Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 008 proceedngs. An Improved Method for GPS-based Network Poston Locaton n Forests 1 Chrstopher L. Hutchens, Bran R. Sarbn, Alyse C. Bowers, Jason D. G. McKllcan, Kyle K. Forrester and R. Mchael Buehrer, Senor Member, IEEE Abstract In ths paper we present a technque for mprovng the locaton performance based on the Global Postonng System (GPS) for networks of nodes n harsh envronments and demonstrate ts effcacy va a combnaton of smulatons and measurements n forests. The technque reles on the use of Ultra-wdeband (UWB) sgnals to measure tme-of-flght (TOF) and consequently the range between nodes to mprove localzaton n harsh forest envronments. Specfcally, we create a system of range equatons based on network connectvty and solve ths system of non-lnear equatons usng a Least-Squares Non-Lnear optmzaton technque usng any avalable GPS nformaton as the ntal estmate. Based on our smulatons and measurements, the mproved technque results n a localzaton accuracy n forests that s on par wth clear-feld reference GPS measurements. Index Terms Global Postonng System, Least squares estmaton, Localzaton, UWB, Non-lnear optmzaton T I. INTRODUCTION HE Global Postonng System (GPS) s desgned to provde accurate poston estmates n clear, lne-of-sght (LOS) locatons where several satelltes are n vew and lttle degradaton (e.g., multpath) n the sgnals s observed. An deal GPS envronment conssts of a feld or brush area wth an unobstructed, overhead vew of the sky. However, GPS s now beng appled n newer ndustres and applcatons (e.g., farmng, warfare, emergency servces, and personal locaton), many of whch have less-than-deal envronments but stll requre accurate postonng. Some of these less-than-deal envronments nclude ndoor-areas, forests, and urban locatons. Problems n these areas arse due to sgnfcant multpath nterference, LOS sgnal obstructon, poor recevedsatellte geometry, or a combnaton of these effects. These common forms of nterference have a sgnfcant mpact on GPS postonng because of the normally low receved GPS sgnal-strengths. By combnng GPS wth some other 1 Ths work was supported through an REU supplement by the Natonal Scence Foundaton under Grant CCF 01019. C. L. Hutchens, B. R. Sarbn, A. C. Bowers, J. D. G. McKllcan, K. K. Forrester are undergraduate students at Vrgna Tech, Blacksburg, VA 00 USA (e-mal: hutchens@vt.edu). R. M. Buehrer s wth the Moble and Portable Rado Research Group a lab wthn Wreless @ Vrgna Tech, Vrgna Tech, Blacksburg, VA 00 USA (e-mal: buehrer@vt.edu). postonng technology whch s robust n harsh envronments, t s possble to mprove the postonng capablty of a network of nodes. Impulse-based Ultra-Wdeband (UWB) s one such canddate technology. UWB can be used to measure the dstance (va tme-of-flght or TOF measurements) between two or more GPS recevers n a harsh, possbly non-los envronment, whch can then be used to mprove the GPS poston estmates. UWB sgnals are defned by the FCC as a sgnal havng a bandwdth greater than or equal to one-ffth of ts center-frequency; or, a total bandwdth of more than 00 MHz [1]. Impulse-based UWB sgnals consst of shortduraton (typcally low duty cycle) pulses wth very low power spectral densty. The short duraton of the pulse makes the UWB sgnal more robust n harsh multpath envronments, snce the reflected components of the sgnal typcally do not nterfere wth the frst-arrvng pulse. Addtonally, UWB s able to penetrate lght obstacles such as nteror walls of buldngs and forest-folage []. Because of these propertes, mpulse-uwb has an advantage over tradtonal narrowband sgnals n poston-locaton applcatons []. UWB also allows for spectral overlay, precse tme-of-flght measurements, and low power, all whle mantanng the sgnal s robustness. Ths paper evaluates the effectveness of usng UWB-based sgnals to ad n the postonng of a network of GPS-enabled nodes. More specfcally, the set of measured dstances between nodes establshes a system of non-lnear equatons whch can be exploted to determne the node locatons. We utlze a non-lnear optmzaton technque to solve the system of non-lnear equatons employng the GPS measurements as an ntal guess of the soluton. Thus, usng the orgnal GPS locaton estmates combned wth rangng nformaton we are able to acheve a more accurate poston estmate. In Secton II we wll brefly descrbe a subset of prevous nvestgatons nto UWB-based postonng. Secton III descrbes the network model assumed and the error metrcs and outlnes the notaton used throughout ths work. Ths work s based on a combnaton of measurements and computer smulatons. Secton IV provdes a descrpton and the results of the GPS measurements taken n ths work ncludng measurements n clear-feld locatons and n varous forest envronments. UWB measurements were also taken to establsh the rangng capabltes of UWB sgnals. These measurements are descrbed n Secton V. The proposed algorthm for mprovng poston locaton s presented n Secton VI. Secton VII provdes performance results based on computer smulatons and the measurements descrbed n 7 1-11/08/$.00 008 IEEE Authorzed lcensed use lmted to: to IEEExplore provded by Vrgna Tech Lbrares. Downloaded on February, 009 at 1: from IEEE Xplore. Restrctons apply.
