CRLB Derivation for Mobile Tracking in NLOS Propagation Environments

Transcription

1 0 Inenaonal Sos on Concaons an Inoaon echnoloes ISCI CLB Deaon o Moble acn n LOS Poaaon nonens Keen Y School o Sen an Geosaal nneen Unes o ew Soh Wales Sne Asala een@eeeo Dewcz Deaen o leconc nneen Macae Unes Sne Asala eewcz@ea Absac hs acle esens heoecal analss o oble acn n non-e-o-sh LOS oaaon enonens Wh soe aoaons concse analcal olas ae ee o he Cae-ao lowe bon CLB o osonn when easeens o sance hean anle an eloc ae eloe o esae he oble oson he ee lowe bon can be se as a eeence o he ealan o aos oble acn alohs n LOS scenaos Kewos-oble osonn; non-e-o-sh oaaon; CLB; sance; eloc; hean anle I IODUCIO Posonn n non-e-o-sh LOS scenaos s a challenn oble Alhoh a concaon a sll be aalable beween a oble an a base saon n he esence o LOS oaaon he snal senh s ch weae coae o LOS oaaon an a bas eo call occs n he e-o-aal OA easeens o OA-base sance easeens he bas eo s sall he onan eo soce n oson eenaon when sn sance easeens o achee sasaco osonal accac he ac o he bas eo s be ae o hs eason a ane o ehos an echnes hae been oose o osonn an acn n LOS scenaos - In hs ae he ocs s no on he eeloen o new ehos b on he heoecal analss o oson esaon eoance when acn oble enals n LOS enonens I nens o eelo lowe bons o see as a eeence o aos ehos Wh soe aheacal anlaons sle eessons o he Cae-ao lowe bon CLB ae ee o bencha he eoance o osonn n LOS scenaos when sance hean anle an eloc easeens ae all lze o oson eenaon Alhoh CLB o osonn has been nesae b an ahos -5 hee ae ew eos n he leae on he CLB eaon o oble acn n LOS scenaos esecall when hean an eloc easeen eos ae consee II POBLM OMAIO Conse ha a ehcle s ae n an ban aea he oson o he ehcle s esae b a cellla newo o anohe sla newo Sose ha he ehcle s whn he ao ane o a o o base saons s chaneable an so o he o ebes so ha sance easeens ae oce as s he ease sance beween he oble an he h base saon a e nsan s he easeen eo conssn o easeen nose an a LOS bas eo an s he e sance escbe b b b ae he oble oson coonaes a e nsan as b b ae he oson coonaes o he h base saon Also asse ha a hean senso an a seeoee ease he hean anle an he eloc o he ehcle esecel as { } ae he eloc eos an { } ae he hean anle eos he eson o nees s ha wha he naenal eoance l o he osonn s when he eo sascs o he sance hean anle an eloc ae en In he ollown he CLB wll be ee o see as sch a eoance l III CLB O MOBIL POSIIOIG Sose ha he oble eaches he h oson ae nall san o he s oson Le s eene he CLB o he h oson esaon when sance hean an eloc ae all eloe Dene he oson eco as Also ene he sance easeen eco as //$00 0 Cown 5

2 an s he sance easeen beween he oble an he h base saon a e nsan hen he lelhoo ncon assocae wh he snlesho oson esaes s en as ϑ 6 e / e G π ϑ ϑ 7 an ae ene as G G / 8 hs can be shown ha he IM s en as 9 } a{ } a{ } a{ 0 Cleal he aboe eecaons can be eene b he olas en n Aen A Wh hean an eloc easeens he elaons beween nehbon coonaes o oble osons ae en b / sn 05 / 05 s asse ha he oble ac seen beween wo nehbon oson ons s ea an he hean econ eans he sae n each sa eo aon can be he wen as / sn / / / / / B non he secon-oe eo es an an se o an sn o he case o sall hean anle easeen eos can be aoae as / / sn / sn / 5 6 As a esl he eenal coonae eos ae ea ncons o he eloc an hean anle eos Dene he eenal coonae eco an s esae as 7 Also ene he eloc eco an he hean eco as 8 hen en he oble osons eloces an hean anles he obabl ens ncon PD o he esae o he eenal coonae eco s escbe b / e / π 9 he eloc an hean anle easeen eos ae asse Gassan ano aables wh zeo eans hs 0 an s he coaance a o Wh soe aheacal anlaons can be shown ha 0 whch ae sec aces whose non-zeo coonens ae calclae accon o / sn sn / sn sn / sn sn / sn sn / sn / sn / sn an he loah on 9 oces he lo-lelhoo ncon as / / π he secon-oe aal eaes o he lo-lelhoo ncon wh esec o he coonens o can be eal ee o be 5

