TOA localization for multipath and NLOS environment with virtual stations

Transcription

1 Lu et al. EURASIP Journal on Wreless Communcatons and etworkng (07) 07:04 DOI 0.86/s RESEARCH TOA localzaton for multpath and LOS envronment wth vrtual statons Delang Lu, Yng Wang *, Peng He, You Zha and Hongyun Wang Open Access Abstract An effectve geometrcal method whch can locate a source based on the tme-of-arrval (TOA) measurements and the floor plan nformaton s proposed n smple non-lne-of-sght (LOS) ndoor envronment the multplebound scatterng sgnal paths can be gnored. The novelty of our work resdes n convertng the LOS problem nto lne-of-sght (LOS) problem based on the vrtual statons (VSs), so that the localzaton algorthm for LOS condtons can be appled n smple LOS condtons. The performance bound of the proposed method s also analyzed. Smulaton results demonstrate the effectveness of the proposed method. Keywords: Localzaton, Tme-of-arrval, on-lne-of-sght, Vrtual staton Introducton Global postonng system (GPS) has played an mportant role for trackng and postonng n outdoors. However, t s lmted n ndoor envronments because the satellte sgnal s serously dsturbed and the postonng accuracy cannot meet the requrements of ndoor localzaton [ 4]. Therefore, ndoor localzaton has receved a hgh amount of attenton over the last years. Among varous ndoor localzaton methods, whch dffer by the type of nformaton and system parameters used, the representatve ones are the tme-of-arrval (TOA), tme-dfference-of-arrval (TDOA), drectonof-arrval (DOA), receved-sgnal-strength (RSS), and ther combnatons. evertheless, LOS and multpath rado propagaton between base staton (BS) and moble staton (MS), whch can cause based range estmates n TOA measurements, wll dramatcally degrade the performance of conventonal TOA localzaton methods. To mtgate the LOS mpact, a varety of technques and algorthms have been proposed n the lterature. Flterng-based method s presented n [5] whch only apples to the trackng of moble tags. The method n [6] struggles to dentfy the LOS paths, from a set of mxed measurements ncludng both LOS and LOS paths. However, * Correspondence: msyngwang@outlook.com Tanjn Unversty of Technology and Educaton, 300 Tanjn, Chna Full lst of author nformaton s avalable at the end of the artcle ths approach requres LOS measurements nvolved and cannot be expected to be effcent when sgnals only propagate through the LOS paths. In [7], TOA scatterng models are adopted to allevate the LOS error, as the dstrbutons of LOS error may not be avalable n the practcal envronment. A robust scheme n [8] utlzes one-bound scatterng and dscards multple-bound scatterng to mprove the accuracy of LOS localzaton. But t needs bdrectonal estmatons of both AOA and TOA measurements, whch means more hardware costs. The VS method has been used to solve the LOS and multpath problem n [9 ]. Usng the known room geometry, the reflectons can be mapped onto vrtual anchors,.e., the known postons of vrtual sources that can be used for estmatng the poston of the recever. However, the methods n [9, 0] only resolved the multpath problem and only consdered the reflectons off the walls, and methods n [] gnored the reflectons and dffractons caused by obstacles as well as the effect of people n the room. In our prevous work [], we proposed a geometrcal approach usng the VS method based on TOA and AOA measurements. But measurng AOA needs array antennas whch wll ncrease the hardware costs. In ths paper, we present a VS method only based on the TOA measurements for the smple LOS envronments the sgnals undergo no more than one-bound scatterng. We assume that the LOS multpath sgnals The Author(s). 07 Open Access Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton 4.0 Internatonal Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded you gve approprate credt to the orgnal author(s) and the source, provde a lnk to the Creatve Commons lcense, and ndcate f changes were made.

