Combination of UWB and GPS for indoor-outdoor vehicle localization

Transcription

1 ombinaion of UW and for indoor-oudoor vehicle localizaion González J., lanco J.L., Galindo., Oriz-de-Galiseo., Fernández-Madrigal J.., Moreno F.., and Marínez J.L. {jgonzalez, Sysem Engineering and uomaion Deparmen Universiy of Malaga, 9071 Malaga, Spain bsrac sensors are saellie-based devices widely used for vehicle localizaion ha, given heir limiaions, are no suiable for performing wihin indoor or dense urban environmens. On he oher hand, Ulra-Wide and (UW), a echnology used for efficien wireless communicaion, has recenly being used for vehicle localizaion in indoor environmens wih promising resuls. This paper focuses on he combinaion of boh echnologies for accurae posiioning of vehicles in a mixed scenario (boh indoor and oudoor siuaions), which is ypical in some indusrial applicaions. Our approach is based on combining sensor informaion in a Mone arlo Localizaion algorihm (also known as Paricle Filer), which has revealed is suiabiliy for probabilisically coping wih a variey of sensory daa. The performance of our approach has been saisfacorily esed on a real robo, endowed wih a UW maser anenna and a receiver, wihin an indooroudoor scenario where hree UW slave anennas were placed in he indoor area. 1 Keywords Vehicle Localizaion, Paricle Filer,, UW. I. ITRODUTIO The problem of vehicle self-localizaion wihin indusrial scenarios is normally ackled by exploiing he paricular characerisics of he applicaion a hand. Differen approaches are usually considered according o he required accuracy, he available sensors and heir cos, he ype of he scenario, i.e. indoor or oudoor, ec. The laer is, apar from oher consideraions, he one ha has major influence when deciding appropriae soluions o he problem of vehicle localizaion. Indoor applicaions normally require a precise esimaion of he vehicle pose since he workspace is smaller and conains a diversiy of objecs o manage and obsacles o 1 This work was suppored in par by he European projec RFT-OOP- T , and he Spanish research conrac DPI avoid. n example in indusrial applicaions are rucks aimed o load and carry goods wihin a warehouse. In general, in hese scenarios riangulaion sysems based on lasers are commonly used, bu hey presen problems when dynamic obsacles or he own environmen configuraion block he line-of-sigh of he beacons. promising soluion for ha are radio signals like UW because of is peneraion capabiliy. On he oher hand, oudoor applicaions normally require less precision, i.e. a vehicle moving hrough a road or some wide space, whose localizaion can be provided by global posiioning sysems (). In a variey of applicaions, vehicles have o perform wihin a mixed indoor-oudoor scenario, and herefore, he combinaion of approaches relying on boh echnologies (UW and ) should be considered. simple soluion may consis of swiching beween differen algorihms based on each echnology according o wheher he vehicle is in- or ouside. However, in he ransiion areas (for example, when he vehicle is enering a warehouse), daa from he boh sources may coexis, hough he signal qualiy from each source may no be good enough for precisely assessing he vehicle pose independenly one from anoher. In hese siuaions, he combinaion of boh sensor daa should be managed coherenly and exploied o improve vehicle localizaion. UW 1 UW Figure 1. provides he global posiion of he vehicle and can be modeled hrough a probabiliy densiy funcion wih a given sandard deviaion. UW beacons (wo in he figure) yield range measuremens wih a cerain error ha can be also probabilisically modeled. The mos probable posiion of he vehicle can be obained by means of he probabilisic combinaion of all sensor readings.