3 o he eenal coonae eco ene b 7 an he aaee eco ene n can be shown ha ; 0 else < < M 0 else M M M < < M 0 0 else else 0 else M 0 else Acconl he coonens o he assocae IM can be eene as G 6 When he sance hean an eloc easeens ae all eloe he on lelhoo ncon s sl eal o he llcaon o he wo lelhoo ncons: 7 an ae ene n 6 an 9 esecel an s asse ha he sance eloc an hean anle easeen eos ae all neenen hs asson s easonable snce he hee een aaees ae esae b een sensos o sses n eneal hs he IM o he nal oson esaes s eal o he s o he wo IMs en b Γ G 8 an G ae en b 9 an 6 esecel he CLB o he esaon o he cen oson on s hen en b Γ 5 Γ 9 Once he CLB o he esaon o each oson on s oce he aeae CLB o all he oson esaes alon he oble ah can be calclae Sose ha hee ae oall L oson ons on he oble ac eane hen he aeae CLB a be coe accon o L CLB CLB 0 L o bencha he SD o he oo ean sae eo MS o he oson esaon he sae oo o he CLB a be se e IV L CLB L UMICAL XAMPL In hs secon he ee heoecal lowe bons ae ealae necall hoh an eale In a heaonal cellla eloen he oble n wll call be sone b a nbe o base saons whch ae whn ao ane o he oble enal heeoe o slc we conse a scenao he oble s able o concae wh o base saons enoe b a sae an aeses alon a ah wh hee ac seens as shown n he oble enal s asse o oe alon he ah san o on P a a consan see o 60 /h he nose s oele as a zeo-ean Gassan aable wh a sana eaon SD o 50 A 0 B P P D 0 0 P 0 P P 0 P C 0 Illsaon o base saon conaon an oble ac shows he CLB o he oson eo ess he sbon aaee o he sance easeen eo bas he wo ces coeson o he case hee s no hean o eloc easeen eo an he case he SDs ae 7 e an 8 /h esecel I can be seen ha he CLB wh cal hean an eloc eos has eoance eaaon o 0 coae o he eal case o zeo hean an eloc eo In seee LOS conons he oson accac wol no be bee han 56 wh cal hean an eloc eos shows he ac o he hean eos on he CLB when he sance bas eo SD s 00 an wo SDs o he eloc eos ae selece I can be seen ha as he SD o he hean eo s eae han e he CLB nceases eal as he hean eo nceases In he case he SDs o he hean eo eloc eo an sance bas eo s e 0 /h an 00 esecel he SD o he oson accac wll no be bee han 5 shows he eec o he oble eloc easeen eos on he CLB when he SD o he hean easeen eo s se a an 7 e esecel an he SD o he sance bas eo s se a 00 he elaon beween he CLB an he SD o he eloc eo s also aoael ea Oe he ane o he eloc eo he CLB nceases b 78 P P 55

4 an 95 e 87% an 6% wh he wo hean eos esecel CL:B /h 7e Dsbon Paaee o Dsance o Bas ec o sance easeen eo bas CLB bon 0/h bon /h SD o Hean Measeen o e ec o hean anle easeen eos CLB bon 7 o bon o SD o Veloc Measeen o /h ec o eloc easeen eos V COCLUSIO In hs s we nesae heoecal eoance o osonn n LOS scenaos he sance easeen nose s Gassan an he sance easeen bas eo s aleh sbe Wh soe aheacal aoaons concse olas o he CLB wee ee o ehcle acn n LOS oaaon enonens when sn easeens o sance hean anle an eloc he heoecal esls oe sel noaon abo he bes acheable oson accac o an osonn sses he esls ae onl ee o he scenao he ane bas eo s aleh an he hean an eloc eos ae Gassan In he case o ohe eo sbons he CLB wol be een an he new olas nee o be ee ACKOWLDGM hs wo was soe n a b aonal aal Scence onaon o Chna ne Gan o 6705 APPDIX A: CLB O SIGL-SHO ALGOIHMS When he nose s Gassan an he bas eo s aleh sbe wh he PD en b e he PD o he easeen eo can be ee as e π / G G / e G / s he sana -ncon G s he SD o he Gassan nose aable an G Dene he sance easeen eco an he oble oson eco as Gen he oble oson eco he on PD o he sance easeen eco can be escbe b 5 G e e 6 π / he lo-lelhoo ncon s hen en b 7 he CLB o he esae o he h coonen o he oson eco s ene as CLB 8 s he she noaon a IM whose coonens ae ene b 6 9 ha s o D osonn he IM s ene as a sae a o sze as ollows: 0 56

