A Novel NLOS Mitigation Approach for Wireless Positioning System

Transcription

1 2 3rd International Conference on Coputer and Electrical Engineering (ICCEE 2) IPCSIT vol. 53 (22) (22) IACSIT Press, Singapore DOI:.7763/IPCSIT.22.V53.No..54 A Novel NLOS Mitigation Approach for Wireless Positioning Syste Chen Jian + and Zhuo Yong-ning National Key Laboratory of Science and Technology on Counications University of Electronic Science and Technology of China Chengdu, P.R.China Abstract. A Non-light-of-sight (NLOS) itigation approach based on GBSBEM was proposed in this paper. The ain idea is to odel the NLOS errors to the elliptical odel and itigate the with a novel ethod. At the first step, the sei-inor of GBSBEM is estiated, then a way to restrain the NLOS errors with the help of the sei-inor is used. When the sei-inor can not be estiated, an optiization ethod based on GBSBEM pdf is presented. The ethod has a good effect to reduce the NLOS error, especially when the NLOS effect is notable. Keywords: nlos itigation; gbsbe; position algorith. Introduction In the wireless positioning techniques, one of the ajor challenges for positioning is the NLOS error. The propagated signal between the MS (Mobile Station) and the BS (Base Station) goes through reflection and refraction of any objects in its path. That causes the position paraeters inaccuracy and akes a large positive error for position syste. The traditional TOA or TDOA position algoriths always base on LOS assuption [], [2]. Thus, how to identify and itigate the NLOS error is a concerned topic in this area. NLOS identification and itigation have been addressed in the literature [3]-[6]. The classical ethod in [3] copares the standard deviation of the range easureents with the threshold value for NLOS identification, but the noise variance is assued known for LOS reconstruction. The approach in [4] uses the available data regarding ranges and the base station (BS) layout to adjust the easured ranges to near the true LOS value. A constrained nonlinear optiization is presented in this paper. However, the coplexity of the optiization akes this easure hard to realize. [5] proposes a TOA position ethod based on the cobination of the probability position ethod and the geoetric position ethod. It can restrain NLOS propagation errors to soe degree. The NLOS identification discussed in [6] is by the help of the channel odel defined in IEEE a. Four scenarios characterize the propagated signal s log-noral pdf in graphs. This ethod can distinguish the LOS/NLOS scenarios under UWB syste, but can not apply for the obile syste. In soe situations, especially under the urban environent, the propagated signal would reflect or refract at least once. That eans all of the BSs considered in the positioning syste should be assued NLOS affected. Channel odeling can perfor the channel output paraeters, such as ulti-path delays, and signal direction of arrival [7]. This paper focuses on the geoetrically based single bounce elliptical odel (GBSBEM), because of its ability to produce spatial channel characteristics that is tied to the physical propagation environent. The GBSBEM has a wide range of application for both analyzing and siulating. + Corresponding author. E-ail address: cdchenjian@63.co.

2 The paper is organized as follow. In section II, the general GBSBEM is introduced, and section III describes the detail of the approach based on GBSBEM for NLOS itigation. Siulation results are presented in section IV followed by concluding rearks in section V. 2. Gbsbe Model The Geoetrically Based Single Bounce Elliptical Model (GBSBEM) is a typical urban cell odel in wireless counication research area, which is applied in any related literature [7],[8], In the odel, both MS and BS are surrounded by scattering obstacles. The odel assues all of the signal propagated fro the ulti-path reflects or refracts only once in the considered environent. The boundary of the elliptical is the furthest borderline of the refraction. The scatters are well-distributed in the region of the elliptical odel. Figure. Geoetrically based single bounce elliptical Model Figure illustrates the geoetry of the GBSBEM, where S is the selected scatter, the MS and BS are assued on the focal spot of the elliptical, d is the distance between the MS and BS. The signal propagates fro the BS to MS by refracting in S, which r s and r b are the distances between the scatter S and the MS and the BS respectively. The distance of NLOS propagation is l, which equals r s add r b. a and b are the sei-ajor and sei-inor axes of the elliptical, and f is the focal radius. The equations are expressed as follow l = rb + rs = 2a 2 a b = f d = 2 f () x y + = a b Assues that the scatters are uniforly distributed in the region of Figure, and the area of the elliptical region is given by π ab. The TOA probability density function (pdf) [8], [9] observed at the BS is given by 2 2( cτ / d) c fτ ( τ) =, β d 2 ( cτ / d) τ τ < τ (2) cτ cτ 2 β = ( ) ( ), d d (3) Where c is the speed of light, τ is the tie delay of a ulti-path coponent, τ is the tie delay between the BS and MS, τ is the axiu TOA of a ulti-path coponent, d is the distance between the BS and the MS. 3. Nlos Mitigation 3. Effect of sei-inor of GBSBEM Assue that there are M BSs available. The range easureent of TOA data can be odeled as rt ( ) = lt ( ) + nt ( ) + NLOSt ( ) j=,, M, (4) j i j i j i j i

