uaeio is a compac mahemaical way o depic oaios. Iiializaio of a quaeio ( ) fom a diecio-coe-maix is give i Equaio 7 (ah & Fael, 998). + + = [3,3] [,] [,] [,] [,] [3,] [,3] [,3] [3,] (7) A iiial diecio-coe-maix is oaied hough special iiializaio pocedues. Whe a IS sas ou o a saioay plafom, he oly acceleaios ae due o he eah s gaviy. Also, he oly oaio duig his aligme is due o he eah s oaio. To mahemaically level he IS, a diecio-coe maix is compued such ha o acceleaios ae sesed i he oh ad eas diecio, ad o agula oaio is sesed aoud he eas gyoscope. Exacio of oll (φ ), pich (θ ), ad headig (ψ ) fom a quaeio ( ) is give i equaios 8, 9, 0 (Fael & ah, 998). Equaio 9 is wie wog i ah & Fael (998). Ug a simila equaio fom Fied & Kayo (997), Equaio 9 has ee coeced. ( ) ( ) ( ) 3, aca + = φ (8) ( ) ( ) 3 = θ (9) ( ) ( ) ( ) 3 3, aca + = ψ (0) The IS gyoscopes measue oll ae ( p ), pich ae ( q ), ad headig ae ( ). To use hese measuemes, iegae he isaaeous ae measuemes ove he measueme-samplig ieval o ge,, ad R. Equaio shows his mahemaically. Equaio shows how o updae he quaeio fom he iegaed aes (ah & Fael, 998). () = d p 0 τ ( ) = d q 0 τ ( ) = d R 0 τ ),, ( R = () () ( ) k R R R = cos cos cos cos () Equaios o coai all he ifomaio eeded o povide IS daa o he idoo avigaio file.

5 . Disace Sesos Disace Sesos ae he way ha he idoo avigaio file seses he eviome (walls of a uildig). Disace sesos ae elaively cheap fo good accuacy. Mos disace sesos ae a acive seso, meaig ha hey sed ou a pulse (ligh o ulasoic) o deec a ojec. Two impoa facos of disace sesos ae hei effecive age ad accuacy. Ligh ype sesos ae moe commo fo disaces less ha a mee, while ulasoics have a age up o es of mees. The mai disadvaage of ulasoic sesos is ha hey have a lowe accuacy ha ligh ype sesos. Ulasoic sesos omally have a accuacy of eh of a mee, while ligh ype sesos have a accuacy of hudedh of a mee. The disiuio of he disace sesos o he physical sucue of he idoo avigaio sysem is impoa. Figue shows a -D example of posiio esimaio wih age measuemes. The uceaiy of he posiio depeds upo oh he qualiy of he age measueme ad he geomey of age sesos. The gay aeas i Figue show he uceaiy i a posiio soluio fom agig a diffee agles. The seup i he middle povides he es geomey. Figue 3 shows examples of good ad ad disace seso aagemes. The oal ume of disace sesos eed o e disiued evely. couesy of (Ege & Misa, 00) Figue The shaded egio epeses he uceaiy i he posiio esimae ased o diffee geomeic cofiguaios (Ege & Misa, 00) Figue 3 Examples of good ad ad geomey aagemes fo he disace sesos To ake all he disace seso measuemes ad ge a posiio, a disace seso file is eeded. The disace seso file, which is pa of he idoo avigaio file, will ake a aiay amou of seso measuemes ad figue ou he use s posiio (fully explaied lae). To calculae a esimaed disace/age fom he use o he wall equies kowledge of whee he walls ae. The digial uildig map is used fo his. Ug he diffeece ewee he measued age ad he esimaed age, he file uses a leas-squaes soluio o solve fo posiio. Tale defies some paamees o e used i he disace seso file. Figue shows picoially he defiiio of he seso mou agle. Figue Seso Mou Agle

