An Efficient Positioning Algorithm using Ultrasound and RF

Transcription

1 5. Internatonal B. Km, C. Journal Park, D.-Y. of Control, Kang, H. Automaton, H. Yun, B.-C. and Ahn, ystems, E. J. Cha, vol. 6, and no.., J. pp. Lee 5-55, August 8 An Effcent Postonng Algorthm usng Ultrasound and RF eung Beom Km, Chansk Park*, Dong-Youn Kang, Hee Hak Yun, Berng-Chearl Ahn, Eun Jong Cha, and ang Jeong Lee Abstract: In ths paper, an effcent postonng algorthm s proposed for a local postonng system usng ultrasound and RF n WN. he proposed postonng algorthm s the modfed avarese method where measurement nose characterstcs are ncluded as a weghtng. Furthermore the ll-condtoned and the sngularty problem occurred when all beacons are nstalled at the same heght are removed. And the method s applcable to D postonng wth beacons only. he experments wth mplemented system show the accurate seamless postonng less than cm error both statc and dynamc experments whle the orgnal avarese method can not provde postons. Keywords: Postonng, RF, ultrasound, WN.. INRODUCION WN (Wreless ensor Networks) conssts of wreless network and spatally dstrbuted sensors montorng temperature, sound, vbraton, pollutants and so on. he mprovements n semconductor and communcaton technology broaden the applcatons of WN; smart homes, health cares, I (Intellgent ransportaton ystem) and envronment montorng. If poston nformaton s avalable n WN, bg applcaton areas wll open. GP (Global Postonng ystem) s a de facto postonng system n navgaton and locaton. GP, however, s dffcult to use ndoors because of very weak sgnal level. Asssted GP (AGP) s appled ndoors wth network assstance and specal hardware, but ts hgh cost and unsatsfactory accuracy prevent an AGP recever from wde spreadng n WN Manuscrpt receved March 5, 7; revsed November, 7; accepted March 8, 8. Recommended by Edtoral Board member Jang Myung Lee under the drecton of Edtor Jae-Bok ong. hs work was supported by the Regonal Research Centers Program of the Mnstry of Educaton and Human Resources Development n Korea. eung Beom Km and ang Jeong Lee are wth the chool of Electrcal and Conmputer Engneerng, Chungnam Natonal Unversty, Gung-dong, Yuseong-gu, Daejeon 5-76, Korea (e-mals: uwbgps@paran.com, eesjl@cnu.ac.kr). Chansk Park, Hee Hak Yun, and Berng-Cheal Ahn are wth the chool of Electrcal and Computer Engneerng, Chungbuk Natonal Unversty, Cheongju, Chungbuk 6-76, Korea (e-mals: {chansp, tzootzme}@cbnu.ac.kr, bcan@cbu. ac.kr). Dong-Youn Kang s wth the Hanyang Navcom Co., Ltd., nseong-dong, Yuseong-gu, Daejeon 5-5, Korea (emal: hg879s@paran.com). Eun Jong Cha s wth the Department of Bomedcal Engneerng, Chungbuk Natonal Unversty, Cheongju, Chungbuk 6-76, Korea (e-mal: ejcha@cbnu.ac.kr). * Correspondng author. applcatons. RI (Receved gnal trength Indcaton) s an nherent by-product from wreless ad-hoc network and t s already used for postonng. But RI s lmted to the non-precse postonng applcatons because of large errors nduced by battery level, fadng and multpath. o overcome ths problem, RI s combned wth other sensors such as ultrasound, IR (Infra Red), WLAN (Wreless Local Area Network) and so on. AHLo [], Crcket [], and U-A [] are examples of combnng RI and ultrasound. In these systems, besdes RI, the arrval tme dfference of ultrasound and RF (Rado Frequency) sgnal s usually measured to provde a precse range measurement. Usng the range measurements, the precse poston can be found. hs paper proposes a postonng algorthm whch has no lmtaton n nstallaton and provdes solutons even f only two beacons are avalable. he lnearzaton method used n GP s not adequate for small regon applcatons such as WN because small errors n ntal guess can cause dvergent soluton. avarese method [] s most common algorthm n WN because t does not requre any ntal guesses. However, t has the ll-condtoned and the sngularty problem: when all the beacons heghts are same, the matrx becomes sngular. And t does not use the measurement covarance as a weght n computng poston and t can t fnd soluton when the number of beacons s less than. he proposed algorthm removes these drawbacks. It wll ncrease avalablty of postonng and flexblty of nstallaton.. POIIONING ALGORIHM.. Rangng wth ultrasound and RF In ths paper, a range measurement s obtaned from the arrval tme dfference between RF and ultrasound. If a node transmts RF and ultrasound smultaneously,

