An Accurate UWB Radar Imaging Method Using Indoor Multipath Echoes for Targets in Shadow Regions

Transcription

1 21 INTERNATIONAL CONFERENCE ON INDOOR POSITIONING AND INDOOR NAVIGATION (IPIN), 1-17 SEPTEMBER 21, ZÜRICH, SWITZERLAND An Accurate UWB Radar Imagng Method Usng Indoor Multpath Echoes for s n Shadow Regons Shuhe Fujta, Takuya Sakamoto and Toru Sato Graduate School of Informatcs, Kyoto Unversty, Yoshda-Honmach, Sakyo-ku, Kyoto 66-81, Japan. Emal: tsato@kuee.kyoto-u.ac.jp Abstract Ultra Wde-Band (UWB) pulse radar provdes promse for survellance systems va ts hgh-range resoluton. To realze a low-cost and hgh-qualty ndoor securty system, we propose a UWB radar magng system usng ndoor multpath echoes for targets n shadow regons. A multpath wave can be used as an approxmaton of an magnary echo from a mrror mage antenna to the target, gnorng phase rotaton and attenuaton. Conventonal studes have only dealt wth locatng pont-lke targets, not estmatng ther shape. We apply nterferometry usng these mrror mage antennas to estmate target shapes. If ths method alone s appled, many false mage ponts are estmated because t s dffcult to determne unquely the correspondng mrror mage antenna to each echo. We propose an effectve falsemage reducton algorthm to obtan a clear mage. Numercal smulatons show that most of the false mage ponts are removed and the target shape s accurately estmated. Fg. 1. Person n Shadow Regon Room s Scan Antenna wth Mechancal Scanner Overvew of survellance system usng UWB pulse radar. I. Introducton In antcpaton of an ncreasngly agng socety, montorng systems for aged care are attractng attenton. Most of the current montorng/securty systems use cameras because of ther low-cost and hgh resoluton capabltes. However, optcal cameras have serous prvacy-related problems. The ntroducton of nfrared cameras s another canddate for montorng systems because they are unlkely to capture surface textures thus reducng prvacy concerns. In general, numerous cameras are needed to cover a total gven area wthout any blnd spots, makng the entre system complcated and costly. A system usng radowaves s a promsng canddate for ths purpose as t has the potental to resolve some of the substantal problems of camera-based systems. Moreover, t has been reported that radowaves enable the detecton of targets n hdden places. Exstng communcaton nfrastructures lke Wreless LAN (WLAN) statons have been employed for postonng purposes [1], [2]. Although these methods are capable of estmatng target locatons, an accurate target shape cannot be obtaned. To obtan the target s shape n addton to ts locaton, a UWB pulse radar has great potental because of ts hgh range resoluton. However, most of the conventonal algorthms, ncludng SAR [], [], provde a target mage for whch the resoluton s lmted to half the wavelength. The SEABED algorthm [], [6], [7] s another approach makng use of /1$26. c IEEE the reversble transform between a receved sgnal and the target boundary, whch can produce mages wth a resoluton much hgher than any conventonal algorthms. However, ths algorthm assumes drect echoes, not mult-path echoes, and thus cannot be appled to a target n a blnd spot. Furthermore, a new approach usng multpath echoes, the tme reversal (TR) method [8], [9], makes t possble to calculate an mage usng only a sngle antenna [1], [11]. Assumng a pont-lke target n a room of known shape, ths method back-propagates the receved sgnal numercally to focus on an mage at the target locaton. The method cannot estmate a target s shape although t gves an accurate target locaton. In ths paper, we propose a new magng method for UWB radar usng a sngle antenna wth a mechancal scanner that combnes the deas of the TR and the nterferometry method [12] to accurately estmate a target shape n a multpath envronment. Ths method also has a partcular advantage over conventonal camera-based systems because t enables the magng of a target n an area that s out of sght. The proposed method pcks up multpath echoes from the receved sgnals to estmate the target shape. The procedure gves a correct target shape wth many undesrable false mages caused by the ambguty of the propagaton paths correspondng to multpath echoes n the receved sgnals. To elmnate these false mages, we propose an effectve false mage reducton algorthm to obtan a clear mage. Frst, we explan the procedure of the proposed magng method, followed by some numercal