2 In his paper we focus on mixed indoor-oudoor vehicle localizaion hrough a probabilisic combinaion of sensor daa acquired from differen sources: UW and. More precisely we propose a Mone arlo localizaion algorihm, also called Paricle Filer [19], ha represens he esimaions of he possible poses of he vehicle by means of a se of weighed samples (paricles). The main advanage of his approach is is abiliy o combine measures from differen sensors considering appropriaely heir probabilisic behavior. In a nushell, his is done by assigning o each paricle a weigh proporional o he probabiliy of receiving he available sensor readings from he pose hey represen. The higher he paricle weigh is, he higher is he confiden (belief) ha he pose represened by he paricle becomes he real pose of he vehicle. Oher ineresing properies of paricle filers are: - They are suiable o work wih almos arbirary sensor characerisics, moion dynamics, and noise disribuions, even non-lineariies, as long as some likelihood model of heir uncerainy can be given. - They can mainain simulaneously differen hypoheses abou he pose of he vehicle. This abiliy permis he localizaion sysem o rack a vehicle wihin complex and self-similar scenarios like parking areas [5]. - Since paricle filers sample he space of possible locaions up o a given sampling densiy, heir compuaional cos can be easily bound, and hey are easy o implemen [1]. In his paper we consider a se of UW beacons for indoor localizaion, for oudoor, and readings from boh sources wihin he overlapped areas. The proposed paricle filer approach copes well wih vehicle localizaion where UW and readings are available, eiher separaely or joinly, as demonsraed in real experimens. The srucure of he paper is as follows: secion gives an overview and a comparison of he UW and echnologies for vehicle localizaion. Secion 3 describes he mahemaical formulaion of Paricle Filers and is use for fusing readings from differen sensors. In secion 4, resuls from real experimens conduced in a mixed environmen are presened, proving he suiabiliy of our approach. Finally, some conclusions and fuure work are oulined.. UW II. UW D SESORS OVERVIEW The Ulra-Wide and (UW) echnology [15],[] was iniially developed by he US Deparmen of Defense in he early 1960s, demonsraing is paricular suiabiliy for radar and highly secure ransmission of informaion. everheless, he firs civil applicaions of his echnology did no appear unil owadays, UW is a well-known echnology for communicaions [4], bu only a few works have exploied i for vehicle localizaion by deriving he disance beween anennas hrough, for insance, he TO of daa packes (Time-Of-rrival) [3]. The main characerisics and advanages of he UW echnology for vehicle localizaion (and also for communicaions) are [8]: -Transmission. Unlike carrier-based sysems which work on a specific frequency, UW works by ransmiing a radio signal over a wide swah of frequencies (in he band beween 3.6 and 10.1 GHz). - Shor pulses and low power consumpion. Since he duraion of pulses is of he order of nanoseconds and hey are usually spread over a wide specrum, he energy of each ransmied pulse is very low (a power specral densiy of 41.5 dm/mhz). Hence, UW can be considered as a safe sysem for wireless ransmission and can coexis, heoreically wihou inerference, wih oher radio communicaion echnologies. -Maerials peneraion: The characerisics of he UW signal ransmission provide his echnology wih a high maerial penerabiliy making i suiable for indoor communicaions and vehicle localizaion. They are no affeced, in heory, by mulipah problems [], [17], alhough are no compleely free from ha problem. -ccurae posiioning: Due o he shor duraion of he ransmied pulses, UW echnology offers inexpensive and accurae posiioning wih cenimeer resoluion. par from he TO mehod used in his work, oher echniques can also be considered for pose esimaion of anennas, such as Direcion-Of-rrival and Signal-Srengh [6].. Global Posiioning Sysem () has become a wellknown and widely accessible echnology for absolue localizaion on he surface of Earh (geolocalizaion) [18], wih applicaions in many differen fields. asically, uses wo radio channels in he microwave band cenered a Mhz and 17.60Mhz. onsidering he radio ime-of-fligh laeraion i achieves an accuracy in localizaion around 1-5 meers in oudoor areas [7]. The main disadvanage of localizaion sysems based only on is ha hey need a good Line-of-Sigh (LOS) o saellies. This drawback is mainly due o he weakness of he signal and heir inabiliy o penerae hrough mos of maerials, which limis he use of o oudoor and open scenarios. Moreover, requires, a leas, four saellies elecronically visible, which is no always possible. The accuracy of can be improved by means of differenial (D) o achieve a resoluion of ens of cenimeers.