2 An Effcent Postonng Algorthm usng Ultrasound and RF 55 the RF sgnal arrves at a beacon much faster than the ultrasound. he beacon measures the nterval between RF and ultrasound arrval tmes and converts to the range by multplyng the speed of ultrasound as shown n (). he range from user u = [ x y z] to a beacon b = [ X Y Z ] can be expressed as = ( t t ) v = r + w, () U RF U where t U denotes the arrval tme of ultrasound, t RF denotes the arrval tme of RF, v U denotes the speed of ultrasound ( v = m / s, and U C represents temperature n Celsus). r = u b = ( X x) + ( Y y) + ( Z z) s the dstance between a node and a beacon, w s AWGN (Addtve Whte Gaussan Nose) measurement nose wth mean and a varance σ. he qualty of range measurements s affected by many factors: errors n ultrasound speed by temperature varatons, the noses n ultrasound detecton crcuts and so on. he temperature nfluence can t be neglgble because ts error grows as the range ncreases. Fortunately, most nodes n WN have temperature sensors and can calbrate the ultrasound speed. If there s no temperature sensor n the nodes, t s requred that some beacons have temperature sensors and transmt the measured temperature to nodes usng ad-hoc network... Overvew of avarese method By gnorng the measurement errors w from (), squarng both sdes to get, and dfferencng wth m where m means the last beacon, m { X + Y + Z } + { Xm + Ym + Zm} = [ Xm X Ym Y Zm Z][ x y z] C () s obtaned. Equaton () can be expressed n a smple form usng vectors as m m m m b b +b b = (b b ) u. () Equaton () holds for the m beacons, and s represented wth a smplfed form as n (5). he user poston can be found applyng L (Least quares) to (5). m b b +bmb m (bm - b ) m bb +bmb m (b = m - b ) u, m m bmb m +bmb m (bm - b m-) () = Bu. (5).. Modfed avarese method.. Weghted avarese method he measurement nose n () s proportonal to the dstance because of the temperature varaton and noses n the ultrasound crcut. It mples that more precse postonng s possble usng ths nformaton as weght whle the orgnal avarese method s not. he errors n two measurements and m are ndependent AWGN wth zero-mean and varance σ. he varance of () s computed as = m r rm = 6σ + σ ( r + rm). σ cov(( ) ( )) (6) nce r w holds, t s natural to assume that r Now (6) becomes. m σ = 6σ + σ ( + ). (7) Usng WL (Weghted Least quares) wth weghtng matrx Q = dag( σ ), the poston and ts covarance s found as n eqs. (8) and (9). Note WL becomes MLE (Maxmum Lkelhood Estmaton) snce the AWGN s assumed = u= ( B Q B) B Q, (8) cov( u) ( B Q B ). (9).. Elmnaton of sngularty problem When all beacons are nstalled on the same heght, the last column of matrx B becomes, so the nverse of ( B B ) or ( - B Q B ) can not be found. Even though all beacons are nstalled n dfferent heghts, ( B B ) or ( B Q - B) become llcondtoned matrx f the heght dfference s not so large. When beacons are nstalled nsde buldngs, t s very hard to make a large heght dfference. o solve ths sngularty and ll-condtoned problem, ths paper presents an alternatve postonng method usng () nstead of (). m ( X + Y ) + ( Xm + Ym) = [ Xm X Ym Y] x y [ ]. () Equaton () can be obtaned n smlar manner used n (5) where u XY = [ x y] s dmensonal user poston, XY s ( m ) measurement vector wth th element of ( X + Y ) + m Ym m ( X + ) and B XY s ( m ) matrx wth th

3 56. B. Km, C. Park, D.-Y. Kang, H. H. Yun, B.-C. Ahn, E. J. Cha, and. J. Lee row of [ X X Y Y ]. m m XY =BXYu XY () Applyng WL to (), the horzontal poston ( x, y ) s found wthout a sngularty problem. he estmator of heght z s calculated usng () wth the fxed ( x, y ). he hgher accurate heght can be found by averagng the estmators of heght from all beacons. ( Z z) = ( X x) ( Y y) () Note the matrx Q = dag( σ ) defned n (7) can be used as a weghtng matrx wthout modfcaton, and covarance of poston s cov( u xy ) = - xy xy ( B Q B )... Modfed avarese method n D he avalable beacons are frequently less than because of obstacles. If only beacons are avalable, t s mpossble to fnd postons. In ths case by assumng that heght s fxed as z F, horzontal D poston can be found. Because the heght of a node remans constant on a flat floor usually, ths assumpton s reasonable. he heght can be fxed to an estmated