2 a (6) a () 6 2 Antenna a () a () a (1) a () Fg. 2. System model A wth a shadow regon smulaton results to show the performance of the proposed method compared wth conventonal methods. II. System Model For smplcty, we deal wth a 2-dmensonal problem n ths paper. It s assumed that a radar system s nstalled on a mechancal scanner n a room as n Fg. 1. We assume that the room s confgured as a known polygonal shape. A human target s located at an unknown poston n the room. The room has a blnd area blocked by walls. In ths paper, the areas that cannot receve drect waves from the antenna are called shadow regons. Fgure 2 shows an example of the shadow regons blocked by a wall n a room. Fgure shows a model of the system, where an antenna and a crcular target are located n an L-shaped room. In an deal envronment, the target and the room are made of perfect electrc conductor (PEC) materal. We defne real space as the space where the target and antenna are located. We express real space wth the parameters r = (x,y). The target s modeled as a smple-shaped PEC object n the shadow regon llustrated as the regon panted gray n Fg. 2. The antenna s used for both transmttng and recevng, and s scanned along a straght lne. The -th antenna locaton s expressed as x = Δx + x, where Δx s the nterval of the antenna locaton. The antenna scans along a lne y = y n the x drecton. Rased-cosneshaped UWB pulses, wth a center frequency of 79 GHz and a bandwdth of 1. GHz, are transmtted and echoes are receved by the same antenna. The antenna s assumed to have an deally unform beam pattern wth a beam wdth of 18 and wth the man lobe n the drecton of the y-axs. We defne s (X, Z) as the receved sgnal at the antenna locaton r = (X,y ), where we defne Z n terms of tme t and the speed of the radowave c as Z = ct. The ray tracng method [1], [1] s used to calculate the receved sgnal. In ths method, the propagaton of electrc waves s modeled wth multple straght lnes; the receved sgnal s calculated as the summaton of all the components of the paths. The sgnal s (Z) receved at r = (X,y ) s calculated as s (Z) = A n w(z cτ n ), (1) n Fg.. Mrror mage ponts for model A. where n s the number of paths from the antenna to the target, A n and τ n represent the ampltude and relatve delay of the n-th component, and w(z) s the reference waveform. The undesred drect reflectons ncludng drect crosstalk are subtracted from the receved data. To subtract these from the data measured n an actual envronment wth a target, the drect echoes from the walls are measured n advance. The drect echoes should be measured perodcally because the envronment can change over tme. A flter matched to a transmtted waveform s appled to the raw sgnal s (X, Z) to obtan a fltered sgnal s(x, Z). The magnary space expressed wth (X, Z) s called the data space. For convenence, we ntroduce mrror mage antennas that are located at symmetrcal postons wth respect to the room walls as n Fg.. Each multpath wave can be modeled wth an magnary echo from the correspondng mrror mage antenna. These mrror mage antennas can be treated as the actual antennas, asde from the reflecton coeffcent of the walls nvolved. The j-th mrror mage antenna for the -th antenna poston s located at a ( j) = (x ( j),y ( j) ) = (Δx ( j) + x ( j) j),y( )( =,, M; j =,, N), where M s the number of antenna locatons, N s the number of mrror mage antennas, and Δx ( j) s the nterval of the j-th mrror mage antenna s locaton. In the case j =, t represents an actual antenna locaton. III. Conventonal Method A. SEABED Method A hgh-speed UWB radar magng method, SEABED [] has been proposed based on a smplfed target model. Ths method uses a reversble boundary scatterng transform (BST) between the pont n real space (x,y) and the pont n data space (X, Z ), whch s extracted from the output of the matched flter s(x, Z), where Z = Z/2. The nverse BST (IBST) s expressed as { x = X Z dz /dx, (2) y = Z 1 (dz /dx) 2, ()