3 . vs. UW ased on he general characerisics of boh echnologies aforemenioned, hey are no sraighforward comparable bu complemenary. owadays, is a cheap echnology ha offers a sufficienly accurae localizaion in oudoor and open areas, almos around he world, in erms of a global frame (laiude, longiude, aliude). On he oher hand, UW provides more reliable and precise resuls, in erms of relaive localizaion wih respec o a local frame, a he expense of covering he working area wih cosly anennas. This makes UW echnology only applicable o indoor and relaively small workspaces. Therefore, exploiing he bes of boh echnologies may become he soluion for a large variey of mixed indooroudoor applicaions, like he one considered in his work. In he following, he proposed approach for combining and UW measures is deailed. III. PROILISTI LOLIZTIO D SESOR FUSIO. Problem Saemen Mehods for sequenial ayesian filering provide a grounded probabilisic framework for racking he sae of a sysem which is observable only hrough indirec and noisy measuremens. These echniques mainain a probabiliy disribuion ha capures he knowledge abou he sae of he sysem a a given insan of ime. This disribuion changes over ime following he evoluion model of he sysem and i is updaed wih each observaion by means of probabilisic sensor models. While closed form filers exis for Gaussian disribuions and sysems wihou srong nonlineariies ([10],[11]), we employ here a Paricle Filer ([14],[1]), due o some imporan advanages wihin he scope of he presen problem. Firsly, a paricle filer can cope wih arbirary disribuions, which enables performing global localizaion of he vehicle a sar-up or mainaining muli-modal disribuions in he presence of ambiguiies. Secondly, he probabilisic observaion model of UW sensors is srongly nonlinear and leads o disribuions ha could be hardly approximaed only by Gaussians. We derive nex he equaions of our paricle filer for robus UW- localizaion. Our purpose is o localize he robo wihin a planar environmen provided a se of beacons wih known 3D posiions { Β k} k = 1. Le s, u, and z denoe he sysem sae, he robo acions, and he observaions for any given ime sep, respecively. lhough we are ineresed in he robo pose (which we will denoe as x ), he sysem sae is augmened wih he se of unknown biases { b k} k = 1 of each UW beacon, ha is: s = x, b,..., b (1) { } 1 s discussed elsewhere [9], his provides a grea improvemen in erms of robusness agains he effecs of muli-pah for his kind of radio echnology. ow, by noicing ha he sysem sae s evolves as a Markov chain we can wrie down our esimaion problem ino he well-known sequenial form: p( s u1:, z1: ) p( z s, u1:, z1: 1 ) p( s u1:, z1: 1 ) = p( z s) p( s s 1, u) p( s 1 u1: 1, z1: 1) ds () 1 Observaion model Evoluion model To implemen his recursive equaion as a Paricle Filer M we sar wih a se of M samples in he sae space { s 1}, i= 1 called paricles, which are approximaely disribued according o he disribuion for he previous ime sep 1 (a uniform disribuion can be assumed iniially if here is no any informaion abou he robo pose). ccording o imporance sampling [1], a weigh ω 1 is also associaed o each paricle o compensae poenial mismaches beween he densiy of samples a a given area of he sae space and he acual (unknown) densiy. Following he mos common algorihm for paricle filering, Sequenial Imporance Sampling wih Resampling (SIR) [16], he se of paricles for he nex ime sep is generaed by means of he following seps: 1. Generae he new paricles by drawing samples from a cerain proposal disribuion, qs ( s 1, u, z).. Updae he weigh ω 1 for all he new samples based on he value of he observaion likelihood of each paricle. 3. Perform a resampling sep in order o preven he loss of paricle diversiy if a measure of qualiy of he paricles, for insance, he effecive sample size [1], falls below a given limi. One of he mos popular choices for he proposal disribuion is o draw samples from he sysem ransiion model, ha is, qs ( s 1, u, z) = ps ( s 1, u). In his case, updaing he imporance weighs simply becomes: ω ω 1 p( z s ) (3) ha is, he produc of he previous weigh wih he observaion likelihood evaluaed a each sae hypohesis s. In he nex subsecion we discuss in deail how o compue his erm, which is in charge of fusing he sensorial daa from he UW beacons and he. Regarding he sysem ransiion model, here are wo separae processes involved, one for each par of he augmened sae vecor s. For he common case of robo acions u, represened by incremenal odomery readings, he robo pose x is updaed by adding he pose change saed by he odomery o he previous pose and corruping i wih a cerain noise. This models he fac ha odomery measuremens can be inaccurae due o, for example,