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 008 proceedngs. TABLE 1. GPS PRECISION IN VARIOUS ENVIRONMENTS Envronment Std. Devaton (m) Average Error (m) Mn Error (m) Max Error (m) Clear Feld (reference) 0.0817 1.07 0.101.09 Lght Forest 1.08 7.71 1.9 18. Lght Forest.0 8.0 1.79.1 Medum Forest.097 9.8 1.8.097 Sectons IV and V. Secton VIII provdes conclusons. II. PREVIOUS UWB POSITIONING WORK From prevous research nvolvng UWB-based postonng, the precson of the reference measurements s crtcal. Research conducted at the Unversty of Tennessee nvolvng ndoor D-postonng radar used an optotrak system to place antennas and recevers wth sub-mllmeter accuracy [], and as a result they were able to confrm the use of UWB rangng to measure sub-centmeter ranges accurately. Others (specfcally [], [], and []) have establshed that the effects of multpath nterference and lght LOS obstructons on UWB sgnals for both rangng and data transmsson are very low. Yu and Opperman proposed a UWB-postonng system based on moble tags whch are referenced to known recever locatons []. Ther work s smlar to the research hghlghted n ths paper, but dffers n the fact that ther system reles on havng manually defned postons for the recevers. A majorty of the recent work on poston locaton for networks of nodes (e.g., [7],[8],[9]) reles on measurements to known anchors and uses the poston of the anchors combned wth the range/angle measurements. Our current work dffers from the majorty of exstng work n that (a) t s a means for mprovng GPS, (b) t utlzes non-lnear optmzaton for determnng poston, and (c) we provde measurement data along wth our smulaton results to establsh the effcacy of the approach. III. SYSTEM MODEL AND SET-UP In ths work we assume a network of N nodes each equpped wth a GPS recever and a UWB transcever deployed n a forest (or some other harsh envronment) as shown n Fgure 1. We assume that the nodes (or a majorty of the nodes) obtan ntal estmates of ther poston based on GPS. Due to the folage and ground cover, some nodes may not be able to obtan ther poston estmate whle others wll lkely have poor estmates. The poston of the th node n two dmensons s represented by the two-dmensonal vector x =[x,y ] T. The estmated poston of the th node s represented by x and the error n the estmate s represented by e = x x where y s the norm of the vector y. For ths study, we assume that all of the nodes are statonary. Once the nodes have ndependently determned (or attempted to determne) ther poston va GPS, they obtan range estmates usng TOF measurements based on a packet handshake. Only those nodes that are wthn communcaton range of each other (represented by the dashed lnes n Fgure 1) obtan these estmates. In ths study we assumed the use of a UWB physcal layer. The resultng range measurements are then used to mprove the GPS measurements as descrbed n Secton IV. Connecton Node Fgure 1. Example sensor network assumed n ths work IV. MEASURED GPS PERFORMANCE The work presented n ths paper s based on a combnaton of measurements and smulaton. In order to establsh the accuracy of the overall system, we must frst determne the accuracy of the GPS component whch provdes the ntal estmates. To determne the accuracy of GPS n a forest (the harsh envronment of nterest n ths work), measurements were taken n the Jefferson Natonal Forest near Blacksburg, Vrgna n a varety of condtons. The GPS recever used to measure GPS precson was a Garmn GPSMap 0Cx a hgh-end, consumer-grade handheld. Because ths was an off-the-shelf consumer product, the GPS unt provdes a black-box style nterface wth the nternal detals hdden. In order to overcome not havng a known reference, t was decded that averagng multple ponts n a known pattern (e.g., n a square) would yeld a pseudoreference, assumng the measurement errors were unbased. Each measurement set conssted of 0 