3 a (7) a (8) a () a () a (1) a () a () a (6) X[m] Z[m] Fg.. System model B wthout shadow regons. Fg. 6. Receved sgnals after applyng the matched flter... True Shape Estmated Shape 1 I(r) Fg.. Image estmated by the SEABED method. Fg. 7. Image estmated by the TR method. where dz /dx 1 holds. Although t s reported that the SEABED method can obtan a hgh-qualty mage, ths method can be appled only to measurements usng drect echoes receved wthout any multpath sgnals as n Fg.. Fgure shows the estmated mage by applyng the IBST to the system model shown n Fg.. Here, a crcular target wth a radus of. m located at (.m,. m) s assumed. We also set the other parameters (x,y ) = (.1m, 1.m), Δx =.1m, and M = 8. In Fg., although SEABED provdes an accurate target shape, we can obtan only a small part of t because we use only drect echoes from the target wthout any multpath echoes. B. Tme-Reversal Imagng Method The tme reversal (TR) method s another approach to UWB radar magng that s lkely to be applcable even to multpath echoes [11]. In the TR method, extended to shadow regon magng, the mage I(r) sformulatedas N N I(r)= H(p, q, r) (X, s r a (p) + r a (q) ) 2, () p= q= where H(p, q, r) s the functon defned as 1 (r Π p Π q ), H(p, q, r) = (r Π p Π q ). In Eq. (), Π p s the shadow regon from the locaton of the p-th antenna. Equaton () ndcates that the mage I(r) s produced by summng all the sgnals usng dfferent antenna pars after compensatng for the tme delay. The functon H(p, q, r) prevents the summaton from ncludng contradctory components that propagate through the PEC walls. We apply ths method to the system model shown n Fg.. Fgure 6 shows the receved sgnals s(x, Z) for the system model n Fg.. Here, the observaton tme s t 1 nsec, correspondng to a range of m. We assume N = 6, whch means that the mage s produced wth multpath echoes wth the number of reflectons less than or equal to three. Fgure 7 shows the mage obtaned by the TR method. The mage s normalzed usng the maxmum value of I(r). In ths fgure, although the target locaton s estmated, a target shape cannot be seen, meanng that ths method cannot be used for radar magng n multpath envronments. ()

4 (X,Z,1 ) (X,Z,2 ) (X,Z, ) (X,Z,1 ) (X,Z,2 ) Fg. 8. (X 2,Z 2,1 ) (X 2,Z 2,2 ) (X 2,Z 2, ) (X 1,Z 1,1) Too small Schematc of extractng pars of range ponts. X[m] Extracted Range Ponts IV. Proposed Method A. Extracton of Range Pont Pars Ths secton descrbes the proposed magng algorthm for obtanng hgh-resoluton mages n an ndoor envronment. In ths subsecton, we explan the procedure for the ntal data processng of the receved sgnals. (X, Z,k ) s defned as a range pont that s extracted from the peak ponts of s(x, Z) as δ s(x, Z)/δ Z =, (6) s(x, Z) ρ max s(x, Z), (7) where X s the -th actual locaton of an antenna and Z,k s the k-th peak of the sgnal receved at (X,y ). The parameter ρ s emprcally determned. The peak ponts are extracted by fndng the local maxmum ponts wth the quas-newton method. Only the sgnal satsfyng Eq. (7) s the target for ths search. The ntal values for the search are set to mδz s, where mδz s satsfes the condton: s(x, mδz s ) = max {s(x, (m 1)ΔZ s ), s(x, mδz s ), s(x, (m+1)δz s )}. (8) ΔZ s s the samplng nterval of Z. The sampled data of the sgnal s(x, Z) s nterpolated usng the snc functon n ths search. Moreover, we pck up pars of adjacent range ponts satsfyng the condton Z,u Z +1,v T, (9) where T s the length of the transmtted pulse. The schematc for ths procedure s llustrated n Fg. 8. We set T =.2m for the assumed system model usng a pulse wth a bandwdth of 1. GHz. The black dots connected wth sold lnes n Fg. 9 show the pars of range ponts extracted by the procedure descrbed above, where we set ρ =.. B. Interferometry Imagng n an Indoor Envronment In ths subsecton, we descrbe the proposed magng method usng the range ponts extracted n the prevous subsecton. Note that the receved echoes nclude both monostatc and bstatc radar echoes. If the transmttng and recevng propagaton paths are dentcal, as n the left-hand part of Fg. 1, ths s nterpreted as a monostatc radar sgnal wth a sngle actual/magnary antenna. In contrast, other reflected echoes propagate along