2 Lu et al. EURASIP Journal on Wreless Communcatons and etworkng (07) 07:04 Page of 7 undergo one-bound scatterng (reflecton of dffracton) at most, because multple-bound scatterng can be gnored as they suffer from severe fadng and may be too weak to be observed [9]. We frst develop a geometrc TOA model for LOS envronments, establsh the VSs, and derve the path estmaton algorthm to estmate the realstc sgnal propagaton paths as well as the possble postons of the unknown MS by the TOA measurements between every BS and MS. Then, we determne the fnal poston of the MS based on the least squares prncple. Fnally, the performance bound of the proposed algorthm s analyzed and the smulatons are run to demonstrate the effectveness of the proposed algorthm. The paper s organzed as follows: In Secton, the proposed VS method s descrbed n detal. Secton 3 wll provde the analytc performance bound of the proposed method. Secton 4 analyzes the performance of our model by smulatons. Secton 5 concludes the research efforts. The TOA-based VS algorthm. Motvaton A typcal TOA-based localzaton algorthm for LOS condtons conssts of two knds of parameters: one s dstance parameters whch contan the measured dstances between every BS and the poston of the unknown MS; the other s poston parameters whch nclude the postons of BSs. In the followng analyss, we wll take the least squares (LS) algorthm as an example of localzaton algorthm for LOS condtons. To measure the tme-of-arrval between a BS (transmtter) and a MS (recever), we usually detect the peak of the receved sgnal arrvng on the frst detectable path, and the tme delay τ of the peak s the measurement of the TOA. The estmated dstance between the transmtter and the recever s ^d ¼ τ c, n whch c s the speed of rado wave propagaton. Under LOS condtons, the drect path s always the strongest path so that the ampltude s hgher than the threshold. Therefore, the frst detectable path s the drect path. However, paths arrvng n close vcnty of the drect path wll shft the peak of the frst path causng modest postve rangng errors [3]. So, the measured range ^d LOS between a BS and a MS can be expressed as [4]: ^d LOS ¼ d þ e ðþ d s the Eucldean dstance between the anchor and the tag and e represents the Gaussan random nose wth zero-mean and standard devaton σ. But under LOS condtons, the drect path s blocked by objects stuated between the transmtter and the recever and may not be detected at all. Therefore, the measured range ^d LOS can be gven by: ^d LOS ¼ d þ b LOS þ e ðþ b LOS s the propagaton delay mposed by LOS. Because e can be neglected n comparson wth b LOS, the measured range s always larger than the true dstance under LOS condton ^d LOS > d ð3þ As a result, f we use ^d LOS as the dstance parameters of conventonal LS algorthm, the localzaton error wll be larger n LOS condtons. So, many efforts have been made to estmate the Eucldean dstance d from the measured dstance ^d LOS n order to reduce the dfference between them [7]. But the other knd of parameters has not been attached mportance yet, and the postons of the BSs. Instead of usng the locatons of real BSs, we employ the postons of VSs. We stll use the measured dstance n LOS condton as the dstance parameters of LS algorthm. Then, f we can estmate whch path (drect path, reflecton path, or dffracton path) s the frst detectable path between every BS and the MS, the VSs can be establshed so that reflectons and dffractons can be treated equvalently as sgnals comng from the VSs through the drect paths from the MS s perspectve. Therefore, the LOS problem has been converted nto LOS problem, and the LS algorthm can be appled n LOS condtons va the cooperaton of several VSs.. Geometrc TOA model for LOS and establshment of VSs Based on the above analyss, n order to estmate the dstance between BS and MS, we measure the frst detectve path length ^l, whch can be expressed as ^l ¼ l FP þ e ð4þ l FP represents the frst detectable path length and s the BS number, =,,, M. Consder a MS wth unknown poston at X =[x, y] T, recevng sgnal from a BS at known postons, namely, X =[x, y ] T, T denotes the transpose operator and s the BS number. The TOA measurement between the BS and the unknown MS s ^l.the VS s set up at X k h ¼ x k ; y k T,k s the VS number of the th real BS, and the estmated vrtual path length s ^l ζ v, ξ s the path type, and ξ =,,or3represents the drect path, reflecton path, and dffracton path, respectvely. In ndoor envronments wth obstacles ncludng people, there are manly four knds of sgnal paths: drect paths, reflecton paths, dffracton paths, and penetraton paths.