measurements around a 0m by 0m square-pattern, wth measurements taken every meters. The measured GPS data ponts were then ftted to the square usng least-squares, whch provded estmates for average error and the standard devaton of the error. Results from these measurements are shown n Table 1. The error was calculated as the Eucldean dstance between the GPS provded locaton and the true locaton. Specfcally, e = x x. As can be seen from Table 1, there was lttle dfference between varous forest envronments as compared to the degradaton between a forest and a clear feld. Specfcally, the measurements n a clear feld were wthn 1m of the true locaton whereas the average error measured n a forest ranged from 7.8m n a lght forest to 9.7m n a medum forest. 7 Authorzed lcensed use lmted to: to IEEExplore provded by Vrgna Tech Lbrares. Downloaded on February, 009 at 1: from IEEE Xplore. Restrctons apply.
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 008 proceedngs. V. MEASURED UWB PERFORMANCE In order to characterze the potental accuracy of UWBbased rangng, measurements were taken usng both a computer-controlled-track and trpods. The GHz wde UWB sgnal was produced usng a Tektronx AWG710 Arbtrary Waveform Generator followed by a 0W Class-A power amplfer nto ether a Horn- or Bcone-style antenna. The transmt power was farly hgh and would requre pulse averagng to replcate n practce. A Tektronx DPO7080 Dgtal Phosphor Osclloscope (DPO) proceeded by a lownose-amplfer connected to a Horn or Bcone antenna was used to measure the transmtted sgnal. The DPO was confgured to sample at GS/s. A reference measurement was taken wth the recevng antenna placed at a short dstance from the transmttng antenna for calbraton purposes. The expected TOF was then calculated usng the known-dstance. The system delay was determned by subtractng the expected TOF value from the total tme. Ths system delay was appled to all subsequent measurements n order to determne TOF. All but one of the forest measurements were taken wth a track placed parallel along a path from m to 0m away from the transmtter. The transmttng antenna was fxed n place on top of a trpod, and the recever was moved n 0 ncremental steps of cm along the track (accurate to ±10 µm). The track was moved ether m or m between measurements. For the desgnated TOF measurement, a m by m grd wth 9 ponts was mapped. Due to tme constrants, a trpod was used for the recever nstead of the track. Durng ths measurement set t became apparent that there would not be enough precson n terms of placng the equpment n order to make the results useful. The mapped-out-area for the desgnated TOF measurement had up to 0cm of error n one pont, whch s extremely sgnfcant compared to the expected errors of approxmately.cm. It was concluded that t would not be feasble to manually confgure a grd wth the needed precson, especally n an envronment consstng of uneven ground and fallen trees. Thus the earler measurements nvolvng the track were used to determne the precson, and a secondary reference set of measurements was taken n a hghly controlled envronment (a unform hallway) to determne system delays at varous dstances. The results of all of these measurements, shown n Table, gve an average standard devaton of approxmately 7mm. Note that the sgnal-to-nose rato n these measurements was farly hgh, due to the equpment used. The SNR of an actual applcaton would depend on the update rate of the system and the power lmts of UWB transmssons. These measurements would correspond to a farly slow update rate and represent a lower lmt on the error. 