a path dfferent from the transmttng propagaton path. Ths echo corresponds to a bstatc radar arrangement as n the rght-hand part of Fg Fg Z[m] Extracted pars of range ponts. The nterferometry method [12] s employed for magng usng the extracted pars of range ponts. Interferometry s a commonly used technque for drecton-of-arrval (DOA) estmaton usng the phase dfference between multple echoes receved wth dfferent antennas. By extendng ths prncple, the target shape s provded by solvng the ntersecton ponts of the followng two ellpses: r a (p) + r a (q) = Z,u, (1) r a (p) + r a (q) = Z +1,v. (11) Ths can be used for estmatng the DOA by measurng the dfference between the delays of the multple echoes receved by dfferent antennas. In the case p = q, as shown n the lefthand part of Fg. 1, the soluton s gven by the ntersecton of two crcles rather than ellpses. The schematc of ths nterferometry method s llustrated n Fg. 11, where an ellpse wth foc a (1) and, and another ellpse wth foc a (1) and are used to calculate the target locaton. We apply these methods to all possble combnatons of pars of range ponts and antennas to obtan an estmated mage. Fnally, f the estmated pont falls outsde the room, the pont s removed. The mage estmated by ths method s shown n Fg. 12, where a broken lne and the black dots represent the actual target shape and the estmated mage respectvely. Although ths mage s a correct estmate of the crcular target, t also has many false mage ponts because t contans ncorrect combnatons of a range of ponts and antennas. Ths s because ncorrect pars of antennas and range ponts are used to produce the mage. C. False Image Reducton Method The problem s that we cannot know whch echo corresponds to whch par of antennas at ths stage. Frst, we calculate a rough mage usng the conventonal TR method to estmate the approxmate locaton of targets as n Fg. 7. We estmate the maxmum pont r max from the mage n Fg. 7. Next, we pck up consstent combnatons of range ponts that

5 Tx/Rx Tx 1 Back Forward Forward 8 6 Forward Back Forward 2 Monostatc Radar Arrangement Back Rx Back Bstatc Radar Arrangement True Shape Estmated Shape Fg. 1. Two types of propagaton paths. Fg. 12. Estmated mage ponts wthout false mage reducton process (1) a +1 a (1) Fg. 11. Schematc of bstatc nterferometry. A (Inclnaton to the left) B (Inclnaton to the rght) satsfy the relatonshp between the actual/magnary antenna scannng drecton and the estmated range values. We only use antenna pars based on the nclnaton of the lnes connectng the range ponts. In ths process, echoes are dvded nto two groups A and B as n Fg. 1. Each antenna par s classfed as a member of ether group A or group B. Applyng the nterferometry method, we add the followng condton: ( Z,u Z +1,v r max a (p) + r max a (p) +1 + ) +1, (12) ( Z,u < Z +1,v r max a (p) + < r max a (p) + ). (1) In addton, we assume that true mage ponts exst wthn the vcnty of the pont r max for r r max <μ. The target shape estmated by the proposed method s shown n Fg. 1, where the whte square symbol represents the estmated target locaton r max, and where we set μ =.m and r max = ( 2. m,.1 m). In ths fgure, most of the false mages are removed and the true target shape s accurately Fg. 1. Schematc of false mage reducton process. estmated. Compared wth the mage estmated by the TR method shown n Fg. 7, the proposed method provdes more sgnfcant mages for recognzng the target shape wth a clear surface. The RMS error of the estmated shape s.7 mm. Of course, ths error s not realstc because a noseless envronment s assumed here. We analyze the performance n a nosy envronment n the next secton. Note however that the bandwdth and center frequency have much to do wth the estmaton accuracy and the wdth of the estmated regon. If the bandwdth s narrower, there can be more nterference n the receved sgnals, whch deterorates the accuracy of the estmated mage as the extracted peak ponts nclude range errors. Moreover, the reflecton coeffcent changes wth center frequency. If the reflecton coeffcent s smaller, the number of usable range ponts decreases for the condtonal equaton shown n Eq. (7), whch causes the dmnuton of the estmated regon.