3 Lu et al. EURASIP Journal on Wreless Communcatons and etworkng (07) 07:04 Page 3 of 7.. Drect paths Assumng that the sgnal propagates from the BS at X to the MS at X through a drect path, l FP n (4) can be expressed as l FP ¼ kx Xk ð5þ represents the -norm. For the consstency of the whole model, we also set VS X at the real BS poston X, and the estmated vrtual path length ^l v s equal to the measured path length ^l ^l v ¼ ^l ð6þ.. Penetraton paths When sgnal propagates through obstacles, t slows down and gets dspersed [5]. But these effects can be neglected n comparson wth other LOS errors. The only effect of penetraton we consder n our work s attenuatng the sgnal strength whch may affect the frst detectve path. Indoor envronments are often populated wth people. The experment results n [6] revealed that no addtonal rangng error occurs due to the presence of the human body n TOA measurements wth the proper choce of the detecton threshold. The results also showed that the power of the drect path s strongly attenuated by the presence of the human body. Therefore, we treated human body effects equvalently as penetraton effects...3 Reflecton paths In our work, we assume that all reflectons are specular reflectons [8, 9]. Assumng that the sgnal propagates from the BS at X to the MS at X through a reflecton path, the path length we measured wth the TOA method s ^l. As depcted n Fg. a, we represent the reflector A j B j as a lne y ¼ m j x þ c m j ð7þ x ¼ c j m j ¼ j =,,, represents the number of obstacle. The VS at x k and the real staton X are a par of symmetry ponts of lne A j B j, so the poston of the VS can be expressed as 8 m j x >< m y =m j c j j X k ¼ ð8þ c j x >: m y j ¼ It looks lke that the sgnal transmts from x k to X through a drect path. Therefore, l FP n (4) can be gven as Fg. TOA model of reflecton and dffracton. a Reflecton. b Dffracton l FP ¼ X X k The vrtual path length can be estmated as ^l v ¼ ^l ð9þ ð0þ If the reflecton happens, the estmated length of the frst detectable path should be larger than the dstance between the VS and the pont P, whch s the ntersecton pont of lne A j B j and lne ^xx k. ^X X k > P X k ðþ..4 Dffracton paths Assumng that the sgnal propagates from the BS at X to the MS at X through a dffracton path, the path length we measured s ^l. As depcted n Fg. b,

4 Lu et al. EURASIP Journal on Wreless Communcatons and etworkng (07) 07:04 Page 4 of 7 the dffracton happens at pont A j and ts poston s consdered as a known vector. So, l FP n (4) can be gven as l FP ¼ X k X þ X k X ðþ We can get x k x n () from the floor plan nformaton. We establsh the VS at pont A j, so that t looks lke the sgnal transmts from the VS to the MS at X t through a drect path and the vrtual path length can be estmated as ^l3 v ¼ ^l X k X ðþ If the dffracton happens, ^X X k > X k X ð4þ In ths work, we assume that the LOS envronment s smple that the sgnals undergo no more than one-bound scatterng (reflecton or dffracton), and mult-bound scatterng can be gnored as they sufferfromseverefadngandmaybetooweaktobe observed [8]. In LOS ndoor envronment, the floor plan can be easly obtaned. Then, we can develop a group of VS for every BS based on the above analyss..3 Path estmaton algorthm After consderng all possble sgnal paths and establshng VSs for them, we choose one VS from every VS group x k ; xk ; ; xk M M ; we can get the correspondng vrtual path length ^l ζ v ; ^lζ v ; ;^l ζ M vm. Then, we can utlze the exstng TOA localzaton algorthm, least squares for example, to obtan a possble poston ^X k ;k ; ::;k M of the MS by (5), and so on; we can get all the possble postons of the MS, the total of whch s K K KM. ^X k ;k ; ;k M ¼ A T A A T b ð3þ A ¼ 4 x k xk y k yk x k xk M M y k yk M M 3 5 x k x k þ y k y k b ¼ 6 4 x k x k M M þ y k y k M M þ ^lp v þ ^lp v 3 ^lp v 7 5 ^lp If the TOA measurements have no errors, then vm a k ; a k ; ; a M k M X M ^X a ;a ; ;a M X k ^l ξ ¼ 0 ¼ ð4þ But f the errors do exst, then we try to mnmze the left part of (6), ½a ; a ; ; a M ¼ arg mn D k ;k ; k M D k ;k ; k M ¼ XM ¼ k ½;K ;k ½;K ; ;k M ½;K M ^X t k ;k ; ;k M X k ^l ξ Then, ^X a ;a ; ;a M s the estmated MS poston. ð5þ 3 Analytcal performance bound The Cramer-Rao lower bound (CRLB) s defned as the lower bound on the varance of the desred parameters of the estmator (n our case, ths s the localzaton parameter X). The bound states that the varance of any unbased estmator s at least as hgh as the nverse of the Fsher nformaton. An unbased estmator that acheves ths bound s sad to be an effcent estmator that provdes the lowest possble mnmum mean square error. In ndoor envronment, there may be several paths between a BS and a MS because of the multpath problem. To get the CRLB of the proposed localzaton algorthm, we use a new parameter p k to represent the probablty that the path number of the measured TOA from the th BS s k, k =,,, K. When the ndoor sgnal channel s stable and the measured path s the same path between the BS and the MS n every TOA measurements. There s only one path number q p k ¼ k ¼ q 0 k q ð6þ When the ndoor sgnal channel s complcated wth relatvely large flow of people, the measured path may be not the same n every TOA measurements, so p k needs to be practcally measured. The Fsher nformaton matrx of the proposed method can be gven as

5 Lu et al. EURASIP Journal on Wreless Communcatons and etworkng (07) 07:04 Page 5 of 7 ( ) T J 0 ¼ E lnf Λjw w ð Þ lnf Λjw w ð Þ ¼ K KX K P j j¼ w lnf Λ jjw w lnf Λ jjw T ð7þ J xxj þ J yyj ¼ σ J xxj J yyj J xyj ¼ X ¼ 6 X 4 ¼! x x k X σd k ¼ x x k y y k σd k y y k σd k! P j¼ ¼ p p p P j¼ ¼ p p p P j¼k ¼ p K p p P j¼k K K ¼ p K p K p K Λ j¼ ¼ Λ ; Λ ; ; Λ Λ j¼ ¼ Λ ; Λ ; ; Λ Λ j¼k ¼ Λ K Λ Λ Λ j¼k K K ¼ Λ K Λ K Λ K r ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff Λk ¼ x x k þ y y k þ n k Then, we can get x x y y d V H j¼ ¼ d V x x d V x x d V x x K K d V x x K ¼ K d V 6 4 x x K K d V y y d V y y d V y y K 3 K d V y y K K d V 7 y y K 5 K d V ; ;H j¼k K K ð0þ 4 Smulaton results To evaluate the performance of the proposed VS method, smulatons have been conducted. As shown n Fg., three BSs were located at BS (6, 8), BS (4, 6), and BS3 (4, 5), respectvely. The MS was located at three test ponts, A (3, 6), B (6, ), and C (6, ). The frst detectable path between every anchor and every test pont were assumed as the fgure shows. We also set two people, P and P, so that the LOS path may be not the frst detectable path n some condtons. When the MS was located at pont A, two paths were LOS and the other one s onebound scatterng path; when at pont B, one path was LOS and the others were one-bound scatterng paths; when at pont C, all three paths were one-bound scatterng paths. Fgures 3 and 4 llustrates the root mean square error (RMSE) comparson and the cumulatve dstrbuton functon (CDF) comparson among the SDP (semdefnte programmng) algorthm [7], ML [0], and TSWLS [0] estmators wth and wthout usng our VS method respectvely wth σ = m. One thousand ndependent runs are smulated to obtan the RMSE. The CRLB n Fg. 3 s obtaned n the stuaton whch the ndoor sgnal channel s complcated, andweassumethatp ¼ p ¼ p k. As Fgs. 3a and J 0 ¼ K KX K j¼ K K σ CRLB ¼ trðj 0 Þ ¼ X K P j H T j QH j ðþ j¼ PjJ xxj þ J yyj ðþ J xxj J yyj J xyj Fg. Smulaton envronment

6 Lu et al. EURASIP Journal on Wreless Communcatons and etworkng (07) 07:04 Page 6 of 7 Fg. 3 ALE comparson. a Pont A. b Pont B. c Pont C Fg. 4 CDF comparson. a Pont A. b Pont B. c Pont C 4a llustrated, when the MS was located at pont A, most paths were LOS paths, the performances of the fve algorthms were almost the same. When the MS was located at pont B the LOS problem s more serous than that at A, the algorthms whch used our VS method had a better performance than others, as Fgs. 3b and 4b show. When the MS was located at pont C, the LOS path dd not exst, the two algorthms whch used our VS method are much more accurate than those that dd not use our VS method, and the advantage of the VS method s more obvous. 5 Conclusons In ths paper, we have proposed a VS method for convertng the LOS problem nto LOS problem by usng vrtual statons, so that the conventonal localzaton algorthm