6 Tale aamees fo he disace seso file α ρ h seso mou agle wih espec o he IS i he ody coodiae fame (Figue ) Measued age fo he h disace seso i he ody coodiaes fame Eρ Esimaed age fo he h disace seso W ( x, y,ψ ) Fucio o calculae he disace/age o a wall fom he digial uildig map ias Seso ias fo he h disace seso (iiially zeo) Equaios 3 o 9 ae he equaios o solve fo he use s posiio fom he age measuemes. ( ρ ias ) cos( α ) ( ρ ias ) ( α ) ρ = (3) 0 ( ρ ) + ( ρ ) x y Μ = () E ( x y ψ α ) ρ = W, +, (5) Z = Μ Eρ (6) Eρ x Eρ H = M Eρ x Eρ Eρ y Eρ M Eρ y Eρ δ X = (8) T T ( H H ) H Z + δx = (9) Whe he disace sesos make a age measueme, he measueme is i he ody coodiae fame. Equaio 3 oaes he measueme ( ρ ) io a veco i he avigaio coodiae fame ( ρ ). is ceaed fom he IS aiudes as descied i Equaios 6 o. Equaio calculaes he measued hoizoal age i he avigaio coodiae fame ( M ). Eρ is he esimaed hoizoal age o he closes wall calculaed fom he digial map ased o cue locaio ad cue diecio/headig (Equaio 5). Takig he measued age ad suacig wha he file hiks he age should e (he esimaed age), a eo is fomed (Equaio 6). Z is a aay of he eo measuemes fom all he disace sesos a ime k. Equaio 7 is he way o fill he geomey maix ( H ) (Ege & Misa, 00). Thee is o ias em i he H maix ecause a ias is o commo o each age measueme. Ulike GS, each age measueme has is ow ias em ad cao e solved fo diecly i his leas-squaes soluio. The leas-squaes equaio is defied i Equaio 8 (Ege & Misa, 00). efoe equaio 9 ca e used, a easoailiy check is pefomed. This will keep he file fom movig he use hough a wall. (7)

A polem ha he disace seso file has o ake io accou is he fac ha his is a oliea polem. This is o-liea ecause as he file updaes he use s posiio, he pa of he wall ha is aged fom also chages.

7 ias fo each disace seso ges calculaed y uildig a age measueme diffeece ale. Ug pas esiduals fom each disace seo, a ias ca e calculaed fo each disace seso y aveagig he measueme eos ove he legh of he ale. A polem ha he disace seso file has o ake io accou is he fac ha his is a oliea polem. This is o-liea ecause as he file updaes he use s posiio, he pa of he wall ha is aged fom also chages. This ca e demosaed i Figue 5. To deal wih he o-lieaiy, he file is u i a loop uil he file has sopped movig he posiio (homes i o a aswe). Figue 5 The olieaiy of agig off of walls.3 Digial Map of a uildig Maps of he uildig ae vey impoa o he idoo avigaio file. Sice compues ca soe los of daa elaively cheaply, i is feasile o soe a uildig s ieal sucues. I is assumed i his pape ha he use has a pe-made map. 3 Simulaio A simulaio of he idoo avigaio sysem has ee developed o demosae he coceps descies i he pevious secio. Figue 6 shows a high-level lock diagam of he simulaio. Figue 6 Simulaio lock Diagam The simulaio sas y geig a use s sae fom he ajecoy geeao. The sae of he use is posiio, velociy, acceleaio, jek, aiude, aiude aes, ad aiude acceleaios. Aiude is oll, pich, ad headig. The ajecoy geeao follows a se of opeao eeed ime sequeced commads. As ime pogesses, he commads ae followed. The ajecoy geeao i he simulaio is kiemaically coec: he deivaive of posiio is velociy, he deivaive of velociy is acceleaio, ad he deivaive of acceleaio is jek. Sice he