6 . True Shape Estmated Shape Maxmum Pxel of TR Image True Shape Estmated Shape Maxmum Pxel of TR Image Fg. 1. Estmated mage ponts wth false mage reducton process. Fg. 16. Estmated mage ponts for S/N=.dB True Shape Estmated Shape Maxmum Pxel of TR Image RMS Error [mm] S/N [db] Fg. 1. RMS error of the proposed method vs. S/N. Fg. 17. Estmated mage ponts for a target n a lne-of-sght area. V. Performance Evaluaton of the Proposed Method A. Nose Tolerance Assumng the same scenaro as n the prevous secton, we show the magng accuracy of the proposed method wth nosy data. To produce a nosy sgnal numercally, whte Gaussan nose s added to the raw sgnals s (X, Z). We defne S/N asthe rato of the peak nstantaneous sgnal power to the averaged nose power after applyng the matched flter. The RMS error of the estmated shape usng the proposed method s shown n Fg. 1. Ths fgure shows that the RMS error s relatvely small, at less than mm for S/N 2. db. The TR method provdes an accurate estmaton of r max for S/N 1.7 db, whereas the nterferometry method fals to estmate accurate mage ponts for S/N 2. db. We have confrmed that the mage estmated by the TR method cannot estmate an accurate target locaton, leadng to a poor performance of the proposed method. Therefore, the proposed method requres S/N to be larger than 2. db. The mage estmated n nosy envronments s shown n Fg. 16 for S/N =. db. In Fg. 16, although there are napproprate false ponts, most of the estmated ponts are located on the target surface, gvng an accurate mage estmaton. B. Performance Evaluaton wth Other Models Ths subsecton dscusses the performance of the proposed method wth dfferent models. Frst, we apply the proposed method to model B shown n Fg.. The target mage obtaned s shown n Fg. 17. Ths result verfes that the regon contanng mages s extended compared wth Fg. because the proposed method uses not only the drect echo but also multpath echoes for magng. The estmaton RMS error s 1.78 mm. Next, we show the performance of the proposed method assumng the envronment shown n Fg. 18, modelng the corner of a hallway. The estmated mage s shown n Fg. 19. In ths fgure, a dfferent part of the target boundary s accurately estmated. The estmaton RMS error s.19mm. Fnally, we apply the proposed method to an ellptcal PEC target n model A shown n Fg.. Fgure 2 shows an example of the estmated mage for the target wth an nclnaton angle of 12, where part of the target shape s correctly estmated wth an estmaton RMS error of.2 mm. We have also appled the proposed method to the same ellptcal targets wth varous nclnaton angles over the range 6 ψ 12 and confrmed the average estmaton RMS error to be 2.7mm.