3 Where rj( t is the range easureent, lj( t is the true distance between the BSj and the MS, nj( t is the easureent error, NLOS j( t is the NLOS error at tie saplet i. The easureent error is usually odeled as Gaussian, i.e. nj( t~ N(, σ j) where σ j is in the order of 5 [3]. The NLOS error NLOS j( t can be odeled as the frequently used odels for delay profiles which are exponential, unifor or delta rando variable []. The range easureents can be soothed by odeled as N n j( j( ) i n= r t = a n t, (5) Where aj ( n ) is the unknown coefficients gotten by the least squares technique. The soothed easureents are represented as N n ( ) ˆ j i j( ) i n= s t = a n t, (6) When the NLOS errors exist and can not be ignored, the LOS propagation path can be reconstructed by the GBSBEM. The initial value of sei-inor of GBSBEM should be estiated. Fro the urban structure or the geo-inforation syste, the sei-inor can be estiated. Assue that the sei-inor is b. The value of sei-inor is less than the sei-ajor obviously. That is b< a (7) a = ax( sj ) 2 So, the half of the LOS path between the BSj and the MS, which is also the focal radius of the GBSBEM can be estiated by f = a b, (8) The LOS path between the MS and the BSj is d = 2 f = ( x x ) + ( y y ), (9) LOS s j s j It is well known that the location accuracy usually decreases as the NLOS errors increase. This indicates that the selection of the initial value is very iportant. When the initial value is appropriate, the NLOS error can be itigated effectively. Of course, if the estiator does not rely on the initial values, the ethod should be ore practical. 3.2 NLOS Mitigation with GBSBEM s pdf When getting a large nuber of easureents, the estiator can calculate the average value of the soothed easureents. Let the average value is μ s, That is expressed as N μs = sj( t, () N i= By the pdf of GBSBEM described in (2), the ean value of the easureent can also be expressed as τ μ = τ fτ ( τ) dτ τ d cτ 2 cτ β c d 3 d ax( s j ) τ = c in( s j ) τ = c d = cτ = ( ) + 3 ( ) τ τ ()

4 Where τ is the iniu tie delay of NLOS propagation and τ is the axiu tie delay of NLOS propagation, c is the speed of light. Assue that d cτ cτ τ 2 μs = μ = ( ) + 3 ( ) (2) βc d 3 d τ d = cτ The τ can be calculated by nuerical ethod and the LOS path between the MS and the BSj is dlos = cτ. (3) This indicates that the iniu of sj( t should be near the LOS path. If the iniu of sj( t is far fro the true distance between the MS and the BSj, the accuracy of calculated value would decrease. With at least three reconstructed LOS values, the estiator can calculate the position of the MS. 4. Siulations The siulations are perfored to confir the validity of the proposed ethod, organizing as following steps:. When the urban is typically distributed, the perforance of NLOS itigation by the proposed ethod is presented. 2. The coparison between the classical positioning ethods and the proposed ethod is presented. 4. The siulation of NLOS itigation The distance between the MS and the given BS is r = r+ n randn() + NLOS rand(), (4) Where r is the true distance between the MS and the given BS. n randn() is the AWGN noise which is certainly existed in the environent. NLOS rand() is the NLOS noise which is a large positive bias copared to AWGN noise. The siulation trajectory has 2 tie saples with the saple interval equals to s. The MS is static and the distance between the MS and BS is 2. The NLOS error causes positive bias of 2. The easured data positively deflects off the true data. When the sei-inor of GBSBEM is estiated, the bias of the data can be odified. The perforance of the proposed ethod is illustrated in Figure 2. To inspect the perforance of the proposed ethods under different situations, RMSE is needed which describes average error of each siulation for different situations. The definition of RMSE is RMSE = E[( x xˆ) + ( y yˆ) ], (5) Table I gives the RMSE of the siulation results. Table I. The RMSE of above siulations scenarios RMSE() The easured distance The soothed easureent Siulation under situation.7