4 slippage or uncalibraed parameers. For more deails abou hese models please refer o [] or [0]. The apparen bias of UW ranges due o muli-pah ypically remains consan unil new obsacles ener or leave he pah of he UW signal. Since accurae models for hese effecs may be exremely hard o obain, even having a deailed represenaion of all he elemens in he environmen, we employ here he following approximae evoluion model [9]. each ime sep, here is a probabiliy Pc [0,1] for he bias b k no o change, ha is, b =. On he oher hand, we consider a change k, bk, 1 in bias wih a probabiliy of 1 Pc. In hose cases, he change in he bias is modeled as a uniform disribuion, bu accouning for he consrain ha biases mus be nonnegaive. Ineresingly, his condiion can be easily incorporaed ino he paricle filer, while a Gaussian filer could no cope wih i. his poin we have described he basis of paricle filering using he sysem evoluion model as proposal disribuion q(). We mus remark ha his choice leads o a highly efficien implemenaion, alhough oher proposals [1] may be considered in he case of a sufficienly large number of sensors. From our real experimens and simulaions we have verified ha his choice for he proposal disribuion is well suied o a pracical number of UW beacons, e.g. up o 10 beacons a sigh a each insan of ime. Regarding he UW sensors, we can model he range values as having an unknown bias plus a zero-mean addiive Gaussian noise characerized by σ UW. Since he bias b k, has been esimaed joinly o he sysem sae, he sensor model mus accoun for he Gaussian noise only: p( z UW [] ) ( [] [], i i i,, ; UW k s = rk + bk zk,, σuw) (7) Here r k, sands for he expeced 3D euclidean disance beween he UW anenna onboard of he vehicle and he k h UW beacon, localized a k. Figure illusraes he observaion likelihood disribuions obained for each of he individual sensors and how hey are fused. a) b) c) d). Probabilisic Observaion Models s exposed in (3), paricle weighs are updaed hrough he [] observaion likelihood funcion p( z i s ). The inuiive idea behind his process is assigning higher weighs o hose hypoheses ha bes explain he sensor readings, discarding in he resampling seps hose paricles ha perform poorly. Wihou loss of generaliy we consider ha he observaion z conains one reading and a range reading for each UW beacon a each ime sep. Formally, we denoe he observaion variables by he se: UW,1 UW, z = { z, z,..., z } (4) Since i is plausible o consider ha he random errors in each of hese individual measuremens are independen, he observaion likelihood can be facorized as: UW ( ) ( ) ( k, ) p z s = p z s p z s (5) k = 1 The sensor can be appropriaely modeled by a D Gaussian over he ground plane, ha is: ( ) ( ;, ) p z s = x z Σ (6) where he associaed covariance Σ should be a funcion of he number of saellies observed a each insan of ime. For example, for 8 saellies we se a sandard deviaion value of meers. e) f) Figure. UW and likelihood probabiliies and heir combinaion. a) Disribuion for 3 UW beacons and he. The marked recangle deermines he area of conjuncion of all measures. b)-d) deailed and separaed view of each UW disribuion wihin he conjuncion area. e) The disribuion. f) The resuling combinaion of all disribuions, ha yields he probabiliy disribuion of he vehicle localizaion. We mus highligh ha neiher he nor he UW sensors provide informaion abou he orienaion of he robo in our curren work. In pracice, odomery readings incorporaed hrough he robo moion model are enough o provide an accurae esimaion of he robo heading. nyway, if he robo was equipped wih wo or more UW devices, he process for fusing heir measuremens would be he same as discussed above and we would have a good esimaion of he robo absolue heading. Finally, we mus accoun for no all he measuremens in (4) o be available simulaneously (as in he real experimens described laer on). In hese cases he likelihood for he absen readings can be se o any arbirary consan value. Looking a he general ayesian filer equaions (), i is clear ha any consan value, i.e. consan beween differen paricles, does no modify he esimaed probabiliy disribuion, which is normalized a each sep.