5 Le s ee he hee een coonens o he IM wh a ocs on s Snce s en b 6 hen he s coonen o he IM can be ee o be G G b e G G G e e π 5 he eale eaon can be on n Aen B hee s no close-o eesson o he neal n ; howee he neal can be sole b sn a n-on Hean aae 7 ha s he neal s coe accon o n G κ 6 } { κ ae he en coecens an } { ae he en secc aable ales In he sae wa anohe coonen o he IM can be ee as b G 7 he he las nnown coonen o he IM can be ee n he sae wa as G 8 hen he CLB o he esaon o he snle oson on a e nsan can be calclae b CLB 9 s eloe APPDIX B: DIVAIO O H IM COMPO he s eae o he PD n 6 can be wen as 50 e e G G π 5 aon 50 can be eaane no e Acconl e e 5 an neaon oe 5 oces e e 5 Man se o he ollown esls: G G I a e e e π e e e e G G G G G I I π π 55 57

6 we oban G G e 56 Le s now ee he secon eae o he PD an s neal I can be shown ha e e e G G G π π 57 hs he secon eae o he PD becoes e e 6 G G G G G π π π 58 Slal an neaon oe 58 an an se o 55 we oban G G G G 59 nall cobnn he esls n 56 an 59 oces he esls as en b CS W Wan Z Wan an B O Dea A OA-base locaon aloh ecn he eos e o none-o-sh LOS oaaon I ans Vehcla echnolo ol 5 6 an 00 K G Lee an G-I ee he neo-on eho o an oal eaen o bas n laeaon locaon I ans Vehcla echnolo ol 55 no 9-0 l 006 K Y an Y Go Ioe osonn alohs o none-osh enonens I ans Vehcla echnolo ol 57 no -5 l 008 CK Seow an SY an on-e-o-sh localzaon n lah enonens I ansacons on Moble Con ol 7 no Ma L Con an W Zhan one-o-sh eo aon n oble locaon I ans Weless Concaons ol Ma P Bahl an V Paanabhan ADA: an n-b -base se locaon an acn sse n Poc I Con on Coe Concaons IOCOM M ezaa M Kaeh H s an aawa Sascal eoance o sbsace achn oble localzaon sn eeenal aa n I Wosho on Snal Pocessn Aances n Weless Concaons n C ezan C Desns an S Aes Geolocaon n nes wh an lse esonse nenn an neal newos I ans Weless Concaons ol Ma H Mao K Y an M n Posonn o LOS oaaon: aloh eaons an Cae-ao bons I ans Vehcla echnolo ol Se hoas D G Ccshan an D I Laenson A obs locaon esao achece wh base Kalan len o OA aa o weless sses n Poc I In S Sea Sec echnes an Alcaons Se Lao an B-S Chen obs oble locaon esao wh LOS aon sn neacn lle oel aloh I ans Weless Concaons ol 5 no o 006 K Y I Sha an Y Go Gon-Base Weless Posonn Wle-I Pess 009 Pawa AO Heo III M Pens S Coeal an O Dea elae locaon esaon n weless senso newos I ans Snal Pocessn ol 5 no A 00 Y H Kobaash an H Sa On e-o-aal osonn n a lah enonen I ans Veh echnol ol 55 no Se K Y -D localzaon eo analss n weless newos I answeless Con ol 6 no Oc S M Ka naenals o Sascal Snal Pocessn: saon heo Ue Sale e : Pence Hall 99 7 W H Bee CC Sana Maheacal ables an olae CC Pess