5 The true distance The true distance only affected by AWGN noise The easured distance The soothed easureent Range distance due to the proposed ethod range distance() tie(sec) Figure 2. The perforance of the NLOS itigation by GBSBEM 4.2 The siulation of position perforance The above siulation illustrates the NLOS itigation perforance of a single BS. To discuss the proposed ethod sufficiently, the siulation for position algoriths is needed. LLOP [2] is a classical TOA based algorith, which can itigate the NLOS error in soe degree. Chan algorith [] is a TDOA based algorith, which uses WLS to restrain the NLOS error. The positioning estiation accuracy is checked for the scenarios of 5BS. The ratio of the NLOS error to the true distance is given by db. The coordinates of the BSs are BS (x=2, y=2), BS2 (x2=-2, y2=2), BS3 (x3=-2, y3=-2), BS4 (x4=2, y4=-2), BS5 (x5=, y5=). The coordinate of the MS is (x=4, y=6). The propagation fro the BS to MS is corrupted by NLOS error. The LLOP algorith chooses three of the five BSs randoly while the Chan algorith chooses all of the. The perforance is illustrated in Figure 3 and Figure 4. It can be seen that when the NLOS error has inor ipact, the proposed ethod could not efficiently restrain the NLOS error for LLOP. However, when NLOS error badly affects the true easureent, the effect of the proposed ethod has shown and the perforance of positioning has been iproved a lot. The iproveent of the positioning accuracy can also be seen fro Figure Chan Algorith when 5 BSs available LLOP when 3 BSs available Proposed ethod used in Chan algorith when 5 BSs available Proposed ethod used in LLOP when 3 BSs available RMSE() ratio of NLOS error to the true distance( db) Figure 3. RMSE of different ethods

6 2 Chan Algorith when 5 BSs available LLOP when 3 BSs available Proposed ethod used in Chan algorith Proposed ethod used in LLOP 8 CDF( %) Conclusion postition error( ) Figure 4. The position error of the proposed ethod copared to the Chan and LLOP algorith NLOS error greatly affects the accuracy of the positioning syste. In this paper, a novel p-ositioning approach based on GBSBEM is proposed. Theoretic analysis and siulation results show the good perforance of this ethod, especially in bad NLOS environent. 6. Reference [] Y. T. Chan, A siple and efficient estiator for hyperbolic location, IEEE Trans. Signal Process, Vol. 42, No. 8, Aug, 994, pp [2] J. Caffery, A new approach to the geoetry of TOA location, in Proc. IEEE Ven. Technol. Conf, vol. 4, 2, pp [3] M. P. Wylie and J. Holtzan, The non-line-of-sight proble in obile location estiation, in Proc. IEEE Int. Conf, Universal Personal Coun, 996, pp [4] Venkatraan, S, Caffery, J., Jr. and You, H. R. Location using LOS range estiation in NLOS environents, in IEEE Conference, Vol. 2, 22, pp [5] Wang Wei, Xiong Jin-Yu and Zhu Zhong-Liang, A new NLOS error itigation algorith in location estiation, IEEE Trans, Vehicular Technoloty, Vol, 54, 25, pp [6] Guvenc, I., Chia-Chin Chong and Watanabe F. NLOS Identification and Mitigation for UWB Localization Systes, in Wirless Counications and Networking Conference, 27, WCNC , pp [7] Paul Petrus, Jeffrey H. Reed, and Theodore S. Rappaport, Geoetrical-based Statistical Macrocell Channel Model for Mobile Environent, IEEE Transactions on Counications, Vol.5, No.3, March 22. [8] Mostafa, S. A., Elraly, S. H. and Ragheb, M. K., Adaptation of Angle-of-Arrival Estiation in Mobile Counications Using Geoetrically Based Channel Models, in the 2 nd International Conference on Wireless Broadband and Ultra Wideband Counications, AUSWIRELESS , pp [9] Liberti J C, Rappaport T S. A geoetrically based odel for line-of-sight ultipath radio channels. in IEEE 46 th Vehicular Technology Conference. Atlanta: IEEE, 996. pp [] B. L. Le, K. Ahed, H. Tsuji. Mobile Location Estiator With NLOS Mitigation Using Kalan Filtering. IEEE Wireless Counications and Networking, Vol. 3, March 23, pp