value when more than beacons are avalable or an assumed value such as a heght of a vehcle or a human. Wth fxed heght, () s expressed as { X Y Z } { X Y Z } m m + m + m [ ] ( Zm Z) zf = Xm X Ym Y [ x y]. () When more than beacons are avalable, the D poston s found usng () where D s ( m ) measurement vector wth th element of { } { } m X + Y + Z + Xm + Ym + Zm ( Zm Z ) z. he covarance s cov( ) = Q = dag F σf D D F ( Zm Z) σz F ( σ + ) where σ = and the error of a fxed heght s assumed AWGN wth zero mean and σ z F varance. D = Bxyu xy () Note () also can have sngularty problem f Xm = X or Y m = Y holds for all beacons,.e. all beacons are n a lne. he sngularty problem s elmnated by usng the smlar method descrbed n the prevous secton. If just beacons are avalable, t s mpossble to fnd D poston wth () because unknowns can not be found wth a scalar D. A mnmum norm estmator can be appled but the result s not relable. When just beacons are avalable, n ths paper, (5) whch s a drect expanson of () s used. y = ax+ b, (5) where a = ( X X)/( Y Y) and b = ( ) ( ). X X Y Y Z zf Z zf ( Y Y) By nsertng (5) and equaton s obtaned as x where z = z nto (), a quadratc F + α x+ β =, (6) α = ( X + a( Y b)) /( + a ) and β = F ( X + ( Z z ) )/( + a ) for =,. From (6), x-canddates are found and a proper one s chosen based on the known beacon coordnates; the canddate not n the nterval [ X, X] s dscarded.. EXPERIMENAL REUL hree experments are performed to evaluate the proposed algorthm. he frst s statc experments to show the ll-condtoned problem, the second s statc experments to show the effect of the number and geometry of beacons, and the thrd s dynamc experments usng a lne-tracer... ystem mplementaton An ultrasound transmtter and a recever crcut are added to Crossbow MICAz whch uses ZgBee as wreless communcaton. he overall hardware s conssted of a RF, an ultrasound crcut and a mcrocontroller. A RF s made wth Chpcon s CC for ZgBee and A/R-P of KOMAN ECHNIC for an ultrasound transmtter and recever. An Atmel s AVR Amega8 s used as a mcroprocessor. A node makes the khz frequency pulse to drve ultrasound transducer usng PWM (Pulse Wdth Modulaton) controller n Amega8. An ultrasound recever s n a beacon fxed at a known poston and an ultrasound transmtter s n a moble node. o transmt an ultrasound sgnal to all beacons n a test bed drectly, both transmtter and recever use ultrasound sensors wth a wde beam pattern of degree. By removng the cap of ultrasound transducer and trmmng the gan of amplfer, the coverage becomes wder. Note n ths paper we mplemented an actve moble structure for convenence but the

4 An Effcent Postonng Algorthm usng Ultrasound and RF 57 proposed postonng algorthm can be used n a passve moble structure also. o synchronze between RF and ultrasound, the FD (tart of Frame Delmter) sgnal from CC s used. FD sgnal s generated when a data frame s transmtted or receved usng ZgBee communcaton, therefore by usng the FD sgnal to transmt ultrasound, synchronzaton s done. At a beacon, the actvaton of FD means the arrval of RF sgnal. By startng a tmer when the FD actvates and stoppng a tmer when an ultrasound arrves, the tme nterval between RF and ultrasound s measured... tatc experments wth dfferent heghts Four beacons are nstalled at the corners of a test bed n (m, m,.m), (.m, m,.5m), (m,.m,.5m), (.m,.m,.75m). 5 range measurements are gathered and saved at each 9 reference ponts. he referenced ponts are on the bottom of test bed wth cm grd. Wth beacons, there s no dfference between the avarese method and weghted avarese method as - can be seen n (8) where ( ) - B Q B B Q = ( B B) B = B holds. he horzontal and vertcal trajectores usng the avarese methods are shown as Fg.. Red o s a true poston; blue x s an estmated poston n Fg.. Note the avarese method has the hgh accuracy of horzontal postons but the large error of vertcal postons because of the llcondtoned matrx problem caused by small dfference n heght. From (5), n the center of the test bed ( B B) B = and the thrd row related to the vertcal poston s about tmes larger than the other rows. o the heght s more nfluenced by the error of the range measurements. Fg. shows the results usng the modfed avarese method n (). he horzontal and vertcal errors of both methods at 9 ponts are summarzed n able. It shows dramatc reducton of vertcal error. However, the horzontal error becomes large because n ths method the heght of all beacons are assumed same and ths error s propagated nto the horzontal error. o get more accurate poston wth the proposed method, the heght of beacons should be same (a) Horzontal trajectory (a) Horzontal trajectory. z[m] - z[m] (b) Vertcal trajectory. Fg.. Horzontal and vertcal trajectory usng the avarese method (b) Vertcal trajectory. Fg.. Horzontal and vertcal trajectory usng the modfed avarese method..5.5