8 simulaio simulaes sesos measuemes, he simulaio mus esue ha he acceleaio ad aiude ae daa is liealy coiuous wih espec o ime (e Sae ARL RD, 00). The ajecoy equaios ha make he use u/move fom waypoi o waypoi ae doe y applyig jek ad aiude acceleaio o he use saes. This way, oly jek ad aiude acceleaio ae o-coiuous i ime. y iegaig jek ad aiude acceleaios up o posiio ad aiude, ue moio is achieved. Tale descies he paamees used i he simulaio. Figue 7 shows he ue use ajecoy ad ue wall posiios. Tale Simulaio aamees Simulaio Rae 00 Hz ume of Moe alo Rus 0 Digial Map 0 mee y 0 mee oom Waypoi ad Headig ommads Walk aoud he oom, show i Figue 7 Huma Wole ±.0 i pich ad oll ± 0.5 i headig Figue 7 Tue use ajecoy ad ue wall posiios used i he simulaio The idoo avigaio file is ieded fo huma use. Theefoe, a paamee o make he moio of he use moe huma-like is added (huma wole). This wole accous fo he wave-like moio humas exhii duig walkig. A evey disace seso updae, ue age measuemes fo each disace seso ae calculaed ug he ue use sae ad he ue digial uildig map. Each calculaed age has o have he oll, pich ad headig of he use calculaed i i. These age measuemes ae he couped o simulae a ue disace seso. The ieial avigaio sysem is simulaed i he same mae. The idicaed map is made a he egiig of he simulaio y coupig he ue map wall coodiaes. This simulaes a map suvey eo. Measuemes used i he simulaio ae depede o he accuacies of he compoes. Tale 3 shows he umes used i he simulaio.

9 Tale 3 Seso Eos i Simulaio Acceleomees Gyoscopes Map Eo Disace Seso Disace Seso updae ae ume of Disace Sesos 5 mg (σ) oise 0. mg (σ) ias ADXL0 MEM Acceleomee (Aalog Devices Ic, 00) 0.05 deg/sec (σ) oise 0.00 deg/sec (σ) ias Gyochip II (Gloalspec Ic, 00) 0. mee (σ) 0.% of he age (σ) oise 0.0 mee (σ) ias age measuemes ae wihi 0.05 o mees each seso ges i s ow uique ias Ulaseso ofiguale Maeial Seso (Seix opoaio, 00) secod aaged 90 apa Resuls All figues i his secio ae ased o Tale ad Tale 3 specificaios uless ohewise oed. The figues wee ceaed y uig he simulaio 0 imes i a Moe-alo fashio. The esuls show ae he RMS of he 0 us adial posiio accuacy. O he same figue, a saigh lie of he fom y = mx + is fi o he RMS daa. The slope (m) is he eo gowh ove ime (mees pe secod). The ias (mees) is he iiial accuacy a he egiig of he simulaio. As descied i he Disace Seso secio, he idoo avigaio file is sesiive o he aageme of he disace sesos. Figue 8 shows he diffeece ewee he fou geomey aagemes of Figue 3. Figue 8 The diffeece ewee disace seso geomeies

The epeaed spikes i Figue 8 esul fom he use s ajecoy ad is elaioship o he walls i he oom. The use s ajecoy is epeaig aou evey miue. ewee disace file updaes, he use s posiio is slave o he IS.

10 The epeaed spikes i Figue 8 esul fom he use s ajecoy ad is elaioship o he walls i he oom. The use s ajecoy is epeaig aou evey miue. ewee disace file updaes, he use s posiio is slave o he IS. A oe poi i he ajecoy, he posiio of he use is such he disace seso file cao make a updae. This is ecause he use s assumed posiio is oo ea a wall. This also causes he esimaed ages o fall elow he sesos miimum opeaig age. To coiue o he polem, he disace file does o allow movig he use hough a wall. Figue 9 shows he use s idicaed posiio ad he idicaed wall posiios. Figue 9 Idicaed use s ajecoy ad idicaed wall posiios used i he simulaio The disace seso updae ae is also a impoa faco. ewee updaes, he IS cools he idicaed posiio. The IS is owhee ea as accuae as he disace seso measuemes. So he loge ieval ewee updaes, he moe he use s posiio difs. I is impoa o have a updae ae compaile wih he dyamics of he use ad he amou of IS dif. Figue 0 shows hee updae aes: secod, 0 secods, ad 0 secods. 0 secods is he wos ecause he use has o ely o he IS oo much. Also, he use has fiished aou a hid of he ajecoy wihou eve havig ake oe disace seso posiio updae. Figue 0 The diffeece ewee disace seso updae aes

The ee he map, he ee he posiio fix. Figue The diffeece ewee map suvey eos Figue peses he esul of a hou u. The eo gowh is due o he IS headig eo gowig ove ime.