1 1 10 8 TABLE. UWB PRECISION AT VARIOUS DISTANCES DISTANCE (M) STD DEV (M) MAX ERROR (M).m 0.0088 0.01 m 0.009 0.019 10m 0.0088 0.071 1m 0.008 0.010 0m 0.0070 0.071 0m 0.00 0.0199 0 0 8 10 GPS Standard Devaton VI. IMPROVED POSITION ESTIMATION ALGORITHM A key to mprovng network localzaton performance when relyng on GPS for poston nformaton s the fact that the nodes postons must satsfy certan constrants based on the dstances between nodes. Specfcally, gven the set of UWB range measurements, the postons of the nodes deally must satsfy the followng set of non-lnear equatons: r1 = ( x1 x ) + ( y1 y ) : rmn = ( xm xn ) + ( ym yn ) for all nodes m and n n communcaton range of each other. However, ths assumes that we know the dstances between nodes exactly. Gven that the estmates are nosy, we cannot solve the above set of non-lnear equatons exactly. Thus, we seek a soluton z = [x 1, y 1, x, y, x, y, x N, y N ] that mnmzes the square error. That s we want to fnd Varyng GPS Standard Devaton Fgure. Impact on the performance of the standard ( ) ( ) z = mn r x x y y opt j j j z, j To solve ths non-lnear optmzaton problem, we used the Levenberg-Marquardt algorthm, an teratve technque whch combnes the method of steepest descent and the Gauss- Newton method. As wth most teratve solutons, the qualty of the ntal soluton s mportant for non-lnear optmzaton problems. In ths work we use the GPS-provded poston nformaton as the ntal soluton. 7 Authorzed lcensed use lmted to: to IEEExplore provded by Vrgna Tech Lbrares. Downloaded on February, 009 at 1: from IEEE Xplore. Restrctons apply.
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 008 proceedngs. VII. SIMULATION RESULTS To determne the effcacy of the approach descrbed n the prevous secton, smulatons were used to measure the accuracy n terms of Eucldean dstance error. For the smulatons t was assumed that the true locatons were dstrbuted randomly n a square area (100m x 100m), and that the GPS errors were zero-mean Gaussan (n x and y coordnates) defned by some standard devaton. UWB ranges were smulated as Gaussan nose error plus a unformly dstrbuted bas to represent non-lne-of-sght measurements as approprate. The error parameters were derved from the measurements. All smulaton parameters are shown n Table. TABLE. STANDARD SIMULATION PARAMETERS Number of Nodes 0 Square Area Wdth 100m Maxmum Range Lmt m Std. Dev. Of m Std. Dev. Of UWB Error 0.01m The smulatons represent a typcal large-area (100m x 100m), low-node-densty confguraton. The number of nodes, area sze, and maxmum range lmt all drectly contrbuted to the overall connectvty of the system and thus mpacted performance. In the case where a node s not connected to any other nodes and thus could not mprove ts poston estmate, the GPS poston estmate s used. Fgure corresponds to the observed accuracy of the orgnal (.e., GPS) and the mproved system as the qualty of the envronment (specfcally the GPS accuracy) worsens. Fgure shows the mpact of ncreasng the UWB rangng error. Clearly ncreasng the error n ether measurement degrades overall accuracy. However, the mproved system shows more robustness to ncreasng GPS error as was antcpated. Clearly, the UWB rangng error does not have any mpact on the orgnal GPS measurements. Fgures,, and each examne the mpact of connectvty on the performance of the proposed system. As the number of sensors or the communcaton range ncreases, more nformaton s avalable to correct GPS errors and thus the performance mproves. As the area ncreases (Fgure ), the performance degrades snce connectvty wll suffer for a fxed node communcaton range. However, together the fgures show that for moderate values of area sze, communcaton range, and node densty substantal mprovements n localzaton accuracy are achevable. Specfcally, we can see n the fgures that although the rms error s approxmately - 8m n a forest usng GPS only, the error can be reduced to less than m (nearly 1.m) usng rangng between nodes. Ths s nearly the accuracy achevable n clear-sky condtons. As a fnal comparson, we examne the mpact of NLOS errors on the performance of the proposed