5 IV. EXPERIMETS In order o es he proposed mehod for vehicle localizaion we have carried ou real experimens wihin a mixed indoor-oudoor scenario, combining UW and readings. In our es scenario, he parking area and he main enrance of he ompuer Science building of he Universiy of Malaga (see figure 3), hree UW beacons were placed o cover he indoor par and mos of he oudoors (alhough he UW signals are weaker in he oudoor par). UW- combinaion akes place in ha oudoor par. Wihin his scenario, a mobile robo equipped wih an UW anenna (PulsOn10 [1]), a receiver, and a laser scanner is commanded o rack a circular pah previously recorded. During navigaion, daa from UW,, and he combinaion of boh, when available, is used for esimaing he robo pose. The real posiion of he robo (ground ruh) is calculaed by maching he laser measuremens wih a map of he environmen previously creaed [13]. he beacons, being significanly reduced when UW measuremens are combined wih (see figure 5). 3 1 a) 4m 3 1 b) 4m Figure 3. Our mobile robo navigaing in a mixed scenario a he parking of he ompuer Science building of he Universiy of Malaga In his seup, we have compared hree differen siuaions: i) he robo only relies on he odomeric sysem o follow he pah, ii) he robo posiion is esimaed hrough our filer paricle approach by also considering UW range measuremens, and iii) he informaion is also combined in he filer o improve robo localizaion when i is available. Figure 4 shows he resuls of our experimens. Figure 4a-b depic he pah o be followed and one-loop rajecory racked by he robo considering only UW and UW+, respecively. Figure 4c depics he localizaion error for each case during he whole experimen (around wo loops). In his char, he shadowed areas represen he pars of he experimen where and UW daa is combined for improving he vehicle localizaion, while in he res, only UW measuremens are available. oice ha in he zone covering from area o (indoor par) only UW daa is available yielding an accepable localizaion error (0 cm. a maximum). The porion beween and corresponds o he oudoor area (in fac, a large ransiion area), where is available and weak measuremens coming from he UW beacons are sporadically presen. oe ha he localizaion error when considering UW only is higher as he robo goes far from Error (m) UW and Only UW Odomery Time (s) c) Figure 4. Esimaed pahs and localizaion errors. Plos (a) and (b) show he considered scenario where indoor areas are shown in dark and he fixed beacons are marked as circles. (a) Real (hick line) and racked pah employing odomery and UW range measuremens (doed line). (b) Real (hick line) and racked rajecory using odomery, UW range measuremens and posiion esimaions (doed line). (c) Errors in he esimaion of he robo posiion along wo loops employing differen sensory informaion: only odomery (black doed line), odomery and UW (hin line), and odomery, UW and (hick line). The shadowed areas represen pars of he navigaion where and UW readings were combined. lso noe ha, despie he navigaion beween and going indoor, he error in he posiion esimaion is unexpecedly high. This is because a ha poin he vehicle usually loses he connecion wih he farher UW beacons for a cerain ime, being available only he range measuremen of one beacon and he odomery. s soon as he oher beacons are accessible a some ime, he sysem re-