11 o mae how he digial map of he uildig is ceaed, hee will e esidual map eos (suvey eos). The map eo will show up diecly i he RMS adial posiio accuacy. Figue shows he eo fom havig o map eo, a 0. mee (σ) eo, ad a 0.5 mee (σ) eo. The map eo is vey impoa ecause he idoo avigaio file cao do ayhig special o miigae he effecs. The ee he map, he ee he posiio fix. Figue The diffeece ewee map suvey eos Figue peses he esul of a hou u. The eo gowh is due o he IS headig eo gowig ove ime. Afe aou 55 miues, hee appeas o e o daa. This is ecause he idoo avigaio file ges los. The headig eo is so lage (0 degees) ha he file cao wok. Ug ohe sesos ca clamp he headig eo, u hey ae o discussed i his pape. [y = x() + 0.9] Figue Simulaio of he idoo avigaio file ove oe hou

12 5 oclusio Idoo avigaio is saig o come of age. Wih GS o availale idoos, ew echiques will eed o e hough ou. This pape offes oe mehodology o solve he idoo avigaio polem. y ug commecially availale hadwae ad iellige algoihms, idoo avigaio wihou GS is possile. The idoo avigaio polem is solved specifically y comiig muliple daa souces. omiig diffee daa souces educes he idividual so-comigs of each seso aloe. Ug he iellige algoihms discussed i his pape miimizes hose eos. The simulaio poves he heoy ad gives a isigh io some ieeg aspecs of he idoo avigaio sysem. The aageme of he disace sesos o he use/plafom is impoa. y plaig a good layou fo he disace sesos, ee posiio accuacies ca e achieved. ecause he IS has a lage eo gowh ae, he fequecy a which disace seso measuemes ae made has o e ake io accou. y leig he IS asiio oo log ewee measuemes will cause he idoo avigaio file o ge los. A way o ge ee accuacies is o ge moe accuae maps. Map eos will make o eak he idoo avigaio sysem. The simulaio esuls of he idoo avigaio sysem ae vey good. osiio accuacies of less ha half a mee fo aou hou is he kid of accuacy ha is equied y a mode idoo avigaio sysem. Recommedaios fo fuhe sudy ae Add a 3-axis mageic oh seso o clamp he aiudes eos fom difig. Use a Kalma file o esimae IS eos ad disace seso misaligme eos. omie ulasoic sesos wih opical sesos o achieve he opimum accuacies fo vaiale disaces. Use wo digial cameas i a seeogaphic seup o deemie ages. 6 Refeeces Aalog Devices, Ic. (00), ADXL0, hp://poducs.aalog.com/poducs/ifo.asp?poduc=adxl0, (6 Jue, 00). ah, M., Fael, A.J., (998), The Gloal osiioig Sysem & Ieial avigaio, McGaw-Hill ompaies, Ic. ew Yok, pp 37-5 Ege,., Misa,., (00), Gloal osiioig Sysem, Sigals, Measuemes, ad efomace, Gaga-Jamua ess. Licol, Massachuses, pp Fied, W.R., Kayo, M., (997), Avioics avigaio Sysems, Joh Wiley & Sos, Ic. ew Yok, pp GloalSpec Ic. (00), Gyochip II, hp:// (6 Jue, 00). e Sae ARL RD (00), Tajecoy Oupu Geeao ool Loops. e Sae ARL, Wamise A. May, M.., (00), Geophysical ad Ieial avigaio Techology, e Sae ARL, Wamise A. Seix opoaio, (00), Ulaseso ofiguale Maeial Seso, hp:// (6 Jue, 00)

Supplementary Information

Supplementary Information Supplemeay Ifomaio No-ivasive, asie deemiaio of he coe empeaue of a hea-geeaig solid body Dea Ahoy, Daipaya Saka, Aku Jai * Mechaical ad Aeospace Egieeig Depame Uivesiy of Texas a Aligo, Aligo, TX, USA.