5 58. B. Km, C. Park, D.-Y. Kang, H. H. Yun, B.-C. Ahn, E. J. Cha, and. J. Lee able. errors usng the avarese and modfed avarese method. Algorthm Modfed avarese Result avarese Horzontal Vertcal Mean.8cm 6.78cm Max.cm 8.7cm Mn.99cm 5.5cm Mean.cm.9cm Max 8.6cm.8cm Mn 6.9cm.cm.. tatc experments wth same heghts In ths experment, confguratons of the test bed are same as the prevous secton except four beacons are nstalled at the same heght of.m. Wth ths confguraton the avarese method dverges, therefore the results of the modfed avarese method only are gven n ths secton. o see the effect of number of beacons and ts geometry, some beacons are ntentonally removed durng the processng. If more than beacons are avalable, D poston s found. When only beacons are avalable, the modfed avarese method n D s used to fnd D poston (a) Beacons (, ) (b) Beacons (, ). Fg.. Horzontal rajectory usng the D modfed avarese method wth only beacons (a) Beacons (,,, ) (a) Beacon and beacon (b) Beacons (,, ). Fg.. Horzontal rajectory usng the D modfed avarese method wth and beacons. (b) Beacon and beacon. Fg. 5. Relatve geometry and dluton of precson wth beacons.

6 An Effcent Postonng Algorthm usng Ultrasound and RF 59 able. errors usng modfed avarese method n D and D. Algorthm Modfed avarese D D Result Beacons Beacons Beacons Horzontal Vertcal Mean.85cm.cm.cm Max 5.5cm 7.8cm.5cm Mn.cm.9cm.96cm Mean.6cm.6cm - Max.6cm.cm - Mn.8cm.8cm - he postonng results wth the D modfed avarese method are shown n Fg.. he mean horzontal error s.85cm () wth beacons whle.cm wth beacons. he left upper corner of Fg. (b) clearly shows the effect of absence of beacon. he postonng results wth the D modfed avarese method are shown n Fg.. It also clearly shows the effect of the number and geometry of beacons. he error patterns n Fg. are explaned wth Fg. 5. he poston s determned n the ntersecton area of two crcles where the covarance of measurement error represents the wdth of arc, and the area of ntersecton of two crcles s the uncertanty n poston. he poston accuracy s affected by not only the measurement error but also the relatve geometry of a node and beacons. It s analogous to the concept of DOP (Dluton of Precson) n GP [5]. he horzontal and vertcal errors are summarzed n able. It shows the more beacons are nstalled, the hgher accuracy s obtaned. And t s possble to fnd an accurate poston at the cm level f at least beacons are avalable... Dynamc experments A lne-tracer as a moble robot s made to evaluate the performance of the mplemented system n dynamc envronments. he ultrasound transmtter n the lne-tracer s nstalled at 5.5cm heght. he test bed, beacon and node are shown n Fg. 6, the total length of the track s 8.m. he speed of the lnetracer s.8cm/sec and t takes one mnute to run the track. 86 measurements are taken whle the lnetracer runs 5 tmes wth the 6Hz output rate. Durng the processng scenaros are assumed; scenaro uses all beacons for the frst 7 epochs, scenaro uses beacon and only for 7~6 epochs and scenaro uses beacon and only for 7~86 epochs. he horzontal trajectory of the lne-tracer s shown Fg. 6. est bed:.m.m.m (W D H). y [cm] y [cm] x [cm] cenaro cenaro cenaro (a) Horzontal trjectores from scenaros x [cm] (b) Zoomed trajectory [~55]. cenaro cenaro cenaro Fg. 7. Horzontal trajectory of dynamc experment. n Fg. 7. Blue sold lne x s the result usng D modfed avarese method at scenaro. Red dashed lne + and green dash-dot lne * are the results usng D modfed avarese method at scenaro and respectvely. Fg. 7(b) shows the zoomed result. he results of scenaro show the accuracy less than cm. he results of scenaro and show a shft along the y-axs. he results wth beacon and are opposte to the results wth beacon and. It s nfluenced by the geometry as explaned n Fg. 5.