6 localizes he vehicle. I is imporan o remark, ha albei hree beacons are, a leas, necessary for esimaing he vehicle pose by riangulaion, our probabilisic approach mainains a reduced error during some periods of ime when informaion from only wo or even one of hem are available. Robo pose esimaion Robo pose esimaion (a) (b) Ground ruh Measuremen Ground ruh Measuremen Figure 5. Vehicle localizaion in a ransiion area where and UW signal from a beacon are available. a) Vehicle localizaion using only he UW range and odomery. b) Pose esimaion when also combining measuremen. V. OLUSIOS D FUTURE WORK In his paper, we have implemened and evaluaed a probabilisic framework for vehicle localizaion ha combines differen sensory sources. Our approach, based on paricle filer, considers UW, and he combinaion of boh echnologies o reliably esimae he pose of a vehicle ha moves boh in indoor and oudoor scenarios. This permis a vehicle o robusly perform in a variey of siuaions, for example in some indusrial environmens. Resuls from real experimens have been presened proving he suiabiliy of he proposed approach wih a mobile robo. In he fuure we plan o combine more sensory sources, such as inerial navigaional sysems and visual landmarks, wihin a more complex scenario. REFEREES [1] Douce,., de Freias,., and Gordon,. Sequenial Mone arlo mehods in pracice. Springer-Verlag, 001. [] Eliazar,.I. and Parr, R. Learning probabilisic moion models for mobile robos. M Inernaional onference Proceeding Series, 004. [3] Elaher. and Kaiser Th. Posiioning of Robos using Ulrawideband Signals. IR workshop on dvanced conrol and Diagnosis, Karlsruhe, Germany, ovember 004 [4] F, ew Public Safey pplicaions and roadband Inerne ccess among uses Envisioned by F uhorizaion of Ulra- Wideband Technology,F 0-48, Feb. 14,00. [5] Fox, D., urgard, W., Dellaer, F., and Thrun, S. Mone arlo localizaion: Efficien posiion esimaion for mobile robos. Proc. of he aional onference on rificial Inelligence (I), vol. 113, [6] Gezici S., Tian Z., Giannakis G.., Kobayashi H., Molisch.F., Vincen H., and Sahinoglu Z., Localizaion via UW IEEE Signal Processing Magazine, vol. 71, [7] Hofmann-Wellenhof., Lichenegger H., and ollins J. Theory and Pracice, Third, revised Ediion, Springer-Verlag Wien, usria, 199, 1993 and [8] Joniez E., Ulra Wideband Wireless, Magazine of Innovaion Technology, Sepember 004. [9] Jourdan, D.., Deys, J.J., Jr., Win, M.Z., and Roy,., Mone arlo localizaion in dense mulipah environmens using UW ranging, IEEE Inernaional onference on Ulra- Wideband, 5-8 Sep. 005, pp [10] Julier, S.J. and Uhlmann, J.K. new exension of he Kalman filer o nonlinear sysems. In. Symp. erospace/defense Sensing, Simul. and onrols, Vol. 3, [11] Kalman, R.E. new approach o linear filering and predicion problems. Journal of asic Engineering, Vol. 8, nº 1, 1960, pp [1] Liu, J.S. Meropolized independen sampling wih comparisons o rejecion sampling and imporance sampling. Saisics and ompuing, vol. 6, n., 1996, pp [13] Marínez J.L., González J., Morales J., Mandow., and García- erezo. Geneic and IP Laser Poin Maching for D Mobile Robo Moion Esimaion. Journal of Field Roboics. John Wiley & Sons Ld. Vol.: 3(1), 006. [14] Risic,., rulampalam, S., and Gordon,. eyond he Kalman Filer: Paricle Filers for Tracking pplicaions. rech House Ed [15] Roy S., Foerser J.R., Somayazulu V.S., and Leeper D.G., Ulrawideband radio design: The promise of high-speed, shorrange. [16] Rubin, D.. Using he SIR algorihm o simulae poserior disribuions, ayesian Saisics, vol. 3, 1988, pp [17] Sarmieno, R. de rmas, V. Lopez, J.F. Moniel-elson, J.., and unez,., Rapid acquisiion for ulra-wideband localizers, Ulra Wideband Sysems and Technologies, 00, 00 IEEE onference on, 1-3 May 00 Pages: [18] Spilker J.J. signal srucure and performance characerisics. Journal of he Insiue of avigaion, vol. 5, no., pp , Summer [19] Thrun S., Fox D., urgard W., and Dellaer F., Robus Mone arlo Localizaion for Mobile Robos. rificial Inelligence 18(001), pp [0] Thrun, S., urgard, W., and Fox, D. Probabilisic Roboics. The MIT Press, 005. [1] Time Domain. hp:// [] Yang L. and Giannakis G.. Ulra-wideband communicaions: n idea whose ime has come. IEEE Signal Processing Mag., vol. 1, no. 6, pp. 6 54, ov. 004.