technque. The plot n Fgure 7 shows the performance of the scheme when there s a m NLOS bas present n a varyng percentage of the nodes. We can see that even n the presence of a large bas error the performance mproves unless 80% of the ranges are based. VIII. CONCLUSIONS The results of the smulatons, shown n Fgures through 7, ndcate that even wth lmted rangng nformaton, poston locaton can stll be mproved usng range nformaton between GPS-enabled nodes. Increasng the number of sensors or the communcaton range mproves the soluton, whle ncreasng the area sze or the error n the UWB-rangng or GPSpostonng worsens t. It should be noted that the number of sensors, range lmt, and area sze wll not cause the mproved soluton to be less accurate than the orgnal GPS soluton. As long as the UWB rangng s reasonably accurate, the results of the optmzaton wll always be better than GPS postonng alone. For more deal stuatons such as small-area, hgh nodedensty confguratons, the optmzed soluton wll be greatly mproved over standard GPS. In such a case, performance n a forest can rval open-feld clear-sky GPS measurements. ACKNOWLEDGMENTS We would lke to thank Chrs Anderson and Hars Volos for ther gudance durng ths research. For ther help n takng measurements, we would also lke to thank Chrs Headley, Francsco Muller, and Jesse Reed. We also gratefully acknowledge the support of the Natonal Scence Foundaton through the Research Experence for Undergraduates (REU) program va a supplement to Grant CCF 01019. REFERENCES [1] Defntons, 7 CFR, pt 1.0 (00). [] K. Swak, "Ultra-wde band rado: ntroducng a new technology," Proceedngs of the Vehcular Technology Conference (VTC Sprng 001), pp.1088-109, 001. [] C. Zhang, et. al., Development of an UWB Indoor D Postonng Radar wth Mllmeter Accuracy, Mcrowave Symposum Dgest 00, IEEE MTTS- Internatonal, pp.10-109, June 00. [] M.Z. Wn and R.A. Scholtz, Impulse rado: how t works, IEEE Comm. Letters, vol., no., pp.-8, Feb. 1998. [] M. Tuchler, V. Schwarz, and A. Huber, Locaton accuracy of an UWB localzaton system n a mult-path envronment, IEEE Internatonal Conference on Ultra- Wdeband, 00. pp.1-19, -8 Sept 00. [] K. Yu and I. Oppermann, Performance of UWB poston estmaton based on tme-of-arrval measurements, Internatonal Workshop on Ultra Wdeband Systems, 00. Jont wth Conference on Ultrawdeband Systems and Technologes. pp.00-0, 18-1 May 00. [7] N. Patwar, A. O. Hero III, M. Perkns, N. S. Correal and R. J. O Dea, Relatve locaton estmaton n wreless sensor networks, IEEE Transactons on Sgnal Processng, vol. 1, no. 8, pp. 17 18, Aug. 00. [8] N. Patwar, et. al., Locatng the nodes: cooperatve localzaton n wreless sensor network, IEEE Sgnal Processng Magazne, vol., no., pp. -9, 00. [9] S. Venkatesh and R. M. Buehrer, NLOS mtgaton usng lnear programmng n ultrawdeband locaton-aware 7 Authorzed lcensed use lmted to: to IEEExplore provded by Vrgna Tech Lbrares. Downloaded on February, 009 at 1: from IEEE Xplore. Restrctons apply.
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 008 proceedngs. networks, IEEE Transactons on Vehcular Technology, vol., no., pp. 18-98, Sept. 007.. Varyng Maxmum Range Lmt of UWB Measurements..... Varyng UWB Rangng Standard Devaton 1. 0 10 1 0 UWB Rangng Standard Devaton Fgure. Impact of the standard devaton of the rangng error on the localzaton error..... Varyng Area Sze 1. 0 0 100 10 Maxmum Range Lmt Fgure. Impact of varyng the maxmum range of UWB communcaton. 7 Varyng Number of Nodes.... 1 0 0 10 0 0 0 0 0 70 80 90 Number of Sensors Fgure. Impact of varyng the number of nodes on localzaton performance 1. 0 0 100 10 00 Area Sze Fgure. Impact of the area sze on localzaton error Fgure 7. Impact of NLOS error on localzaton error 77 Authorzed lcensed use lmted to: to IEEExplore provded by Vrgna Tech Lbrares. Downloaded on February, 009 at 1: from IEEE Xplore. Restrctons apply.