7 1 1 - a (6) a (7) a (8) a () a () a (1) a () a (). True Shape Estmated Shape Maxmum Pxel by TR ψ= Fg System model C for a hallway. True Shape Estmated Shape Maxmum Pxel of TR Image Fg. 2. Estmated mage ponts for an ellptcal target Fg. 19. Image estmated for system model C. VI. Conclusons Ths paper proposes an magng method for a target n a shadow regon usng a sngle antenna. Frst, we establshed that conventonal methods do not provde suffcent resoluton of a target n a shadow regon. To obtan a hgh-resoluton mage, we proposed an magng method usng the prncple of nterferometry and appled ths method to each of the mrror mage antennas. In addton, we proposed a false mage reducton algorthm usng an approxmate target locaton obtaned by the TR method and the nclnaton of the estmated pars of echoes n the data space. In ths process, most of the false mage ponts were removed and the target boundary was estmated accurately. We also nvestgated the performance of the proposed method for nosy data and clarfed that an accurate mage s obtaned when S/N s hgher than about 2 db. Moreover, we nvestgated the performance of the proposed method n dfferent system models, confrmng the effectveness of the proposed method n a varety of stuatons. However, we only nvestgated the performance evaluaton of the proposed method by the restrcted deal system model. In an actual ndoor envronment, some addtonal factors adversely affect the performance of our proposed algorthm, such as clutters, nterference, antenna radaton pattern nulls, polarzaton msmatch, and dynamc range. Furthermore, targets and walls are not made of PEC n an actual envronment, and snce S/N s lower than n the deal envronment the estmaton accuracy s also lower and the estmated regon s dmnshed. These are ssues to be addressed n the future. References [1] S. Ikeda, H. Tsuj, and T. Ohtsuk, Indoor event detecton wth Egenvector spannng sgnal subspace for home or offce securty, IEICE Trans. Commun., vol. E92-B, pp , 29. [2] K. Pahlavan, F. O. Akgul, M. Hedar, A. Hatam, J. M. Elwell, and R. D. Tngley, Indoor geolocaton n the absence of drect path, IEEE Wreless Communcatons, vol. 1, no. 6, pp. 8, 26. [] C. Le, T. Dogaru, L. Nguyen, and M. R. Ressler, Ultra wdeband (UWB) radar magng of buldng nteror: Measurements and predctons, IEEE Trans. Geosc. Remote Sens., vol. 7, no., pp , 29. [] X. Zhuge, T. G. Savelyev, A. G. Yarovoy, and L. P. Lgthart, UWB array-based radar magng usng modfed Krchhoff mgraton, 28 IEEE Internatonal Conference on Ultra-WdeBand (ICUWB28), vol., pp , 28 [] T. Sakamoto, A fast algorthm for -D magng wth UWB pulse radar systems, IEICE Trans. Commun., vol. E9-B, pp. 66 6, 27. [6] S. Kdera, Y. Kan, T. Sakamoto, and T. Sato, A fast and hghresoluton -D magng algorthm wth lnear array antennas for UWB pulse radars, IEICE Trans. Commun., vol. E91-B, no. 8, pp , 28 [7] T. Sakamoto, Y. Matsuk and T. Sato, A novel UWB radar 2-D magng method wth a small number of antennas for targets wth arbtrary shapes and moton, 29 IEEE Internatonal Conference on Ultra-WdeBand (ICUWB29), pp. 9-11, 29. [8] E. A. Marengo and F. K. Gruber, Subspace-based localzaton and nverse scatterng of multple scatterng pont targets, EURASIP J. Appl. Sgnal Process., vol. 27, pp , 27. [9] Y. Jn and J. M. E. Moura, Tme-reversal detecton usng antenna arrays, IEEE Trans. Sgnal Process., vol. 7, pp , 29. [1] T. Sakamoto and T. Sato, Tme-reversal UWB magng wth a sngle antenna n mult-path envronments, rd European Conference on Antennas and Propagaton (EuCAP) 29, pp. 2 7, 29. [11] T. Sakamoto and T. Sato, A method of estmatng a room shape wth a sngle antenna n a multpath envronment, th European Conference on Antennas and Propagaton (EuCAP) 21, pp , 21. [12] D. Massonet and K. L. Fegl, Radar nterferometry and ts applcatons to changes n Earth s surface, Rev. Geophys., vol. 6, no., pp. 1, [1] M. F. Iskander and Z. Yun, Propagaton predcton models for wreless communcaton systems, IEEE Trans. Mcrowave Theory Tech., vol., pp , 22. [1] M. C. Lawton and J. P. McGeehan, The applcaton of a determnstc ray launchng algorthm for the predcton of rado channel characterstcs n small-cell envronments, IEEE Trans. Veh. Technol., vol., pp , 199.