7 Lu et al. EURASIP Journal on Wreless Communcatons and etworkng (07) 07:04 Page 7 of 7 for LOS condtons can be appled to smple LOS condtons the multple-bound scatterng sgnal paths can be gnored. We utlzed only TOA measurements and the floor plan of the ndoor envronment and establshed TOA model consderng reflecton, dffracton, penetraton, and human body effect n LOS envronments, and the performance bound of the VS method was also analyzed. Smulaton results confrmed the robustness of our VS method n terms of RMSE and ALE. 6. Y Klc, AJ Al, A Mejernk, W Scanlon et al., The effect of human-body shadowng on ndoor UWB TOA-based rangng systems, n Proc. 9th Workshop on Postonng avgaton and Communcaton (WPC), 0, pp CS Ta, SY Tan, CK Seow, Robust non-lne-of-sght localzaton system n ndoor envronment. Electron Lett 46((8), (00) Acknowledgements The experments of ths research were fnancally supported the by atonal atural Scence Foundaton of Chna under Grant Authors contrbutons DL conceved and desgned the study. YW carred out most of the analyses. DL and YW drafted the manuscrpt. PH and YZ performed the experments. HW modfed the Englsh expressons. All authors read and approved the fnal manuscrpt. Competng nterests The authors declare that they have no competng nterests. Publsher s ote Sprnger ature remans neutral wth regard to jursdctonal clams n publshed maps and nsttutonal afflatons. Author detals Shjazhuang Mechancal Engneerng College, Shjazhuang, Chna. Tanjn Unversty of Technology and Educaton, 300 Tanjn, Chna. Receved: 3 March 07 Accepted: 9 May 07 References. Z L, K Lu, Y Zhao, Y Ma, MaPIT: an enhanced pendng nterest table for D wth mappng bloom flter. IEEE Commun Lett 8(), (04). Z L, L Song, H Sh, Approachng the capacty of K-user MIMO nterference channel wth nterference counteracton scheme. Ad Hoc etw 58, 86 9 (07) 3. Z L, Y Chen, H Sh, K Lu, D-GSM-R: a novel hgh-speed ralway communcaton system va named data networkng. EURASIP J Wrel Commun etw 48, 5 (06) 4. X Lu, Z L, P Yang, Y Dong, Informaton-centrc moble ad hoc networks and content routng: a survey. Ad Hoc etw 58, (07) 5. K Yu, E Dutkewcz, Improved kalman flterng algorthms for moble trackng n LOS scenaros, n Proc. IEEE WCC, 0, pp K Yu, Y Guo, on-lne-of-sght detecton based on TOA and sgnal strength, n Proc. 9th IEEE Int. Symp. PIMRC, 008, pp S Al-Jazzar, J Caffery, H You, Scatterng-model-based methods for TOA locaton n LOS envronments. IEEE Trans Veh Technol 56(), (007) 8. CK Seow, SY Tan, on-lne-of-sght localzaton n multpath envronments. IEEE Trans Mob Comput 7(5), (008) 9. P Setlur, GE Smth, F Ahmad et al., Target localzaton wth a sngle sensor va multpath explotaton. IEEE Trans Aerosp Electron Syst 48(3), (0) 0. KWK Lu, HC So, Range-based source localzaton wth pure reflector n presence of multpath propagaton. IEEE Electron Lett 46(3), (00). P Messner, K Wtrsal, Multpath-asssted sngle-anchor ndoor localzaton n an offce envronment, n Proc. 9th IEEE IWSSIP, 0, pp. 5. D Lu, K Lu, Y Ma et al., Jont TOA and DOA localzaton n ndoor envronment usng vrtual statons. IEEE Commun Lett 8(8), (04) 3. B Alav, K Pahlavan, Modelng of the TOA based dstance measurement error usng UWB ndoor rado measurements. IEEE Commun Lett 0(4), (006) 4. A Alsnd, B Alav, K Pahlavan, Measurement and modelng of ultrawdeband TOA-based rangng n ndoor multpath envronments. IEEE Trans Veh Technol 58(3), (009) 5. Iya, A Muqabel, U Johar, MA Landols, Ultra-wdeband characterzaton of obstructed propagaton, n Proc. 7th IWCMC, 0, pp