7 55. B. Km, C. Park, D.-Y. Kang, H. H. Yun, B.-C. Ahn, E. J. Cha, and. J. Lee. CONCLUION hs paper proposed an effcent postonng algorthm usng ultrasound and RF n WN. By modfyng the avarese method, the proposed algorthm mproves accuracy, avalablty and flexblty; the error covarance of range measurements s derved and used n WL as a weghtng matrx to get hgher accuracy, the ll-condtoned and the sngularty problem are solved so that all beacons can be nstalled at the same heght and D postonng s possble wth beacons only. From the statc and dynamc experments wth the mplemented system, the seamless postonng wth the accuracy less than cm error s possble whle the avarese method dverges. he proposed method s expected to be easly adopted n many WN applcatons such as smart homes, health cares, I, envronmental montorng and moble robots. REFERENCE [] A. avvdes, C. C. Han, and M. B. rvastava, Dynamc fne-graned localzaton n Ad-Hoc wreless sensor networks, Proc. of the Internatonal Conference on Moble Computng and Networkng (MobCom), pp , July. [] N. B. Pryantha, he Crcket Indoor Locaton ystem, Ph.D. hess, Massachusetts Insttute of echnology, June 5. [] D. H. Lee, J. J. Park,. Y. Km, Y.. Mun, and M. H. Lee, A study on the applcaton of U- A system for the ndoor postonng technology of ubqutous computng, Journal of Control, Automaton, and ystems Engneerng (Korean), vol., no. 9, pp , eptember 6. [] C. avarese, rangulaton, Robust Postonng Algorthms for Dstrbuted Ad Hoc Wreless ensor Networks, M.. hess, Unversty of Calforna at Berkeley, pp. -,. [5] C. Park, D. J. Cho, E. J. Cha, D. H. Hwang, and. J. Lee, Error analyss of -dmensonal GP atttude determnaton system, Internatonal Journal of Control, Automaton, and ystems, vol., no., pp. 8-85, 6. AJ, I and WN. Chansk Park receved the B.., M.., and Ph.D. degrees n Electrcal Engneerng from eoul Natonal Unversty n 98, 986, and 997 respectvely. He s currently wth the chool of Electrcal and Computer Engneerng, Chungbuk Natonal Unversty, Cheongju, Korea. Hs research nterests nclude GN, DR, Dong-Youn Kang receved the B.. and M.. degrees n the chool of Electrcal and Computer Engneerng, Chungbuk Natonal Unversty, Cheongju, Korea, n 6 and 8. He s workng on the Hanyang Navcom, Daejon, Korea. Hs research nterests nclude PN and WN. Hee Hak Yun receved the B.. degree n the chool of Electrcal and Computer Engneerng, Chungbuk Natonal Unversty, Cheongju, Korea, n 7. He s workng on the master s course n the same unversty. Hs research nterests nclude GN and WN. Berng-Chearl Ahn receved the B.. degree from eoul Natonal Unversty n 98, the M.. degree from KAI n 98, and the Ph.D. degree n Electrcal Engneerng from Unversty of Msssspp n 99. He s currently wth the chool of Electrcal and Computer Engneerng, Chungbuk Natonal Unversty. Hs research nterests nclude appled electromagnetcs and antennas. Eun Jong Cha receved the B.. degree n Electronc Engneerng from eoul Natonal Unversty n 98 and the Ph.D. degree n Bomedcal Engneerng from the Unversty of outhern Calforna n 987. He s currently a Professor and Char of the Bomedcal Engneerng Dept. of the Medcal chool, Chungbuk Natonal Unversty, Cheongju, Korea. Hs research nterests nclude physologcal systems and medcal nformatcs. GN and WN. eung Beom Km receved the B.. degree n Electroncs Educaton, M.. degree and Ph.D. canddate n Electroncs Engneerng from Chungnam Natonal Unversty, Daejeon, Korea, n 998,, and, respectvely. He s workng on the Hankuk Communcaton Co., Inc., eoul, Korea. Hs research nterests nclude ang Jeong Lee receved the B.., M.., and Ph.D. degrees n Electrcal Engneerng from eoul Natonal Unversty n 979, 98, and 987 respectvely. He s currently wth the chool of Electrcal and Computer Engneerng, Chungnam Natonal Unversty, Daejeon, Korea. Hs research nterests nclude robust control and navgaton systems.